Studies of Shock Wave Interactions with Homogeneous and Isotropic Turbulence
NASA Technical Reports Server (NTRS)
Briassulis, G.; Agui, J.; Watkins, C. B.; Andreopoulos, Y.
1998-01-01
A nearly homogeneous nearly isotropic compressible turbulent flow interacting with a normal shock wave has been studied experimentally in a large shock tube facility. Spatial resolution of the order of 8 Kolmogorov viscous length scales was achieved in the measurements of turbulence. A variety of turbulence generating grids provide a wide range of turbulence scales. Integral length scales were found to substantially decrease through the interaction with the shock wave in all investigated cases with flow Mach numbers ranging from 0.3 to 0.7 and shock Mach numbers from 1.2 to 1.6. The outcome of the interaction depends strongly on the state of compressibility of the incoming turbulence. The length scales in the lateral direction are amplified at small Mach numbers and attenuated at large Mach numbers. Even at large Mach numbers amplification of lateral length scales has been observed in the case of fine grids. In addition to the interaction with the shock the present work has documented substantial compressibility effects in the incoming homogeneous and isotropic turbulent flow. The decay of Mach number fluctuations was found to follow a power law similar to that describing the decay of incompressible isotropic turbulence. It was found that the decay coefficient and the decay exponent decrease with increasing Mach number while the virtual origin increases with increasing Mach number. A mechanism possibly responsible for these effects appears to be the inherently low growth rate of compressible shear layers emanating from the cylindrical rods of the grid.
Modification of homogeneous and isotropic turbulence by solid particles
NASA Astrophysics Data System (ADS)
Hwang, Wontae
2005-12-01
Particle-laden flows are prevalent in natural and industrial environments. Dilute loadings of small, heavy particles have been observed to attenuate the turbulence levels of the carrier-phase flow, up to 80% in some cases. We attempt to increase the physical understanding of this complex phenomenon by studying the interaction of solid particles with the most fundamental type of turbulence, which is homogeneous and isotropic with no mean flow. A flow facility was developed that could create air turbulence in a nearly-spherical chamber by means of synthetic jet actuators mounted on the corners. Loudspeakers were used as the actuators. Stationary turbulence and natural decaying turbulence were investigated using two-dimensional particle image velocimetry for the base flow qualification. Results indicated that the turbulence was fairly homogeneous throughout the measurement domain and very isotropic, with small mean flow. The particle-laden flow experiments were conducted in two different environments, the lab and in micro-gravity, to examine the effects of particle wakes and flow structure distortion caused by settling particles. The laboratory experiments showed that glass particles with diameters on the order of the turbulence Kolmogorov length scale attenuated the fluid turbulent kinetic energy (TKE) and dissipation rate with increasing particle mass loadings. The main source of fluid TKE production in the chamber was the speakers, but the loss of potential energy of the settling particles also resulted in a significant amount of production of extra TKE. The sink of TKE in the chamber was due to the ordinary fluid viscous dissipation and extra dissipation caused by particles. This extra dissipation could be divided into "unresolved" dissipation caused by local velocity disturbances in the vicinity of the small particles and dissipation caused by large-scale flow distortions from particle wakes and particle clusters. The micro-gravity experiments in NASA's KC-135
Subfilter scalar-flux vector orientation in homogeneous isotropic turbulence.
Verma, Siddhartha; Blanquart, G
2014-06-01
The geometric orientation of the subfilter-scale scalar-flux vector is examined in homogeneous isotropic turbulence. Vector orientation is determined using the eigenframe of the resolved strain-rate tensor. The Schmidt number is kept sufficiently large so as to leave the velocity field, and hence the strain-rate tensor, unaltered by filtering in the viscous-convective subrange. Strong preferential alignment is observed for the case of Gaussian and box filters, whereas the sharp-spectral filter leads to close to a random orientation. The orientation angle obtained with the Gaussian and box filters is largely independent of the filter width and the Schmidt number. It is shown that the alignment direction observed numerically using these two filters is predicted very well by the tensor-diffusivity model. Moreover, preferred alignment of the scalar gradient vector in the eigenframe is shown to mitigate any probable issues of negative diffusivity in the tensor-diffusivity model. Consequentially, the model might not suffer from solution instability when used for large eddy simulations of scalar transport in homogeneous isotropic turbulence. Further a priori tests indicate poor alignment of the Smagorinsky and stretched vortex model predictions with the exact subfilter flux. Finally, strong filter dependence of subfilter scalar-flux orientation suggests that explicit filtering may be preferable to implicit filtering in large eddy simulations. PMID:25019887
Clustering of vertically constrained passive particles in homogeneous isotropic turbulence
NASA Astrophysics Data System (ADS)
De Pietro, Massimo; van Hinsberg, Michel A. T.; Biferale, Luca; Clercx, Herman J. H.; Perlekar, Prasad; Toschi, Federico
2015-05-01
We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale η , that maximizes the clustering of the particles.
Pressure and higher-order spectra for homogeneous isotropic turbulence
NASA Technical Reports Server (NTRS)
Pullin, D. I.; Rogallo, R. S.
1994-01-01
The spectra of the pressure, and other higher-order quantities including the dissipation, the enstrophy, and the square of the longitudinal velocity derivative are computed using data obtained from direct numerical simulation of homogeneous isotropic turbulence at Taylor-Reynolds numbers R(sub lambda) in the range 38 - 170. For the pressure spectra we find reasonable collapse in the dissipation range (of the velocity spectrum) when scaled in Kolmogorov variables and some evidence, which is not conclusive, for the existence of a k(exp -7/3) inertial range where k = absolute value of K, is the modulus of the wavenumber. The power spectra of the dissipation, the enstrophy, and the square of the longitudinal velocity derivative separate in the dissipation range, but appear to converge together in the short inertial range of the simulations. A least-squares curve-fit in the dissipation range for one value of R(sub lambda) = 96 gives a form for the spectrum of the dissipation as k(exp 0)exp(-Ck eta), for k(eta) greater than 0.2, where eta is the Kolmogorov length and C is approximately equal to 2.5.
The structure of intense vorticity in homogeneous isotropic turbulence
NASA Technical Reports Server (NTRS)
Jimenez, J.; Wray, A. A.; Saffman, P. G.; Rogallo, R. S.
1992-01-01
The structure of the intense vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers in the range Re(sub lambda) = 36-171. In accordance with previous investigators, this vorticity is found to be organized in coherent, cylindrical or ribbon-like, vortices ('worms'). A statistical study suggests that they are just especially intense features of the background, O(omega'), vorticity. Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow. An interesting observation is that the Reynolds number based on the circulation of the intense vortices, gamma/nu, increases monotonically with Re(sub lambda), raising the question of the stability of the structures in the limit of Re(sub lambda) approaching infinity. One and two-dimensional statistics of vorticity and strain are presented; they are non-gaussian, and the behavior of their tails depends strongly on the Reynolds number. There is no evidence of convergence to a limiting distribution in our range of Re(sub lambda), even though the energy spectra and the energy dissipation rate show good asymptotic properties in the higher Reynolds number cases. Evidence is presented to show that worms are natural features of the flow and that they do not depend on the particular forcing scheme.
Bulk viscosity effect on freely decaying compressible homogeneous isotropic turbulence
NASA Astrophysics Data System (ADS)
Pan, Shaowu; Johnsen, Eric
2015-11-01
Despite growing interests in compressible turbulence, the effect of bulk viscosity has been long ignored. For certain gases, the bulk viscosity may be 1000 times greater than the shear viscosity and thus modify energy transfer and dissipation mechanisms. In this study, we use direct numerical simulations to investigate the role of bulk viscosity on decaying isotropic compressible turbulence. Our results show that bulk viscosity exhibits a negligible decrease on enstrophy, but moderate and significant increases on the turbulent kinetic energy and Taylor-scale Reynolds number, respectively. A Helmholtz decomposition of the velocity field indicates that the bulk viscosity has a negligible effect on the solenoidal part, but exhibits a cross-scale effect on the dilatational component.
Streamlines in stationary homogeneous isotropic turbulence and fractal-generated turbulence
NASA Astrophysics Data System (ADS)
Boschung, J.; Peters, N.; Laizet, S.; Vassilicos, J. C.
2016-04-01
We compare streamline statistics in stationary homogeneous isotropic turbulence and in turbulence generated by a fractal square grid. We examine streamline segments characterised by the velocity difference {{Δ }}u and the distance l between extremum points. We find close agreement between the stationary homogeneous isotropic turbulence and the decay region of the fractal-generated turbulence as well as the production region of the fractal flow for small segments. The statistics of larger segments are very similar for the isotropic turbulence and the decay region, but differ for the production region. Specifically, we examine the first, second and third conditional mean < {[{{Δ }}u]}n| l> . Noticeably, non-vanishing < {[{{Δ }}u]}n| l> for n=1,3 are due to an asymmetry of positive and negative segments, i.e. those for which {{Δ }}u\\gt 0 and {{Δ }}u\\lt 0, respectively. This asymmetry is not only kinematic, but is also due to dissipative effects and therefore < {[{{Δ }}u]}n| l> contains cascade information.
Statistics of pressure and pressure gradient in homogeneous isotropic turbulence
NASA Technical Reports Server (NTRS)
Gotoh, T.; Rogallo, R. S.
1994-01-01
The statistics of pressure and pressure gradient in stationary isotropic turbulence are measured within direct numerical simulations at low to moderate Reynolds numbers. It is found that the one-point pdf of the pressure is highly skewed and that the pdf of the pressure gradient is of stretched exponential form. The power spectrum of the pressure P(k) is found to be larger than the corresponding spectrum P(sub G)(k) computed from a Gaussian velocity field having the same energy spectrum as that of the DNS field. The ratio P(k)/P(sub G)(k), a measure of the pressure-field intermittence, grows with wavenumber and Reynolds number as -R(sub lambda)(exp 1/2)log(k/k(sub d)) for k less than k(sub d)/2 where k(sub d) is the Kolmogorov wavenumber. The Lagrangian correlations of pressure gradient and velocity are compared and the Lagrangian time scale of the pressure gradient is observed to be much shorter than that of the velocity.
NASA Technical Reports Server (NTRS)
Eaton, John; Hwang, Wontae; Cabral, Patrick
2002-01-01
This research addresses turbulent gas flows laden with fine solid particles at sufficiently large mass loading that strong two-way coupling occurs. By two-way coupling we mean that the particle motion is governed largely by the flow, while the particles affect the gas-phase mean flow and the turbulence properties. Our main interest is in understanding how the particles affect the turbulence. Computational techniques have been developed which can accurately predict flows carrying particles that are much smaller than the smallest scales of turbulence. Also, advanced computational techniques and burgeoning computer resources make it feasible to fully resolve very large particles moving through turbulent flows. However, flows with particle diameters of the same order as the Kolmogorov scale of the turbulence are notoriously difficult to predict. Some simple flows show strong turbulence attenuation with reductions in the turbulent kinetic energy by up to a factor of five. On the other hand, some seemingly similar flows show almost no modification. No model has been proposed that allows prediction of when the strong attenuation will occur. Unfortunately, many technological and natural two-phase flows fall into this regime, so there is a strong need for new physical understanding and modeling capability. Our objective is to study the simplest possible turbulent particle-laden flow, namely homogeneous, isotropic turbulence with a uniform dispersion of monodisperse particles. We chose such a simple flow for two reasons. First, the simplicity allows us to probe the interaction in more detail and offers analytical simplicity in interpreting the results. Secondly, this flow can be addressed by numerical simulation, and many research groups are already working on calculating the flow. Our detailed data can help guide some of these efforts. By using microgravity, we can further simplify the flow to the case of no mean velocity for either the turbulence or the particles. In fact
Theoretical and computational studies of isotropic homogeneous turbulence
NASA Astrophysics Data System (ADS)
Huang, Mei-Jiau
Numerical simulations are presented for viscous incompressible homogeneous turbulent flows with periodic boundary conditions. Our numerical method is based on the spectral Fourier method. Rogallo's code is modified and extended to trace fluid particles and simulate the evolution of material line elements. The first part of the thesis is about modifying and applying the code to simulate a passive vector field convected and stretched by the so called ABC flows in the presence of viscosity. The correlation of the geometry of the physical structures of the passive vector with the external straining is investigated. It is observed that most amplifications either occur in the neighborhoods of local unstable manifolds of the stagnation points of the ABC flows, if they exist, especially those with only one positive eigenvalue, or they are confined within the chaotic regions of the ABC flows if there is no stagnation point. The second part of the thesis is an investigation of the power-law energy decay of turbulence. Two decay exponents, 1.24 and 1.54, are measured from simulations. A new similarity form for the double and triple velocity autocorrelation functions using the Taylor microscale as the scaling, consistent with the Karman-Howarth equation and a power-law energy decay, is proposed and compared with numerical results. The proposed similarity form seems applicable at small to intermediate Reynolds number. For flows with very large Reynolds number, an expansion form of energy spectrum is proposed instead. The third part of the thesis is a presentation of the Lagrangian data collected by tracking fluid particles in decaying turbulent flows. The mean growth rates of the magnitudes of material line elements, that of the vorticity due to nonlinear forces, and the mean principal rates of strain tensors are found to be proportional to the square root of the mean enstrophy. The proportional coefficients remain constant during the decay. The mean angles between material
Theoretical and Computational Studies of Isotropic Homogeneous Turbulence
NASA Astrophysics Data System (ADS)
Huang, Mei-Jiau
Numerical simulations are presented for viscous incompressible homogeneous turbulent flows with periodic boundary conditions. Our numerical method is based on the spectral Fourier method. Rogallo's code is modified and extended to trace fluid particles and simulate the evolution of material line elements. The first part of the thesis is about modifying and applying the code to simulate a passive vector field convected and stretched by the so-called ABC flows in the presence of viscosity. The correlation of the geometry of the physical structures of the passive vector with the external straining is investigated. It is observed that most amplifications either occur in the neighborhoods of local unstable manifolds of the stagnation points of the ABC flows, if they exist, especially those with only one positive eigenvalue, or they are confined within the chaotic regions of the ABC flows if there is no stagnation point. The second part of the thesis is an investigation of the power-law energy decay of turbulence. Two decay exponents, 1.24 and 1.54, are measured from simulations. A new similarity form for the double and triple velocity autocorrelation functions using the Taylor microscale as the scaling, consistent with the Karman-Howarth equation and a power-law energy decay, is proposed and compared with numerical results. The proposed similarity form seems applicable at small to intermediate Reynolds number. For flows with very large Reynolds number, an expansion form of energy spectrum is proposed instead. The third part of the thesis is a presentation of the Lagrangian data collected by tracking fluid particles in decaying turbulent flows. The mean growth rates of the magnitudes of material line elements, that of the vorticity due to nonlinear forces, and the mean principal rates of strain tensors are found to be proportional to the square root of the mean enstrophy. The proportional coefficients remain constant during the decay. The mean angles between material
Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence
NASA Technical Reports Server (NTRS)
Domaradzki, J. Andrzej; Rogallo, Robert S.
1990-01-01
Detailed computations were made of energy transfer among the scales of motion in incompressible turbulent fields at low Reynolds numbers, generated by direct numerical simulations. It was observed that, although the transfer resulted from triad interactions that were nonlocal in k space, the energy always transferred locally. The energy transfer calculated from the eddy-damped quasi-normal Markovian (EDQNM) theory of turbulence at low Reynolds numbers is in excellent agreement with the results of the numerical simulations. At high Reynolds numbers, the EDQNM theory predicts the same transfer mechanism in the inertial range that is observed at low Reynolds numbers.
Settling of almost neutrally buoyant particles in homogeneous isotropic turbulence
NASA Astrophysics Data System (ADS)
van Hinsberg, Michel; Clercx, Herman; Toschi, Federico
2015-11-01
Settling of particles in a turbulent flow occurs in various industrial and natural phenomena, examples are clouds and waste water treatment. It is well known that turbulence can enhance the settling velocity of particles. Many studies have been done, numerically and experimentally to investigate this behavior for the case of ``heavy'' particles, with particle to fluid density ratios above 100. Here we investigate the case of almost neutrally buoyant particles, i.e. density ratios between 1 and 100. In the case of light particles the Maxey-Riley equations cannot be simplified to only the Stokes drag and gravity force as pressure gradient, added mass and Basset history force are important as well. We investigate the influence of these forces on the settling velocity of particles and show that the extra forces can both increase or decrease the settling velocity, depending on the combination of the Stokes number and gravity applied.
Grid-generated isotropic homogeneous turbulence at high Reynolds numbers
NASA Technical Reports Server (NTRS)
Rosen, G.
1981-01-01
Consideration is given to an empirical formula for the longitudinal correlation function for grid-generated incompressible fluid turbulence at Reynolds numbers above 12,800. The formula, which relates the longitudinal correlation function to the inverse cube of a dimensionless geometrical ratio, is shown to minimize the global correlation integrals into which the two-point velocity correlation tensor has been substituted subject to a global constraint on the Sobolev concomitent of the longitudinal correlation function. Furthermore, the energy spectrum function associated with the empirical formula is shown to satisfy a tertiary Helmholtz-type linear condition throughout the initial period of decay.
Mixing of a passive scalar in isotropic and sheared homogeneous turbulence
NASA Technical Reports Server (NTRS)
Shirani, E.; Ferziger, J. H.; Reynolds, W. C.
1981-01-01
In order to calculate the velocity and scalar fields, the three dimensional, time-dependent equations of motion and the diffusion equation were solved numerically. The following cases were treated: isotropic, homogeneous turbulence with decay of a passive scalar; and homogeneous turbulent shear flow with a passive scalar whose mean varies linearly in the spanwise direction. The solutions were obtained at relatively low Reynolds numbers so that all of the turbulent scales could be resolved without modeling. Turbulent statistics such as integral length scales, Taylor microscales, Kolmogorov length scale, one- and two-point correlations of velocity-velocity and velocity-scalar, turbulent Prandtl/Schmidt number, r.m.s. values of velocities, the scalar quantity and pressure, skewness, decay rates, and decay exponents were calculated. The results are compared with the available expermental results, and good agreement is obtained.
New forcing scheme to sustain particle-laden homogeneous and isotropic turbulence
NASA Astrophysics Data System (ADS)
Mallouppas, G.; George, W. K.; van Wachem, B. G. M.
2013-08-01
This paper evaluates the effect of forcing to sustain turbulence on the transfer function of the fluid with particles suspended in a homogeneous and isotropic flow. As mentioned by Lucci et al. ["Modulation of isotropic turbulence by particles of Taylor length-scale size," J. Fluid Mech. 650, 5-55 (2010), 10.1017/S0022112009994022], there are three limitations of forcing particle-laden homogeneous and isotropic turbulence: (a) large fluctuations on the temporal evolution of the kinetic energy are created when forcing is active at low wavenumbers, (b) the redistribution of energy is affected when forcing is performed over all wavenumbers, and (c) the nonlinear transfer function of the fluid due to the triadic interactions is affected when forcing is active over a wavenumber range. These limitations make the interpretation of the effects of particles on the energy spectrum of the fluid difficult. A new forcing scheme in physical space has been designed which avoids these limitations in wavenumber space, so the spectral effects of particles can be evaluated. The performance of this forcing scheme is tested using Direct Numerical Simulations. It is shown that the nonlinear transfer function of the fluid with the current forcing scheme is only affected at the wavenumbers it is acting, consistent with the theory. Even so, the spatial coherence and phase spectra between the two-way coupling and the fluid computed from the simulations show that the new forcing scheme is only moderately correlated even for the forced wavenumbers, with correlation coefficient typically about 10%.
Suppression of self-organized structure coarsening in homogenous isotropic turbulence
NASA Astrophysics Data System (ADS)
Takagi, Youhei
2014-11-01
Self-organized structure by spinodal decomposition is often seen in quenched binary mixture. Complex network structure is formed through coarsening process of self-organized structure when the phase separation due to spinodal decomposition proceeds. The phase separation governed by the Cahn-Hilliard equation have been well investigated for stationary fluid in previous studies, however, the turbulent effect on the formation of structures was not fully discussed. In this study, we carried out a numerical simulation for homogenous isotropic turbulence with phase separation, the relation between turbulent vortex formation and self-organized structure coarsening. The governing equations are incompressible Navier-Stokes equation considering phase separation force and Cahn-Hilliard equation with the chemical potential based on the Landau-Ginzburg free energy. From the identification and visualization of turbulent structures, it was found that the local entrainment of small eddy structure suppressed the coarsening process of self-organized structure. The energy used in phase separation was related to the initial process of vortex sheet-tube transition in turbulent flow, and the energy cascade from large turbulent structure to small eddy was different from that without phase separation.
On the decay of homogeneous nearly isotropic turbulence behind active fractal grids
NASA Astrophysics Data System (ADS)
Thormann, Adrien; Meneveau, Charles
2012-11-01
The study of decaying isotropic turbulent flow is an important point of reference for turbulence theories and numerical simulations. For the past several decades, most experimental results appear to favor power-law decay with exponents between -1.2 and -1.4, approximately. More recently, fractal-generated turbulence (Hurst & Vassilicos, PoF 2007, and subsequent papers) using multi-scale passive grids suggest possible faster decay, and non-trivial behavior especially near the grid, where the mean velocity is spatially evolving. In order to generate spatially homogeneous flow using multi-scale injection of kinetic energy at high Reynolds numbers, we use a new type of active-grid consisting of winglets with various fractal shapes. We test space-filling fractal shaped winglets as well as Sierpisky-carpet and Apollonian packing type fractal shapes. Data are acquired using X-wire thermal anemometry. Tests of homogeneity of mean flow and turbulence intensity will be presented as well as decay of kinetic energy and spectral characteristics of the flow. This research is supported by NSF-CBET-1033942. The assistance of Ms. Imbi Salasoo and Mr. Nathan Greene in designing and building the fractal winglets is much appreciated. The authors also thank Mr. Vince Rolin for his assistance with the active grid.
NASA Astrophysics Data System (ADS)
Farge, Marie; Roussel, Olivier; Schneider, Kai
2004-11-01
We compare the extraction of coherent vortices in 3D homogeneous isotropic turbulence computed by DNS using either orthogonal or biorthogonal wavelets. The method is based on a wavelet decomposition of the vorticity field and a subsequent thresholding of the wavelet coefficients (PRL, 87(5), 2001, Phys. Fluids 15(10), 2003). The coherent vorticity is reconstructed from few strong wavelet coefficients while the incoherent vorticity is reconstructed from the remaining weak coefficients. In the orthogonal case the choice of the threshold is motivated from statistical denoising theory and has no adjustable parameters. Using 3% of the coefficients we show that both decompositions extract the coherent vortices out of the turbulent flow. They contain 99.6% of the energy and retain 74% and 68% of the enstrophy in the orthogonal and biorthogonal case, respectively. Concerning the incoherent background flow, it is structureless and decorrelated for the orthogonal decomposition, with a Gaussian velocity PDF. In contrast, the biorthogonal decomposition yields a background flow which exhibits quasi-2D sheet-like structures with an exponetial velocity PDF instead. In conclusion, modeling the incoherent background flow might be more difficult using biorthogonal wavelets for the CVS (Coherent Vortex Simulation, cf. Flow, Turbulence and Combustion 66(4), 2001).
Creating Only Isotropic Homogeneous Turbulence in Liquid Helium near Absolute Zero
NASA Astrophysics Data System (ADS)
Ihas, G. G.; Thompson, K. J.; Labbe, G.; McClintock, P. V. E.
2012-02-01
Flow through a grid is a standard method to produce isotropic, homogeneous turbulence for laboratory study. This technique has been used to generate quantum turbulence (QT) above 1 K in superfluid heliumootnotetextS. R. Stalp, L. Skrbek, and R. J. Donnelly, Phys. Rev. Lett. 82, 4831 (1999). where QT seems to mimic classical turbulence. Efforts have been made recentlyootnotetextG. G. Ihas, G. Labbe, S-c. Liu, and K. J. Thompson, J. Low Temp. Phys. 150, 384 (2008). to make similar measurements near absolute zero, where there is an almost total absence of normal fluid and hence classical viscosity. This presents the difficulty that most motive force devices produce heat which overwhelms the phenomena being investigated. The process of designing and implimenting a ``dissipation-free'' motor for pulling a grid through superfluid helium at millikelvin temperatures has resulted in the development of new techniques which have broad application in low temperature research. Some of these, such as Meissner-affect magnetic drives, capacitive and inductive position sensors, and magnetic centering devices will be described. Heating results for devices which can move in a controlled fashion from very low speed up to 10 cm/s will be presented. Acknowledgement: We thank W.F. Vinen for many useful discussions.
NASA Astrophysics Data System (ADS)
Hammond, Adam; Dou, Zhongwang; Tripathi, Anjan; Liang, Zach; Meng, Hui
2015-11-01
Study of droplet collision and cloud formation should consider the effects of both turbulence and electrostatic charge on particle dynamics. We present the first experimental observation of radial relative velocity (RV) of charged particles in homogeneous and isotropic turbulence (HIT). Charges on particles were generated through triboelectric effect between the inner wall of the chamber and the particles. To measure charge distribution, a particle-laden head-on impinging flow mimicking our HIT chamber conditions was built and holographic particle tracking was applied to quantify particle charges by measuring their displacements in an electric field. Particles were observed to have opposite charges. Next, in our HIT chamber, we measured particle RV by a novel 4-frame particle tracking velocimetry technique with and without charges on particles, wherein charges were neutralized by coating the interior of the HIT chamber with conductive carbon paint. We compared RV under the same turbulence conditions between charged particles and neutral particles and observed that when particles were oppositely charged, their mean inward RV increased at small separation distances. This result is consistent with recent theory and simulations (Lu and Shaw, Physics of Fluids, 2015). This work was supported by the National Science Foundation through a Collaborative Research Grant CBET-0967407.
Parametric Study of Decay of Homogeneous Isotropic Turbulence Using Large Eddy Simulation
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Rumsey, Christopher L.; Rubinstein, Robert; Balakumar, Ponnampalam; Zang, Thomas A.
2012-01-01
Numerical simulations of decaying homogeneous isotropic turbulence are performed with both low-order and high-order spatial discretization schemes. The turbulent Mach and Reynolds numbers for the simulations are 0.2 and 250, respectively. For the low-order schemes we use either second-order central or third-order upwind biased differencing. For higher order approximations we apply weighted essentially non-oscillatory (WENO) schemes, both with linear and nonlinear weights. There are two objectives in this preliminary effort to investigate possible schemes for large eddy simulation (LES). One is to explore the capability of a widely used low-order computational fluid dynamics (CFD) code to perform LES computations. The other is to determine the effect of higher order accuracy (fifth, seventh, and ninth order) achieved with high-order upwind biased WENO-based schemes. Turbulence statistics, such as kinetic energy, dissipation, and skewness, along with the energy spectra from simulations of the decaying turbulence problem are used to assess and compare the various numerical schemes. In addition, results from the best performing schemes are compared with those from a spectral scheme. The effects of grid density, ranging from 32 cubed to 192 cubed, on the computations are also examined. The fifth-order WENO-based scheme is found to be too dissipative, especially on the coarser grids. However, with the seventh-order and ninth-order WENO-based schemes we observe a significant improvement in accuracy relative to the lower order LES schemes, as revealed by the computed peak in the energy dissipation and by the energy spectrum.
NASA Astrophysics Data System (ADS)
Dou, Zhongwang; Pecenak, Zachary; Liang, Zach; Cao, Lujie; Ireland, Peter; Collins, Lance; Meng, Hui
2015-11-01
Particle-pair radial relative velocity (RV) in turbulence plays a critical role in droplet collision and cloud formation. Both simulations and experiments are performed to better understand RV of inertial particles in homogeneous and isotropic turbulence (HIT). However, past experimental measurement of particle RV statistics exhibited large deviations from DNS results (de Jong et al., 2010). In the current study, we identified intrinsic limitations in our previous study and devised a 4-frame particle tracking velocimetry technique to measure particle RV. In a second-generation, enclosed, fan-driven HIT chamber, both tracer and inertial particles were studied at R_ λ of 366. The experimentally measured RV statistics were compared with DNS with excellent agreement. Additionally, for both kinds of particles, the mean inward RV vs. particle separation distance r also matched very well with DNS, but at near-zero r, experimental values were slightly higher. To investigate the cause of this discrepancy, we compared DNS of both mono- and tri-dispersed particles. We found that the tri-dispersed particles exhibited higher mean inward RV at small r than any mono-dispersed particles. This suggests that the increase of mean inward RV in the experiment could be due to the Stokes number (St) distribution present in the particles, while DNS employed single St values. This work was supported by the National Science Foundation through a Collaborative Research Grant CBET-0967407.
Linearly Forced Isotropic Turbulence
NASA Technical Reports Server (NTRS)
Lundgren, T. S.
2003-01-01
Stationary isotropic turbulence is often studied numerically by adding a forcing term to the Navier-Stokes equation. This is usually done for the purpose of achieving higher Reynolds number and longer statistics than is possible for isotropic decaying turbulence. It is generally accepted that forcing the Navier-Stokes equation at low wave number does not influence the small scale statistics of the flow provided that there is wide separation between the largest and smallest scales. It will be shown, however, that the spectral width of the forcing has a noticeable effect on inertial range statistics. A case will be made here for using a broader form of forcing in order to compare computed isotropic stationary turbulence with (decaying) grid turbulence. It is shown that using a forcing function which is directly proportional to the velocity has physical meaning and gives results which are closer to both homogeneous and non-homogeneous turbulence. Section 1 presents a four part series of motivations for linear forcing. Section 2 puts linear forcing to a numerical test with a pseudospectral computation.
NASA Astrophysics Data System (ADS)
Onishi, Ryo; Vassilicos, J. C.
2014-11-01
This study investigates the collision statistics of inertial particles in inverse-cascading 2D homogeneous isotropic turbulence by means of a direct numerical simulation (DNS). A collision kernel model for particles with small Stokes number (St) in 2D flows is proposed based on the model of Saffman & Turner (1956) (ST56 model). The DNS results agree with this 2D version of the ST56 model for St < 0.1. It is then confirmed that our DNS results satisfy the 2D version of the spherical formulation of the collision kernel. The fact that the flatness factor stays around 3 in our 2D flow confirms that the present 2D turbulent flow is nearly intermittency-free. Collision statistics for St = 0.1, 0.4 and 0.6, i.e. for St <1, are obtained from the present 2D DNS and compared with those obtained from the three-dimensional (3D) DNS of Onishi et al. (2013). We have observed that the 3D radial distribution function at contact (g(R), the so-called clustering effect) decreases for St = 0.4 and 0.6 with increasing Reynolds number, while the 2D g(R) does not show a significant dependence on Reynolds number. This observation supports the view that the Reynolds-number dependence of g(R) observed in three dimensions is due to internal intermittency of the 3D turbulence. We have further investigated the local St, which is a function of the local flow strain rates, and proposed a plausible mechanism that can explain the Reynolds-number dependence of g(R).
The length distribution of streamline segments in homogeneous isotropic decaying turbulence
NASA Astrophysics Data System (ADS)
Schaefer, P.; Gampert, M.; Peters, N.
2012-04-01
by Schaefer et al. ["Fast and slow changes of the length of gradient trajectories in homogenous shear turbulence," in Advances in Turbulence XII, edited by B. Eckhardt (Springer-Verlag, Berlin, 2009), pp. 565-572] we will refer to the morphological part of the evolution of streamline segments as slow changes while the topological part of the evolution is referred to as fast changes. This separation yields a transport equation for the probability density function (pdf) P(l) of the arclength l of streamline segments in which the slow changes translate into a convection and a diffusion term when terms up to second order are included and the fast changes yield integral terms. The overall temporal evolution (morphological and topological) of the arclength l of streamline segments is analyzed and associated with the motion of the above isosurface. This motion is diffusion controlled for small segments, while large segments are mainly subject to strain and pressure fluctuations. The convection velocity corresponds to the first order jump moment, while the diffusion term includes the second order jump moment. It is concluded, both theoretically and from direct numerical simulations (DNS) data of homogeneous isotropic decaying turbulence at two different Reynolds numbers, that the normalized first order jump moment is quasi-universal, while the second order one is proportional to the inverse of the square root of the Taylor based Reynolds number Re_{λ }^{-1/2}. Its inclusion thus represents a small correction in the limit of large Reynolds numbers. Numerical solutions of the pdf equation yield a good agreement with the pdf obtained from the DNS data. The interplay of viscous drift acting on small segments and linear strain acting on large segments yield, as it has already been concluded for dissipation elements, that the mean length of streamline segments should scale with Taylor microscale.
Laboratory Study of Homogeneous and Isotropic Turbulence at High Reynolds Number
NASA Astrophysics Data System (ADS)
Pecenak, Zachary; Dou, Zhongwang; Yang, Fan; Cao, Lujie; Liang, Zach; Meng, Hui
2013-11-01
To study particle dynamics modified by isotropic turbulence at high Reynolds numbers and provide experimental data for DNS validation, we have developed a soccer-ball-shaped truncated icosahedron turbulence chamber with 20 adjoining hexagon surfaces, 12 pentagon surfaces and twenty symettrically displaced fans, which form an enclosed chamber of 1m diameter. We use Particle Image Velocimetry (PIV) technique to characterize the base turbulent flow, using different PIV set ups to capture various characteristic scales of turbulence. Results show that the stationary isotropic turbulence field is a spherical domain with diameter of 40 mm with quasi-zero mean velocities. The maximum rms velocity is ~1.5 m/s, corresponding to a Taylor microscale Re of 450. We extract from the PIV velocity field the whole set of turbulent flow parameters including: turbulent kinetic energy, turbulent intensity, kinetic energy dissipation rate, large eddy length and time scales, the Kolmogorov length, time and velocity scales, Taylor microscale and Re, which are critical to the study of inter-particle statistics modified by turbulence. This research is funded by an NSF grant CBET-0967407.
The rotation and translation of non-spherical particles in homogeneous isotropic turbulence
NASA Astrophysics Data System (ADS)
Byron, Margaret
The motion of particles suspended in environmental turbulence is relevant to many scientific fields, from sediment transport to biological interactions to underwater robotics. At very small scales and simple shapes, we are able to completely mathematically describe the motion of inertial particles; however, the motion of large aspherical particles is significantly more complex, and current computational models are inadequate for large or highly-resolved domains. Therefore, we seek to experimentally investigate the coupling between freely suspended particles and ambient turbulence. A better understanding of this coupling will inform not only engineering and physics, but the interactions between small aquatic organisms and their environments. In the following pages, we explore the roles of shape and buoyancy on the motion of passive particles in turbulence, and allow these particles to serve as models for meso-scale aquatic organisms. We fabricate cylindrical and spheroidal particles and suspend them in homogeneous, isotropic turbulence that is generated via randomly-actuated jet arrays. The particles are fabricated with agarose hydrogel, which is refractive-index-matched to the surrounding fluid (water). Both the fluid and the particle are seeded with passive tracers, allowing us to perform Particle Image Velocimetry (PIV) simultaneously on the particle and fluid phase. To investigate the effects of shape, particles are fabricated at varying aspect ratios; to investigate the effects of buoyancy, particles are fabricated at varying specific gravities. Each particle type is freely suspended at a volume fraction of F=0.1%, for which four-way coupling interactions are negligible. The suspended particles are imaged together with the surrounding fluid and analyzed using stereoscopic PIV, which yields three velocity components in a two-dimensional measurement plane. Using image thresholding, the results are separated into simultaneous fluid-phase and solid-phase velocity
Miura, H.; Araki, K.
2014-07-15
Hall effects on local structures in homogeneous, isotropic, and incompressible magnetohydrodynamic turbulence are studied numerically. The transition of vortices from sheet-like to tubular structures induced by the Hall term is found, while the kinetic energy spectrum does not distinguish the two types of structures. It is shown by the use of the sharp low-pass filter that the transition occurs not only in the scales smaller than the ion skin depth but also in a larger scale. The transition is related with the forward energy transfer in the spectral space. Analyses by the use of the sharp low-pass filter show that the nonlinear energy transfer associated with the Hall term is dominated by the forward transfer and relatively local in the wave number space. A projection of the simulation data to a Smagorinsky-type sub-grid-scale model shows that the high wave number component of the Hall term may possibly be replaced by the model effectively.
Clustering of vertically constrained passive particles in homogeneous and isotropic turbulence
NASA Astrophysics Data System (ADS)
van Hinsberg, Michel; de Pietro, Massimo; Biferale, Luca; Clercx, Herman; Toschi, Federico
2014-11-01
We analyze the dynamics of small particles confined within a horizontal fluid slab in a three-dimensional (3D) homogenous isotropic turbulent velocity field. Particles can freely move horizontally as fluid tracers but are vertically confined around a given horizontal plane via a simple linear restoring force. The present model may be considered as the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy or other mechanisms, are capable to maintain themselves in a shallow horizontal layer somewhere below the free surface of oceans or lakes. In the model varying the strength of the restoring force can control the thickness of the fluid slab in which the particles can move. Whenever some confinement is present, particle trajectories deviate from fluid tracers and experience an effectively compressible velocity field. We report a quantification of this effective compressibility as well as a quantification of preferential concentration of tracer particles in terms of the correlation dimension. We found that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale, that maximizes the clustering of the particles. This work is part of the research programmes 11PR2841 and FP112 of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO). The work was partially funded by ERC Grant No 339032.
A priori study of subgrid-scale flux of a passive scalar in isotropic homogeneous turbulence
Chumakov, Sergei
2008-01-01
We perform a direct numerical simulation (DNS) of forced homogeneous isotropic turbulence with a passive scalar that is forced by mean gradient. The DNS data are used to study the properties of subgrid-scale flux of a passive scalar in the framework of large eddy simulation (LES), such as alignment trends between the flux, resolved, and subgrid-scale flow structures. It is shown that the direction of the flux is strongly coupled with the subgrid-scale stress axes rather than the resolved flow quantities such as strain, vorticity, or scalar gradient. We derive an approximate transport equation for the subgrid-scale flux of a scalar and look at the relative importance of the terms in the transport equation. A particular form of LES tensor-viscosity model for the scalar flux is investigated, which includes the subgrid-scale stress. Effect of different models for the subgrid-scale stress on the model for the subgrid-scale flux is studied.
NASA Astrophysics Data System (ADS)
Miura, H.; Araki, K.
2014-07-01
Hall effects on local structures in homogeneous, isotropic, and incompressible magnetohydrodynamic turbulence are studied numerically. The transition of vortices from sheet-like to tubular structures induced by the Hall term is found, while the kinetic energy spectrum does not distinguish the two types of structures. It is shown by the use of the sharp low-pass filter that the transition occurs not only in the scales smaller than the ion skin depth but also in a larger scale. The transition is related with the forward energy transfer in the spectral space. Analyses by the use of the sharp low-pass filter show that the nonlinear energy transfer associated with the Hall term is dominated by the forward transfer and relatively local in the wave number space. A projection of the simulation data to a Smagorinsky-type sub-grid-scale model shows that the high wave number component of the Hall term may possibly be replaced by the model effectively.
NASA Astrophysics Data System (ADS)
Dou, Zhongwang; Pecenak, Zachary K.; Cao, Lujie; Woodward, Scott H.; Liang, Zach; Meng, Hui
2016-03-01
Enclosed flow apparatuses with negligible mean flow are emerging as alternatives to wind tunnels for laboratory studies of homogeneous and isotropic turbulence (HIT) with or without aerosol particles, especially in experimental validation of Direct Numerical Simulation (DNS). It is desired that these flow apparatuses generate HIT at high Taylor-microscale Reynolds numbers ({{R}λ} ) and enable accurate measurement of turbulence parameters including kinetic energy dissipation rate and thereby {{R}λ} . We have designed an enclosed, fan-driven, highly symmetric truncated-icosahedron ‘soccer ball’ airflow apparatus that enables particle imaging velocimetry (PIV) and other whole-field flow measurement techniques. To minimize gravity effect on inertial particles and improve isotropy, we chose fans instead of synthetic jets as flow actuators. We developed explicit relations between {{R}λ} and physical as well as operational parameters of enclosed HIT chambers. To experimentally characterize turbulence in this near-zero-mean flow chamber, we devised a new two-scale PIV approach utilizing two independent PIV systems to obtain both high resolution and large field of view. Velocity measurement results show that turbulence in the apparatus achieved high homogeneity and isotropy in a large central region (48 mm diameter) of the chamber. From PIV-measured velocity fields, we obtained turbulence dissipation rates and thereby {{R}λ} by using the second-order velocity structure function. A maximum {{R}λ} of 384 was achieved. Furthermore, experiments confirmed that the root mean square (RMS) velocity increases linearly with fan speed, and {{R}λ} increases with the square root of fan speed. Characterizing turbulence in such apparatus paves the way for further investigation of particle dynamics in particle-laden homogeneous and isotropic turbulence.
NASA Astrophysics Data System (ADS)
Aliseda, Alberto; Bourgoin, Mickael; Eswirp Collaboration
2014-11-01
We present preliminary results from a recent grid turbulence experiment conducted at the ONERA wind tunnel in Modane, France. The ESWIRP Collaboration was conceived to probe the smallest scales of a canonical turbulent flow with very high Reynolds numbers. To achieve this, the largest scales of the turbulence need to be extremely big so that, even with the large separation of scales, the smallest scales would be well above the spatial and temporal resolution of the instruments. The ONERA wind tunnel in Modane (8 m -diameter test section) was chosen as a limit of the biggest large scales achievable in a laboratory setting. A giant inflatable grid (M = 0.8 m) was conceived to induce slowly-decaying homogeneous isotropic turbulence in a large region of the test section, with minimal structural risk. An international team or researchers collected hot wire anemometry, ultrasound anemometry, resonant cantilever anemometry, fast pitot tube anemometry, cold wire thermometry and high-speed particle tracking data of this canonical turbulent flow. While analysis of this large database, which will become publicly available over the next 2 years, has only started, the Taylor-scale Reynolds number is estimated to be between 400 and 800, with Kolmogorov scales as large as a few mm . The ESWIRP Collaboration is formed by an international team of scientists to investigate experimentally the smallest scales of turbulence. It was funded by the European Union to take advantage of the largest wind tunnel in Europe for fundamental research.
NASA Astrophysics Data System (ADS)
Coleman, S. W.; Vassilicos, J. C.
2009-11-01
Our work focuses on the sweep-stick mechanism of particle clustering in turbulent flows introduced by Chen et al. [L. Chen, S. Goto, and J. C. Vassilicos, "Turbulent clustering of stagnation points and inertial particles," J. Fluid Mech. 553, 143 (2006)] for two-dimensional (2D) inverse cascading homogeneous, isotropic turbulence (HIT), whereby heavy particles cluster in a way that mimics the clustering of zero-acceleration points. We extend this phenomenology to three-dimensional (3D) HIT, where it was previously reported that zero-acceleration points were extremely rare. Having obtained a unified mechanism we quantify the Stokes number dependency of the probability of the heavy particles to be at zero-acceleration points and show that in the inertial range of Stokes numbers, the sweep-stick mechanism is dominant over the conventionally proposed mechanism of heavy particles being centrifuged from high vorticity regions to high strain regions. Finally, having a clustering coincidence between particles and zero-acceleration points, both in 2D and 3D HIT, motivates us to demonstrate the sweep and stick parts of the mechanism in both dimensions. The sweeping of regions of low acceleration regions by the local fluid velocity in both flows is demonstrated by introducing a velocity of the acceleration field. Finally, the stick part is demonstrated by showing that heavy particles statistically move with the same velocity as zero-acceleration points, while moving away from any nonzero-acceleration region, irrespective of their Stokes number. These results explain the clustering of inertial particles given the clustering of zero-acceleration points.
NASA Astrophysics Data System (ADS)
Bassenne, Maxime; Urzay, Javier; Park, George I.; Moin, Parviz
2016-03-01
This study investigates control-based forcing methods for incompressible homogeneous-isotropic turbulence forced linearly in physical space which result in constant turbulent kinetic energy, constant turbulent dissipation (also constant enstrophy), or a combination of the two based on a least-squares error minimization. The methods consist of proportional controllers embedded in the forcing coefficients. During the transient, the controllers adjust the forcing coefficients such that the controlled quantity achieves very early a minimal relative error with respect to its target stationary value. Comparisons of these forcing methods are made with the non-controlled approaches of Rosales and Meneveau ["Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties," Phys. Fluids 17, 095106 (2005)] and Carroll and Blanquart ["A proposed modification to Lundgren's physical space velocity forcing method for isotropic turbulence," Phys. Fluids 25, 105114 (2013)], using direct numerical simulations (DNS) and large-eddy simulations (LES). The results indicate that the proposed constant-energetics forcing methods shorten the transient period from a user-defined artificial flow field to Navier-Stokes turbulence while maintaining steadier statistics. Additionally, the proposed method of constant kinetic-energy forcing behaves more robustly in coarse LES when initial conditions are employed that favor the occurrence of subgrid-scale backscatter, whereas the other approaches fail to provide physical turbulent flow fields. For illustration, the proposed forcing methods are applied to dilute particle-laden homogeneous-isotropic turbulent flows; the results serve to highlight the influences of the forcing strategies on the disperse-phase statistics.
Fichtl, G.H.
1983-09-01
When designing a wind energy converison system (WECS), it may be necessary to take into account the distribution of wind across the disc of rotation. The specific engineering applications include structural strength, fatigue, and control. This wind distribution consists of two parts, namely that associated with the mean wind profile and that associated with the turbulence velocity fluctuation field. The work reported herein is aimed at the latter, namely the distribution of turbulence velocity fluctuations across the WECS disk of rotation. A theory is developed for the two-time covariance matrix for turbulence velocity vector components for wind energy conversion system (WECS) design. The theory is developed for homogeneous and iotropic turbulance with the assumption that Taylor's hypothesis is valid. The Eulerian turbulence velocity vector field is expanded about the hub of the WECS. Formulae are developed for the turbulence velocity vector component covariance matrix following the WECS blade elements. It is shown that upon specification of the turbulence energy spectrum function and the WECS rotation rate, the two-point, two-time covariance matrix of the turbulent flow relative to the WECS bladed elements is determined. This covariance matrix is represented as the sum of nonstationary and stationary contributions. Generalized power spectral methods are used to obtain two-point, double frequency power spectral density functions for the turbulent flow following the blade elements. The Dryden turbulence model is used to demonstrate the theory. A discussion of linear system response analysis is provided to show how the double frequency turbulence spectra might be used to calculate response spectra of a WECS to turbulent flow. Finally the spectrum of the component of turbulence normal to the WECS disc of rotation, following the blade elements, is compared with experimental results.
NASA Astrophysics Data System (ADS)
Nguyen van yen, Romain; Farge, Marie; Schneider, Kai
2012-02-01
Classical statistical theories of turbulence have shown their limitations, in that they cannot predict much more than the energy spectrum in an idealized setting of statistical homogeneity and stationarity. We explore the applicability of a conditional statistical modeling approach: can we sort out what part of the information should be kept, and what part should be modeled statistically, or, in other words, “dissipated”? Our mathematical framework is the initial value problem for the two-dimensional (2D) Euler equations, which we approximate numerically by solving the 2D Navier-Stokes equations in the vanishing viscosity limit. In order to obtain a good approximation of the inviscid dynamics, we use a spectral method and a resolution going up to 8192 2. We introduce a macroscopic concept of dissipation, relying on a split of the flow between coherent and incoherent contributions: the coherent flow is constructed from the large wavelet coefficients of the vorticity field, and the incoherent flow from the small ones. In previous work, a unique threshold was applied to all wavelet coefficients, while here we also consider the effect of a scale by scale thresholding algorithm, called scale-wise coherent vorticity extraction. We study the statistical properties of the coherent and incoherent vorticity fields, and the transfers of enstrophy between them, and then use these results to propose, within a maximum entropy framework, a simple model for the incoherent vorticity. In the framework of this model, we show that the flow velocity can be predicted accurately in the L2 norm for about 10 eddy turnover times.
Spherical cloaking with homogeneous isotropic multilayered structures.
Qiu, Cheng-Wei; Hu, Li; Xu, Xiaofei; Feng, Yijun
2009-04-01
We propose a practical realization of electromagnetic spherical cloaking by layered structure of homogeneous isotropic materials. By mimicking the classic anisotropic cloak by many alternating thin layers of isotropic dielectrics, the permittivity and permeability in each isotropic layer can be properly determined by effective medium theory in order to achieve invisibility. The model greatly facilitates modeling by Mie theory and realization by multilayer coating of dielectrics. Eigenmode analysis is also presented to provide insights of the discretization in multilayers. PMID:19518392
Numerical experiments in homogeneous turbulence
NASA Technical Reports Server (NTRS)
Rogallo, R. S.
1981-01-01
The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.
Homogeneous quantum electrodynamic turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1992-01-01
The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.
Homogeneous quantum electrodynamic turbulence
Shebalin, J.V.
1992-10-01
The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.
Isotropic homogeneous universe with viscous fluid
Santos, N.O.; Dias, R.S.; Banerjee, A.
1985-04-01
Exact solutions are obtained for the isotropic homogeneous cosmological model with viscous fluid. The fluid has only bulk viscosity and the viscosity coefficient is taken to be a power function of the mass density. The equation of state assumed obeys a linear relation between mass density and pressure. The models satisfying Hawking's energy conditions are discussed. Murphy's model is only a special case of this general set of solutions and it is shown that Murphy's conclusion that the introduciton of bulk viscosity can avoid the occurrence of space-time singularity at finite past is not, in general, valid.
Local structures of homogeneous Hall MHD turbulence
NASA Astrophysics Data System (ADS)
Miura, H.; Araki, K.
2011-12-01
Local structures of decaying homogeneous and isotropic Hall MHD turbulence are studied by means of direct numerical simulations. Regions of strong vorticity and strong current density in Hall MHD turbulence are compared to those of single-fluid MHD turbulence. An analysis by the use of a low-pass filter reveals that the introduction of the Hall term can modify not only small-scale structures of the current density but also structures of the vorticity field, especially at the scales smaller than the ion skin depth.
Turbulence in homogeneous shear flows
NASA Astrophysics Data System (ADS)
Pumir, Alain
1996-11-01
Homogeneous shear flows with an imposed mean velocity U=Syx̂ are studied in a period box of size Lx×Ly×Lz, in the statistically stationary turbulent state. In contrast with unbounded shear flows, the finite size of the system constrains the large-scale dynamics. The Reynolds number, defined by Re≡SL2y/ν varies in the range 2600⩽Re⩽11300. The total kinetic energy and enstrophy in the volume of numerical integration have large peaks, resulting in fluctuations of kinetic energy of order 30%-50%. The mechanism leading to these fluctuations is very reminiscent of the ``streaks'' responsible for the violent bursts observed in turbulent boundary layers. The large scale anisotropy of the flow, characterized by the two-point correlation tensor
DNS of Shock / Isotropic Turbulence Interaction
NASA Astrophysics Data System (ADS)
Grube, Nathan; Taylor, Ellen; Martín, Pino
2010-11-01
We discuss DNS of Shock / Isotropic Turbulence Interactions (SITI). We vary the incoming turbulence Mach number up to 0.8 and the convective Mach number up to 5 in order to determine their effects on the interaction. These cases are challenging due to the presence of shocklets in the incoming turbulence as well as significant motion of the main shock. Shock-capturing must be used at all points while still maintaining low enough numerical dissipation to preserve the turbulent fluctuations. We use the linearly- and nonlinearly-optimized Weighted Essentially Non-Oscillatory (WENO) method[1,2]. Particular attention is paid to the inflow boundary condition, where we find the use of snapshots of "frozen" turbulence from decaying isotropic box simulations to be unsatisfactory. We instead use time-varying inflow data generated by a separate forced isotropic turbulence simulation with a specified convection speed. This allows us to access flow conditions where the assumptions of Taylor's Hypothesis are not met. 1.) Mart'in, M.P., Taylor, E.M., Wu, M., and Weirs, V.G., JCP 220(1) 270-89, 2006. 2.) Taylor, E.M., Wu, M., and Mart'in, M.P., JCP 223(1) 384-97, 2007.
Simulation and Modeling of Homogeneous, Compressed Turbulence.
NASA Astrophysics Data System (ADS)
Wu, Chung-Teh
Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression has been simulated by numerically solving the Navier-Stokes equations. The numerical simulations were carried out on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second -order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one -dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. It was found that the ratio of the turbulence time scale to the mean-flow time scale is an important parameter in these flows. When this ratio is large, the flow is immediately affected by the mean strain in a manner similar to that predicted by rapid distortion theory. When this ratio is small, the flow retains the character of decaying isotropic turbulence initially; only after the strain has been applied for a long period does the flow accumulate a significant reflection of the effect of mean strain. In these flows, the Kolmogorov length scale decreases rapidly with increasing total strain, due to the density increase that accompanies compression. Results from the simulated flow fields were used to test one-point-closure, two-equation turbulence models. The two-equation models perform well only when the compression rate is small compared to the eddy turn-over rate. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.
Charge pariticle transport in the non-isotropic turbulences
NASA Astrophysics Data System (ADS)
Sun, P.; Jokipii, J. R.
2015-12-01
The scattering and diffusion of energetic charged particles is not only important for understanding phenomena such as diffusive shock acceleration but it also is a natural probe of the statistical characteristics of magnetohydrodynamic (MHD) turbulence. Although Parker's transport equation (Parker 1965) allows us to describe the propagation of charged particles, the transport coefficients needed in the equation must be determined. Using Quasi-Linear Theory (QLT, e.g. Jokipii (1966)), one finds that coefficients can be related to the correlation function or power spectrum of homogeneous magnetic turbulence. However, different turbulence models will generally have a different influence on particle's scattering and diffusion. Among those models developed in MHD Turbulence, such as isotropic, Slab plus 2D (Tu & Marsch 1993; Gray et al 1996; Bieber et al 1996), etc. Here, using test-particle orbit simulations to calculate the transport coefficients, we study particle transport in synthesized asymmetric turbulence using the form first proposed by Goldreich & Sridhar (1995). We developed and introduce a systematic method to synthesize scale-dependent non-isotropic magnetic turbulences. We also developed and introduce a method to synthesize the 3d turbulent magnetic field from the observed solar wind time series dataset. We present the comparison of their effects on charge particle transport with previous theories and models.
Simulation and modeling of homogeneous, compressed turbulence
NASA Technical Reports Server (NTRS)
Wu, C. T.; Ferziger, J. H.; Chapman, D. R.
1985-01-01
Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.
Simulation and modeling of homogeneous, compressed turbulence
NASA Astrophysics Data System (ADS)
Wu, C. T.; Ferziger, J. H.; Chapman, D. R.
1985-05-01
Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.
Turbulent energy flux generated by shock/homogeneous-turbulence interaction
NASA Astrophysics Data System (ADS)
Sinha, Krishnendu; Quadros, Russell; Larsson, Johan
2015-11-01
High-speed turbulent flows with shock waves are characterized by high localized surface heat transfer rates. Computational predictions are often inaccurate due to the limitations in modeling of the unclosed turbulent energy flux in the highly non-equilibrium regions of shock interaction. In this paper, we investigate the turbulent energy flux generated when homogeneous isotropic turbulence passes through a nominally normal shock wave. We use linear interaction analysis where the incoming turbulence is idealized as being composed of a collection of two-dimensional planar vorticity waves, and the shock wave is taken to be a discontinuity. The nature of the post-shock turbulent energy flux is predicted to be strongly dependent on the incidence angle of the incoming waves. The energy flux correlation is also decomposed into its vortical, entropy and acoustic contributions to understand its rapid non-monotonic variation behind the shock. Three-dimensional statistics, calculated by integrating two-dimensional results over a prescribed upstream energy spectrum, are compared with available direct numerical simulation data. A detailed budget of the governing equation is also considered in order to gain insight into the underlying physics.
Adaptive waveguide bends with homogeneous, nonmagnetic, and isotropic materials.
Han, Tiancheng; Qiu, Cheng-Wei; Tang, Xiaohong
2011-01-15
We propose a method for adaptive waveguide bends using homogeneous, nonmagnetic, and isotropic materials, which simplifies the parameters of the bends to the utmost extent. The proposed bend has an adaptive and compact shape because of all the flat boundaries. The nonmagnetic property is realized by selecting OB'/OC = 0.5. Only two nonmagnetic isotropic dielectrics are needed throughout, and the transmission is not sensitive to nonmagnetic isotropic dielectrics. Results validate and illustrate these functionalities, which make the bend much easier to fabricate and apply, owing to its simple parameters, compact shape, and versatility in connecting different waveguides. PMID:21263493
Mixing and chemical reaction in sheared and nonsheared homogeneous turbulence
NASA Technical Reports Server (NTRS)
Leonard, Andy D.; Hill, James C.
1992-01-01
Direct numerical simulations were made to examine the local structure of the reaction zone for a moderately fast reaction between unmixed species in decaying, homogeneous turbulence and in a homogeneous turbulent shear flow. Pseudospectral techniques were used in domains of 64 exp 3 and higher wavenumbers. A finite-rate, single step reaction between non-premixed reactants was considered, and in one case temperature-dependent Arrhenius kinetics was assumed. Locally intense reaction rates that tend to persist throughout the simulations occur in locations where the reactant concentration gradients are large and are amplified by the local rate of strain. The reaction zones are more organized in the case of a uniform mean shear than in isotropic turbulence, and regions of intense reaction rate appear to be associated with vortex structures such as horseshoe vortices and fingers seen in mixing layers. Concentration gradients tend to align with the direction of the most compressive principal strain rate, more so in the isotropic case.
The signature of initial production mechanisms in isotropic turbulence decay
NASA Astrophysics Data System (ADS)
Meldi, M.
2016-03-01
In the present work the quantification of the time-lasting effects of production mechanisms in homogeneous isotropic turbulence decay is addressed. The analysis is developed through the use of theoretical tools as well as numerical calculations based on the eddy damped quasinormal Markovian (EDQNM) model. In both cases a modified Lin equation is used, which accounts for production mechanisms as proposed by Meldi, Lejemble, and Sagaut ["On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence," J. Fluid Mech. 756, 816-843 (2014)]. The approaches used show that an exponential decay law can be observed if the intensity of the forcing is strong enough to drive the turbulence dynamics, before a power-law decay is eventually attained. The EDQNM numerical results indicate that the exponential regime can persist for long evolution times, longer than the observation time in grid turbulence experiments. A rigorous investigation of the self-similar behavior of the pressure spectrum has been performed by a comprehensive comparison of EDQNM data with direct numerical simulation (DNS)/experiments in the literature. While DNS and free decay EDQNM simulations suggest the need of a very high Reλ threshold in order to observe a clear -7/3 slope of the pressure inertial range, experimental data and forced EDQNM calculations indicate a significantly lower value. This observation suggests that the time-lasting effects of production mechanisms, which cannot be excluded in experiments, play a role in the lack of general agreement with classical numerical approaches. These results reinforce the urge to evolve the numerical simulation state of the art towards the prediction of realistic physical states.
Turbulence generation in homogeneous dilute particle- laden flows
NASA Astrophysics Data System (ADS)
Chen, Jeng-Horng
Homogeneous turbulence generated by the motion of particles in dispersed multiphase flows was studied both theoretically and experimentally, motivated by applications to sprays, particle-laden jets, bubble plumes and rainstorms, among others. The experiments involved uniform fluxes of monodisperse spherical particles falling through a slow upflow of air. Particle fluxes and phase velocities were measured by sampling and phase-discriminating laser Doppler velocimetry (LDV), respectively. Measured particle velocities included mean and fluctuating streamwise and cross-stream velocities and probability density functions (PDF's). Measured continuous-phase velocities included mean and fluctuating streamwise and cross-stream velocities, PDF's and the higher moments of velocity fluctuations such as skewness and kurtosis, energy spectra of velocity fluctuations and integral length scales based on streamwise velocity fluctuations. Continuous-phase velocity measurements included conditional averages for particle wake disturbances and the turbulent inter-wake region surrounding these disturbances as well as overall flow properties. Present and earlier results in the literature provided particle Reynolds numbers of 38-990, particle volume fractions less than 0.01% and turbulence intensities (normalized by mean particle relative velocities) of 0.1-10.0%. Theory included characterization of particle wake disturbances as laminar-like turbulent wakes observed for intermediate particle Reynolds numbers in turbulent environments, characterization of the turbulent inter-wake region by analogy to grid-generated isotropic turbulence, and estimation of overall flow properties by conditional averaging of the properties of the wake disturbances and the turbulent inter-wake region. Present measurements showed that particle wake disturbances during turbulence generation were properly characterized by the properties of laminar-like turbulent wakes. The turbulent inter-wake region was
Some Basic Laws of Isotropic Turbulent Flow
NASA Technical Reports Server (NTRS)
Loitsianskii, L. G.
1945-01-01
An Investigation is made of the diffusion of artificially produced turbulence behind screens or other turbulence producers. The method is based on the author's concept of disturbance moment as a certain theoretically well-founded measure of turbulent disturbances.
Fully developed isotropic turbulence: Symmetries and exact identities
NASA Astrophysics Data System (ADS)
Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás
2015-05-01
We consider the regime of fully developed isotropic and homogeneous turbulence of the Navier-Stokes equation with a stochastic forcing. We present two gauge symmetries of the corresponding Navier-Stokes field theory and derive the associated general Ward identities. Furthermore, by introducing a local source bilinear in the velocity field, we show that these symmetries entail an infinite set of exact and local relations between correlation functions. They include in particular the Kármán-Howarth relation and another exact relation for a pressure-velocity correlation function recently derived in G. Falkovich, I. Fouxon, and Y. Oz [J. Fluid Mech. 644, 465 (2010)], 10.1017/S0022112009993429 that we further generalize.
Stress waves in transversely isotropic media: The homogeneous problem
NASA Technical Reports Server (NTRS)
Marques, E. R. C.; Williams, J. H., Jr.
1986-01-01
The homogeneous problem of stress wave propagation in unbounded transversely isotropic media is analyzed. By adopting plane wave solutions, the conditions for the existence of the solution are established in terms of phase velocities and directions of particle displacements. Dispersion relations and group velocities are derived from the phase velocity expressions. The deviation angles (e.g., angles between the normals to the adopted plane waves and the actual directions of their propagation) are numerically determined for a specific fiber-glass epoxy composite. A graphical method is introduced for the construction of the wave surfaces using magnitudes of phase velocities and deviation angles. The results for the case of isotropic media are shown to be contained in the solutions for the transversely isotropic media.
Coherent Vortex Simulations of 3D isotropic turbulence
NASA Astrophysics Data System (ADS)
Goldstein, Daniel E.; Vasilyev, Oleg V.; Kevlahan, Nicholas K.-R.
2006-11-01
This is the first of three talks on the wavelet filter based dynamically adaptive eddy capturing computational methodology that unifies variable fidelity simulation approaches such as wavelet-based DNS, Coherent Vortex Simulation (CVS), and Stochastic Coherent Adaptive Large Eddy Simulation. The commonality of these approaches is their ability to identify and ``track" on an adaptive mesh energetic coherent vortical structures. In CVS the velocity field is decomposed into two orthogonal parts: a coherent, inhomogeneous, non-Gaussian component and an incoherent, homogeneous, Gaussian component. This separation of coherent and incoherent components is achieved by wavelet thresholding which can be viewed as a non-linear filter that depends on each flow realization. The essence of the CVS approach is to solve for the coherent non-Gaussian component of a turbulent flow field. It has been shown previously that second generation bi-orthogonal wavelet threshold filtering is able to decompose a turbulent velocity field such that the total resulting SGS dissipation is approximately zero. This physically allows a CVS simulation to recover low order statistics with no SGS model. In this work CVS simulations of decaying incompressible 3D isotropic turbulence are compared to DNS results. -6pt
Sudden relaminarisation and lifetimes in forced isotropic turbulence
NASA Astrophysics Data System (ADS)
Linkmann, Moritz; Morozov, Alexander
2015-11-01
We demonstrate an unexpected connection between isotropic turbulence and wall-bounded shear flows. We perform direct numerical simulations of isotropic turbulence forced at large scales at moderate Reynolds numbers and observe sudden transitions from chaotic dynamics to a spatially simple flow, analogous to the laminar state in wall bounded shear flows. We find that the survival probabilities of turbulence are exponential and the typical lifetimes increase super-exponentially with the Reynolds number, similar to results on relaminarisation of localised turbulence in pipe and plane Couette flow. Results from simulations subjecting the observed large-scale flow to random perturbations of variable amplitude demonstrate that it is a linearly stable simple exact solution that can be destabilised by a finite-amplitude perturbation, like the Hagen-Poiseuille profile in pipe flow. Our results suggest that both isotropic turbulence and wall-bounded shear flows qualitatively share the same phase-space dynamics.
The energy decay in self-preserving isotropic turbulence revisited
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Bernard, Peter S.
1992-01-01
The assumption of self-preservation allows for an analytical determination of the energy decay in isotropic turbulence. Here, the self-preserving isotropic decay problem is analyzed, yielding a more complete picture of self-serving isotropic turbulence. It is proven rigorously that complete self-serving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K approximately t (exp -1) and one where K approximately t (sup alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) and where K approximately t (sup -alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) power law decay is the asymptotically consistent high Reynolds number solution; the K approximately 1 (sup -alpha) decay law is only achieved in the limit as t yields infinity and the turbulence Reynolds number vanishes. Arguments are provided which indicate that a K approximately t (exp -1) power law decay is the asymptotic state toward which a complete self-preserving isotropic turbulence is driven at high Reynolds numbers in order to resolve the imbalance between vortex stretching and viscous diffusion.
The energy decay in self-preserving isotropic turbulence revisited
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Bernard, Peter S.
1991-01-01
The assumption of self-preservation allows for an analytical determination of the energy decay in isotropic turbulence. Here, the self-preserving isotropic decay problem is analyzed, yielding a more complete picture of self-serving isotropic turbulence. It is proven rigorously that complete self-serving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K approximately t (exp -1) and one where K approximately t (sup alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) and where K approximately t (sup -alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one point equations, it is demonstrated that the K approximately t (exp -1) power law decay is the asymptotically consistent high Reynolds number solution; the K approximately 1 (sup - alpha) decay law is only achieved in the limit as t yields infinity and the turbulence Reynolds number vanishes. Arguments are provided which indicate that a K approximately t (exp -1) power law decay is the asymptotic state towards which a complete self-preseving isotropic turbulence is driven at high Reynolds numbers in order to resolve the imbalance between vortex stretching and viscous diffusion.
Determining the alpha dynamo parameter in incompressible homogeneous magnetohydrodynamic turbulence
NASA Technical Reports Server (NTRS)
Matthaeus, W. H.; Goldstein, M. L.; Lantz, S. R.
1983-01-01
Alpha, an important parameter in dynamo theory, is proportional to either the kinetic, current, magnetic, or velocity helicity of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first order smoothed equations that describe the alpha effect. In two cases, when alpha is proportional to either the magnetic helicity or velocity helicity, alpha is determined experimentally from two point measurements of the fluctuating fields in incompressible, homogeneous turbulence having arbitrary symmetry. For the other two possibilities, alpha is determined if the turbulence is isotropic.
Symmetry Breaking Drift of Particles Settling in Homogeneous Shear Turbulence
NASA Astrophysics Data System (ADS)
van Hinsberg, M. A. T.; Clercx, H. J. H.; Toschi, Federico
2016-08-01
We investigate the influence of shear on the gravitational settling of heavy inertial particles in homogeneous shear turbulence (HST). In addition to the well-known enhanced settling velocity, observed for heavy inertial particles in homogeneous isotropic turbulence (HIT), a horizontal drift velocity is also observed in the shearing direction due to the presence of a nonzero mean vorticity (introducing symmetry breaking due to the mean shear). This drift velocity is due to the combination of shear, gravity, and turbulence, and all three of these elements are needed for this effect to occur. We extend the mechanism responsible for the enhanced settling velocity in HIT to the case of HST. Two separate regimes are observed, characterized by positive or negative drift velocity, depending on the particle settling velocity.
Symmetry Breaking Drift of Particles Settling in Homogeneous Shear Turbulence.
van Hinsberg, M A T; Clercx, H J H; Toschi, Federico
2016-08-01
We investigate the influence of shear on the gravitational settling of heavy inertial particles in homogeneous shear turbulence (HST). In addition to the well-known enhanced settling velocity, observed for heavy inertial particles in homogeneous isotropic turbulence (HIT), a horizontal drift velocity is also observed in the shearing direction due to the presence of a nonzero mean vorticity (introducing symmetry breaking due to the mean shear). This drift velocity is due to the combination of shear, gravity, and turbulence, and all three of these elements are needed for this effect to occur. We extend the mechanism responsible for the enhanced settling velocity in HIT to the case of HST. Two separate regimes are observed, characterized by positive or negative drift velocity, depending on the particle settling velocity. PMID:27541467
Direction of unsaturated flow in a homogeneous and isotropic hillslope
Lu, N.; Kaya, B.S.; Godt, J.W.
2011-01-01
The distribution of soil moisture in a homogeneous and isotropic hillslope is a transient, variably saturated physical process controlled by rainfall characteristics, hillslope geometry, and the hydrological properties of the hillslope materials. The major driving mechanisms for moisture movement are gravity and gradients in matric potential. The latter is solely controlled by gradients of moisture content. In a homogeneous and isotropic saturated hillslope, absent a gradient in moisture content and under the driving force of gravity with a constant pressure boundary at the slope surface, flow is always in the lateral downslope direction, under either transient or steady state conditions. However, under variably saturated conditions, both gravity and moisture content gradients drive fluid motion, leading to complex flow patterns. In general, the flow field near the ground surface is variably saturated and transient, and the direction of flow could be laterally downslope, laterally upslope, or vertically downward. Previous work has suggested that prevailing rainfall conditions are sufficient to completely control these flow regimes. This work, however, shows that under time-varying rainfall conditions, vertical, downslope, and upslope lateral flow can concurrently occur at different depths and locations within the hillslope. More importantly, we show that the state of wetting or drying in a hillslope defines the temporal and spatial regimes of flow and when and where laterally downslope and/or laterally upslope flow occurs. Copyright 2011 by the American Geophysical Union.
Direction of unsaturated flow in a homogeneous and isotropic hillslope
Lu, Ning; Kaya, Basak Sener; Godt, Jonathan W.
2011-01-01
The distribution of soil moisture in a homogeneous and isotropic hillslope is a transient, variably saturated physical process controlled by rainfall characteristics, hillslope geometry, and the hydrological properties of the hillslope materials. The major driving mechanisms for moisture movement are gravity and gradients in matric potential. The latter is solely controlled by gradients of moisture content. In a homogeneous and isotropic saturated hillslope, absent a gradient in moisture content and under the driving force of gravity with a constant pressure boundary at the slope surface, flow is always in the lateral downslope direction, under either transient or steady state conditions. However, under variably saturated conditions, both gravity and moisture content gradients drive fluid motion, leading to complex flow patterns. In general, the flow field near the ground surface is variably saturated and transient, and the direction of flow could be laterally downslope, laterally upslope, or vertically downward. Previous work has suggested that prevailing rainfall conditions are sufficient to completely control these flow regimes. This work, however, shows that under time-varying rainfall conditions, vertical, downslope, and upslope lateral flow can concurrently occur at different depths and locations within the hillslope. More importantly, we show that the state of wetting or drying in a hillslope defines the temporal and spatial regimes of flow and when and where laterally downslope and/or laterally upslope flow occurs.
NASA Astrophysics Data System (ADS)
Podesta, J. J.
It is known that Kolmogorov's four-fifths law for statistically homogeneous and isotropic turbulence can be generalized to anisotropic turbulence. This fundamental result for homogeneous anisotropic turbulence says that in the inertial range the divergence of the vector third-order moment |v(r) is constant and is equal to -4, where is the dissipation rate of the turbulence. This law can be extended to incompressible magnetohydrodyamic (MHD) turbulence where statistical isotropy is often not valid due, for example, to the presence of a large-scale magnetic field. Laws for anisotropic incompressible MHD turbulence were first derived by Politano and Pouquet. In this paper, the laws for vector third-order moments in homogeneous non-isotropic incompressible MHD turbulence are derived by a technique due to Frisch that clarifies the relationship between the energy flux in Fourier space and the vector third-order moments in physical space. This derivation is different from the original derivation of Politano and Pouquet which is based on the Kn-Howarth equation, and provides some new physical insights. Separate laws are derived for the cascades of energy, cross-helicity and magnetic-helicity, the three ideal invariants of incompressible MHD for flows in three dimensions. These laws are of fundamental importance in the theory of MHD turbulence where non-isotropic turbulence is much more prevalent than isotropic turbulence.
Diffusion of Heat from a Line Source in Isotropic Turbulence
NASA Technical Reports Server (NTRS)
Uberoi, Mahinder S; Corrsin, Stanley
1953-01-01
An experimental and analytical study has been made of some features of the turbulent heat diffusion behind a line heated wire stretched perpendicular to a flowing isotropic turbulence. The mean temperature distributions have been measured with systematic variations in wind speed, size of turbulence-producing grid, and downstream location of heat source. The nature of the temperature fluctuation field has been studied. A comparison of Lagrangian and Eulerian analyses for diffusion in a nondecaying turbulence yields an expression for turbulent-heat-transfer coefficient in terms of turbulence velocity and a Lagrangian "scale." the ratio of Eulerian to Lagrangian microscale has been determined theoretically by generalization of a result of Heisenberg and with arbitrary constants taken from independent sources, shows rough agreement with experimental results. A convenient form has been deduced for the criterion of interchangeability of instantaneous space and time derivatives in a flowing turbulence.
Inverse energy cascade in three-dimensional isotropic turbulence.
Biferale, Luca; Musacchio, Stefano; Toschi, Federico
2012-04-20
We study the statistical properties of homogeneous and isotropic three-dimensional (3D) turbulent flows. By introducing a novel way to make numerical investigations of Navier-Stokes equations, we show that all 3D flows in nature possess a subset of nonlinear evolution leading to a reverse energy transfer: from small to large scales. Up to now, such an inverse cascade was only observed in flows under strong rotation and in quasi-two-dimensional geometries under strong confinement. We show here that energy flux is always reversed when mirror symmetry is broken, leading to a distribution of helicity in the system with a well-defined sign at all wave numbers. Our findings broaden the range of flows where the inverse energy cascade may be detected and rationalize the role played by helicity in the energy transfer process, showing that both 2D and 3D properties naturally coexist in all flows in nature. The unconventional numerical methodology here proposed, based on a Galerkin decimation of helical Fourier modes, paves the road for future studies on the influence of helicity on small-scale intermittency and the nature of the nonlinear interaction in magnetohydrodynamics. PMID:22680722
The structure of correlation tensors in homogeneous anisotropic turbulence
NASA Technical Reports Server (NTRS)
Matthaeus, W. H.; Smith, C.
1980-01-01
The study of turbulence with spatially homogeneous but anisotropic statistical properties has applications in space physics and laboratory plasma physics. The first step in the systematic study of such fluctuations is the elucidation of the kinematic properties of the relevant statistical objects, which are the correlation tensors. The theory of isotropic tensors, developed by Robertson, Chandrasekhar and others, is reviewed and extended to cover the general case of turbulence with a pseudo-vector preferred direction, without assuming mirror reflection invariance. Attention is focused on two point correlation functions and it is shown that the form of the decomposition into proper and pseudo-tensor contributions is restricted by the homogeneity requirement. It is also shown that the vector and pseudo-vector preferred direction cases yield different results. An explicit form of the two point correlation tensor is presented which is appropriate for analyzing interplanetary magnetic fluctuations. A procedure for determining the magnetic helicity from experimental data is presented.
Experimental study of premixed flames in intense isotropic turbulence
Bedat, B.; Cheng, R.K.
1994-04-01
A methodology for investigating premixed turbulent flames propagating in intense isotropic turbulence has been developed. The burner uses a turbulence generator developed by Videto and Santavicca and the flame is stabilized by weak-swirl generated by air injectors. This set-up produces stable premixed turbulent flames under a wide range of mixture conditions and turbulence intensities. The experiments are designed to investigate systematically the changes in flame structures for conditions which can be classified as wrinkled laminar flames, corrugated flames and flames with distributed reaction zones. Laser Doppler anemometry and Rayleigh scattering techniques are used to determine the turbulence and scalar statistics. In the intense turbulence, the flames are found to produce very little changes in the mean and rams velocities. Their flame speed increase linearly with turbulence intensity as for wrinkled laminar flames. The Rayleigh scattering pdfs for flames within the distributed reaction zone regime are distinctly bimodal. The probabilities of the reacting states (i.e. contributions from within the reaction zone) is not higher than those of wrinkled laminar flame. These results show that there is no drastic changes in flame structures at Karlovitz number close to unity. This suggest that the Klimov-Williams criterion under-predicts the resilience of wrinkled flamelets to intense turbulence.
Computation of the sound generated by isotropic turbulence
NASA Technical Reports Server (NTRS)
Sarkar, S.; Hussaini, M. Y.
1993-01-01
The acoustic radiation from isotropic turbulence is computed numerically. A hybrid direct numerical simulation approach which combines direct numerical simulation (DNS) of the turbulent flow with the Lighthill acoustic analogy is utilized. It is demonstrated that the hybrid DNS method is a feasible approach to the computation of sound generated by turbulent flows. The acoustic efficiency in the simulation of isotropic turbulence appears to be substantially less than that in subsonic jet experiments. The dominant frequency of the computed acoustic pressure is found to be somewhat larger than the dominant frequency of the energy-containing scales of motion. The acoustic power in the simulations is proportional to epsilon (M(sub t))(exp 5) where epsilon is the turbulent dissipation rate and M(sub t) is the turbulent Mach number. This is in agreement with the analytical result of Proudman (1952), but the constant of proportionality is smaller than the analytical result. Two different methods of computing the acoustic power from the DNS data bases yielded consistent results.
Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence
NASA Astrophysics Data System (ADS)
Fang, L.; Bos, W. J. T.; Jin, G. D.
2015-12-01
We show by direct numerical simulation (DNS) that the Lagrangian cross correlation of velocity gradients in homogeneous isotropic turbulence increases at short times, whereas its auto-correlation decreases. Kinematic considerations allow to show that two invariants of the turbulent velocity field determine the short-time velocity gradient correlations. In order to get a more intuitive understanding of the dynamics for longer times, heuristic models are proposed involving the combined action of local shear and rotation. These models quantitatively reproduce the effects and disentangle the different physical mechanisms leading to the observations in the DNS.
The Statistical Mechanics of Ideal Homogeneous Turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2002-01-01
Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.
Computation of large-scale statistics in decaying isotropic turbulence
NASA Technical Reports Server (NTRS)
Chasnov, Jeffrey R.
1993-01-01
We have performed large-eddy simulations of decaying isotropic turbulence to test the prediction of self-similar decay of the energy spectrum and to compute the decay exponents of the kinetic energy. In general, good agreement between the simulation results and the assumption of self-similarity were obtained. However, the statistics of the simulations were insufficient to compute the value of gamma which corrects the decay exponent when the spectrum follows a k(exp 4) wave number behavior near k = 0. To obtain good statistics, it was found necessary to average over a large ensemble of turbulent flows.
A non-isotropic multiple-scale turbulence model
NASA Technical Reports Server (NTRS)
Chen, C. P.
1990-01-01
A newly developed non-isotropic multiple scale turbulence model (MS/ASM) is described for complex flow calculations. This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts for modeling multiple scale effects in turbulence. Validation studies on free shear flows, rotating flows and recirculating flows show that the current model perform significantly better than the single scale k-epsilon model. The present model is relatively inexpensive in terms of CPU time which makes it suitable for broad engineering flow applications.
Broken Ergodicity in Ideal, Homogeneous, Incompressible Turbulence
NASA Technical Reports Server (NTRS)
Morin, Lee; Shebalin, John; Fu, Terry; Nguyen, Phu; Shum, Victor
2010-01-01
We discuss the statistical mechanics of numerical models of ideal homogeneous, incompressible turbulence and their relevance for dissipative fluids and magnetofluids. These numerical models are based on Fourier series and the relevant statistical theory predicts that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. However, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We explain this phenomena in terms of broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We review the theoretical basis of broken ergodicity, apply it to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence, and show new results from simulations using GPU (graphical processing unit) computers.
CUDA Simulation of Homogeneous, Incompressible Turbulence
NASA Technical Reports Server (NTRS)
Morin, Lee; Shebalin, John V.; Shum, Victor; Fu, Terry
2011-01-01
We discuss very fast Compute Unified Device Architecture (CUDA) simulations of ideal homogeneous incompressible turbulence based on Fourier models. These models have associated statistical theories that predict that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. Prior numerical simulations have shown that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We review the theoretical basis of this "broken ergodicity" as applied to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence. Our new simulations examine the phenomenon of broken ergodicity through very long time and large grid size runs performed on a state-of-the-art CUDA platform. Results comparing various CUDA hardware configurations and grid sizes are discussed. NS and MHD results are compared.
Hindered Energy Cascade in Highly Helical Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Stepanov, Rodion; Golbraikh, Ephim; Frick, Peter; Shestakov, Alexander
2015-12-01
The conventional approach to the turbulent energy cascade, based on Richardson-Kolmogorov phenomenology, ignores the topology of emerging vortices, which is related to the helicity of the turbulent flow. It is generally believed that helicity can play a significant role in turbulent systems, e.g., supporting the generation of large-scale magnetic fields, but its impact on the energy cascade to small scales has never been observed. We suggest, for the first time, a generalized phenomenology for isotropic turbulence with an arbitrary spectral distribution of the helicity. We discuss various scenarios of direct turbulent cascades with new helicity effect, which can be interpreted as a hindering of the spectral energy transfer. Therefore, the energy is accumulated and redistributed so that the efficiency of nonlinear interactions will be sufficient to provide a constant energy flux. We confirm our phenomenology by high Reynolds number numerical simulations based on a shell model of helical turbulence. The energy in our model is injected at a certain large scale only, whereas the source of helicity is distributed over all scales. In particular, we found that the helical bottleneck effect can appear in the inertial interval of the energy spectrum.
Hindered Energy Cascade in Highly Helical Isotropic Turbulence.
Stepanov, Rodion; Golbraikh, Ephim; Frick, Peter; Shestakov, Alexander
2015-12-01
The conventional approach to the turbulent energy cascade, based on Richardson-Kolmogorov phenomenology, ignores the topology of emerging vortices, which is related to the helicity of the turbulent flow. It is generally believed that helicity can play a significant role in turbulent systems, e.g., supporting the generation of large-scale magnetic fields, but its impact on the energy cascade to small scales has never been observed. We suggest, for the first time, a generalized phenomenology for isotropic turbulence with an arbitrary spectral distribution of the helicity. We discuss various scenarios of direct turbulent cascades with new helicity effect, which can be interpreted as a hindering of the spectral energy transfer. Therefore, the energy is accumulated and redistributed so that the efficiency of nonlinear interactions will be sufficient to provide a constant energy flux. We confirm our phenomenology by high Reynolds number numerical simulations based on a shell model of helical turbulence. The energy in our model is injected at a certain large scale only, whereas the source of helicity is distributed over all scales. In particular, we found that the helical bottleneck effect can appear in the inertial interval of the energy spectrum. PMID:26684120
Interaction of a converging spherical shock wave with isotropic turbulence
NASA Astrophysics Data System (ADS)
Bhagatwala, Ankit; Lele, Sanjiva K.
2012-08-01
Simulations of converging spherical shock waves propagating through a region of compressible isotropic turbulence are carried out. Both converging and reflected phases of the shock are studied. Effect of the reflected phase of the shock is found to be quite different from the expanding shock in the Taylor blast wave-turbulence interaction problem. Vorticity and turbulent kinetic energy are amplified due to passage of the shock. Similar to the latter problem, the vorticity-dilatation term is primarily responsible for the observed behavior. This is confirmed through Eulerian and Lagrangian statistics. Transverse vorticity amplification is compared with linear planar shock-turbulence theory. The smallest eddies, represented by the Kolmogorov scale, decrease in size after passing through the converging shock and this is shown to be related to a decrease in kinematic viscosity and increase in dissipation behind the converging shock. Distortion of the shock due to turbulence is also investigated and quantified. Turbulence also affects maximum compression achieved at the point of shock reflection, when the shock radius is at a minimum. This decrease in compression is quantified by comparing with pure shock simulations.
NASA Astrophysics Data System (ADS)
Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás
2016-06-01
We investigate the regime of fully developed homogeneous and isotropic turbulence of the Navier-Stokes (NS) equation in the presence of a stochastic forcing, using the nonperturbative (functional) renormalization group (NPRG). Within a simple approximation based on symmetries, we obtain the fixed-point solution of the NPRG flow equations that corresponds to fully developed turbulence both in d =2 and 3 dimensions. Deviations to the dimensional scalings (Kolmogorov in d =3 or Kraichnan-Batchelor in d =2 ) are found for the two-point functions. To further analyze these deviations, we derive exact flow equations in the large wave-number limit, and show that the fixed point does not entail the usual scale invariance, thereby identifying the mechanism for the emergence of intermittency within the NPRG framework. The purpose of this work is to provide a detailed basis for NPRG studies of NS turbulence; the determination of the ensuing intermittency exponents is left for future work.
Asymptotic behavior of curvature of surface elements in isotropic turbulence
NASA Technical Reports Server (NTRS)
Girimaji, S. S.
1991-01-01
The asymptotic behavior of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. Several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times, the (first five) moments of the logarithm of characteristic curvature and shape factor asymptote to values that are independent of the initial curvature or shape. This evidence strongly suggests that the asymptotic pdf's of the curvature and shape of material elements are stationary and independent of initial conditions. Irrespective of initial curvature or shape, the asymptotic shape of a material surface is cylindrical with a high probability.
Analysis of homogeneous turbulent reacting flows
NASA Technical Reports Server (NTRS)
Leonard, A. D.; Hill, J. C.; Mahalingam, S.; Ferziger, J. H.
1988-01-01
Full turbulence simulations at low Reynolds numbers were made for the single-step, irreversible, bimolecular reaction between non-premixed reactants in isochoric, decaying homogeneous turbulence. Various initial conditions for the scalar field were used in the simulations to control the initial scalar dissipation length scale, and simulations were also made for temperature-dependent reaction rates and for non-stoichiometric and unequal diffusivity conditions. Joint probability density functions (pdf's), conditional pdf's, and various statistical quantities appearing in the moment equations were computed. Preliminary analysis of the results indicates that compressive strain-rate correlates better than other dynamical quantities with local reaction rate, and the locations of peak reaction rates seem to be insensitive to the scalar field initial conditions.
Large Deviation Statistics of Vorticity Stretching in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Johnson, Perry; Meneveau, Charles
2015-11-01
A key feature of 3D fluid turbulence is the stretching/re-alignment of vorticity by the action of the strain-rate. It is shown using the cumulant-generating function that cumulative vorticity stretching along a Lagrangian path in isotropic turbulence behaves statistically like a sum of i.i.d. variables. The Cramer function for vorticity stretching is computed from the JHTDB isotropic DNS (Reλ = 430) and compared to those of the finite-time Lyapunov exponents (FTLE) for material deformation. As expected the mean cumulative vorticity stretching is slightly less than that of the most-stretched material line (largest FTLE), due to the vorticity's preferential alignment with the second-largest eigenvalue of strain-rate and the material line's preferential alignment with the largest eigenvalue. However, the vorticity stretching tends to be significantly larger than the second-largest FTLE, and the Cramer functions reveal that the statistics of vorticity stretching fluctuations are more similar to those of largest FTLE. A model Fokker-Planck equation is constructed by approximating the viscous destruction of vorticity with a deterministic non-linear relaxation law matching conditional statistics, while the fluctuations in vorticity stretching are modelled by stochastic noise matching the statistics encoded in the Cramer function. The model predicts a stretched-exponential tail for the vorticity magnitude PDF, with good agreement for the exponent but significant error (30-40%) in the pre-factor. Supported by NSF Graduate Fellowship (DGE-1232825) and NSF Grant CMMI-0941530.
Taylor length-scale size particles in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Lucci, Francesco
The present study investigates the two-way coupling effects of finite-size solid spherical particles on decaying isotropic turbulence using an immersed boundary method. The conventional point particle assumption is valid only in the case of particles with a diameter, dp, much smaller than the Kolmogorov length scale, eta. In a simulation with particles of diameter dp > eta the flow around each particle needs to be resolved. In this study, we use a method similar to that of Uhlmann(2005) [55] that adapts the Immersed Boundary(IB) Method developed by Peskin [38] to simulate the flow around suspended spherical solid particles. The main idea of the method is to distribute a number of Lagrangian points uniformly over the surface of the particle. A force is applied at each Lagrangian point to represent the momentum exchange between the particle and the surrounding fluid. An analytic three-point delta function is used to distribute the force to the Eulerian grid points saddling the spherical surface to satisfy the no-slip condition at each Lagrangian point. Decaying turbulence is simulated in a periodic box with a uniform mesh of up to (512)3 grid points and an initial microscale Reynolds number of up to Relambda0 = 110. We compare the single phase flow (SPF) with particle-laden flows with particles of different diameters. The density of the particle varies from 2.56 to 10 times that of the fluid. The effects of the particles on the temporal development of turbulence kinetic energy E(t), its dissipation rate epsilon( t), its two-way coupling rate of change Ψp( t) and frequency spectra E(o) are discussed. In this study, in contrast to particles with dp < eta [15], particles with dp > eta always increase the dissipation rate of turbulence kinetic energy, epsilon( t). In addition, Ψp(t) is always positive, whereas it can be positive or negative for particles with dp < eta. The balance between these two effects caused E(t) to be smaller than that of the single-phase flow
CVS Decomposition of 3D Homogeneous Turbulence Using Orthogonal Wavelets
NASA Technical Reports Server (NTRS)
Farge, Marie; Schneider, Kai; Pellegrino, Giulio; Wray, A. A.; Rogallo, R. S.
2000-01-01
This paper compares the filtering used in Coherent Vortex Simulation (CVS) decomposition with an orthogonal wavelet basis, with the Proper Orthogonal Decomposition (POD) or Fourier filtering. Both methods are applied to a field of Direct Numerical Simulation (DNS) data of 3D forced homogeneous isotropic turbulence at microscale Reynolds number R(sub lambda) = 168. We show that, with only 3%N retained modes, CVS filtering separates the coherent vortex tubes from the incoherent background flow. The latter is structureless, has an equipartition energy spectrum, and has a Gaussian velocity probability distribution function (PDF) and an exponential vorticity PDF. On the other hand, the Fourier basis does not extract the coherent vortex tubes cleanly and leaves organized structures in the residual high wavenumber modes whose PDFs are stretched exponentials for both the velocity and the vorticity.
Local topology of energy transport in isotropic turbulence
NASA Astrophysics Data System (ADS)
Boschung, Jonas; Meneveau, Charles
2012-11-01
Similar to the velocity vector field, whose tangent (stream) lines represent how fluid volume (or mass in constant density flows) is transported in the flow, it is of interest to consider the vector field corresponding to the transport of mechanical energy (Meyers & Meneveau, 2012). The transport includes advection and viscous diffusion. In order to characterize the local topology of this vector field in turbulence, we examine statistical properties of its gradient field. This energy transport field is not divergence-free, due to dissipation and unsteady changes of kinetic energy. Therefore, the first invariant (the trace) of its gradient tensor is not zero, as in compressible flow. The three invariants PE, QE and RE of the energy transport gradient tensor are analyzed using concepts developed earlier for analysis of compressible flows. Data from DNS of isotropic turbulence is used, from the JHU database (Li et al. 2008, JoT), as well as other sources. Contracting node-like topology occurs very frequently, consistent with the dissipative nature of fluid turbulence. Further topological properties are established based on conditional PDFs of the invariants, and flow visualizations are used to develop insights into the local structure of the energy transport vector field. This work is supported by project CMMI-0941530. The authors also thank Prof. J. Meyers, Prof. N. Peters and Mr. P. Schaefer for interesting discussions on this topic.
Homogenous isotropic invisible cloak based on geometrical optics.
Sun, Jingbo; Zhou, Ji; Kang, Lei
2008-10-27
Invisible cloak derived from the coordinate transformation requires its constitutive material to be anisotropic. In this work, we present a cloak of graded-index isotropic material based on the geometrical optics theory. The cloak is realized by concentric multilayered structure with designed refractive index to achieve the low-scattering and smooth power-flow. Full-wave simulations on such a design of a cylindrical cloak are performed to demonstrate the cloaking ability to incident wave of any polarization. Using normal nature material with isotropy and low absorption, the cloak shows light on a practical path to stealth technology, especially that in the optical range. PMID:18958058
Energy transfer and constrained simulations in isotropic turbulence
NASA Technical Reports Server (NTRS)
Jimenez, Javier
1993-01-01
The defining characteristic of turbulent flows is their ability to dissipate energy, even in the limit of zero viscosity. The Euler equations, if constrained in such a way that the velocity derivatives remain bounded, conserve energy. But when they arise as the limit of the Navier-Stokes (NS) equations, when the Reynolds number goes to infinity, there is persuasive empirical evidence that the gradients become singular as just the right function of Re for the dissipation to remain non-zero and to approach a well defined limit. It is generally believed that this limiting value of the dissipation is a property of the Euler equations themselves, independent of the particular dissipative mechanism involved, and that it can be normalized with the large scale properties of the turbulent flow (e.g. the kinetic energy per unit volume u'(exp 2)/2, and the integral scale L) without reference to the Reynolds number or to other dissipative quantities. This is usually taken to imply that the low wave number end of the energy spectrum, far from the dissipative range, is also independent of the particular mechanism chosen to dispose of the energy transfer. In the following sections, we present some numerical experiments on the effect of substituting different dissipation models into the truncated Euler equations. We will see that the effect is mainly felt in the 'near dissipation' range of the energy spectrum, but that this range can be quite wide in some cases, contaminating a substantial range of wave numbers. In the process, we will develop a 'practical' approximation to the subgrid energy transfer in isotropic turbulence, and we will gain insight into the structure of the nonlinear interactions among turbulent scales of comparable size, and into the nature of energy backscatter. Some considerations on future research directions are offered at the end.
Dynamics of Aerosol Particles in Stationary, Isotropic Turbulence
NASA Technical Reports Server (NTRS)
Collins, Lance R.; Meng, Hui
2004-01-01
A detailed study of the dynamics of sub-Kolmogorov-size aerosol particles in stationary isotropic turbulence has been performed. The study combined direct numerical simulations (DNS; directed by Prof. Collins) and high-resolution experimental measurements (directed by Prof. Meng) under conditions of nearly perfect geometric and parametric overlap. The goal was to measure the accumulation of particles in low-vorticity regions of the flow that arises from the effect commonly referred to as preferential concentration. The grant technically was initiated on June 13, 2000; however, funding was not available until July 11, 2000. The grant was originally awarded to Penn State University (numerical simulations) and SUNY-Buffalo (experiments); however, Prof. Collins effort was moved to Cornell University on January 2002 when he joined that university. He completed the study there. A list of the specific tasks that were completed under this study is presented.
Model for drop coalescence in a locally isotropic turbulent flow field.
Narsimhan, Ganesan
2004-04-01
The proposed model views drop coalescence in a turbulent flow field as a two-step process consisting of formation of a doublet due to drop collisions followed by coalescence of the individual droplets in a doublet due to the drainage of the intervening film of continuous phase under the action of colloidal (van der Waals and electrostatic) and random turbulent forces. The turbulent flow field was assumed to be locally isotropic. A first-passage-time analysis was employed for the random process of intervening continuous-phase film thickness between the two drops of a doublet in order to evaluate the first two moments of coalescence-time distribution of the doublet. The average drop coalescence time of the doublet was dependent on the barrier for coalescence due to the net repulsive force (net effect of colloidal repulsive and turbulent attractive forces). The predicted average drop coalescence time was found to be smaller for larger turbulent energy dissipation rates, smaller surface potentials, larger drop sizes, larger ionic strengths, and larger drop size ratios of unequal-sized drop pairs. The predicted average drop coalescence time was found to decrease whenever the ratio of average turbulent force to repulsive force barrier became larger. The calculated coalescence-time distribution was broader, with a higher standard deviation, at lower energy dissipation rates, higher surface potentials, smaller drop sizes, and smaller size ratios of unequal drop pairs. The model predictions of average coalescence-rate constants for tetradecane-in-water emulsions stabilized by sodium dodecyl sulfate (SDS) in a high-pressure homogenizer agreed fairly well with the inferred experimental values as reported by Narsimhan and Goel (J. Colloid Interface Sci. 238 (2001) 420-432) at different homogenizer pressures and SDS concentrations. PMID:14985038
NASA Astrophysics Data System (ADS)
Xanthos, Savvas; Gong, Minwei; Andreopoulos, Yiannis
2010-01-01
Further analysis of the experimental data of the velocity gradient tensor first published by Xanthos et al. [J. Fluid Mech. 584, 301 (2007)] has been carried out and new results are reported here to provide additional insights on the effects of expansion waves interacting with isotropic turbulence. The flow field was generated by the reflection of an incoming shock wave at the open end of a large scale shock tube facility which interacted with the induced flow behind the incident shock wave which passed through a turbulence generating grid. In the present configuration the interaction is free from streamline curvature effects, which cause additional effects on turbulence. The strength of the applied expansive straining was 240 s-1. Rectangular pattern grids of different mesh sizes were used to generate isotropic and homogeneous turbulence with turbulent Reynolds number Reλ based on Taylor's microscale between 450 and 488. Lateral vorticity fluctuations and fluctuations of enstrophy and all stretching vector components are drastically reduced during the interaction. Residual attenuation in the postinteraction flow field was found only in the lateral vorticity fluctuations and in the longitudinal stretching term S11Ω1. Helicity and the helicity angle were computed from the data and the orientation angle of the vorticity vector in reference to the velocity vector was determined. Large fluctuations of the helicity angle were observed which extend from 0° to 180° with most probable values close to 30° and 130° and a mean value of 85°. Rotational dissipation rate was found to be high at these angles. The time-dependent signals of enstrophy, vortex stretching/tilting vector, and dissipation rate were found to exhibit a rather strong intermittent behavior which is characterized by high amplitude bursts followed by low level activities. It was found that the observed strong dissipative events are mostly associated with strong activities in the longitudinal stretching
DNS of fully resolved spherical particles dispersed in isotropic turbulence
NASA Astrophysics Data System (ADS)
Lucci, Francesco; Ferrante, Antonino; Elghobashi, Said
2008-11-01
Our DNS study concerns the interactions between decaying isotropic turbulence and solid spherical particles with diameter, d, larger than the Kolmogorov length scale, η. We employ an Immersed Boundary method similar to that of Uhlmann (JCP, 2005) to resolve the flow around 6400 spherical particles with a volume fraction of φv=0.1. The monosize particles have a diameter, d = 16 ηo. Our simulations, with 256^3 mesh points and Reλ0= 75, cover a range of 38 <=τp/τKo<=149, for the ratio of the particle response time to the initial Kolmogorov time scale. A Lagrangian approach is used to compute the frequency spectrum of the turbulence kinetic energy (TKE) of the fluid phase. The effects of varying τp/τKo on the spectrum and the decay rate of TKE are discussed. The effects of the formation of the particle boundary layer on the viscous dissipation rate of TKE are also discussed.
Preferential concentration of heavy particles in compressible isotropic turbulence
NASA Astrophysics Data System (ADS)
Zhang, Qingqing; Liu, Han; Ma, Zongqiang; Xiao, Zuoli
2016-05-01
Numerical simulations of particle-laden compressible isotropic turbulence with Taylor Reynolds number Reλ ˜ 100 are conducted by using a high-order turbulence solver, which is based on high-order compact finite difference method in the whole flow domain and localized artificial diffusivities for discontinuities. For simplicity, only one-way coupling (i.e., the influence of fluid on particles) between the carrier flow and particles is considered. The focus is on the study of the preferential concentration of heavy particles in dissipative scale of turbulence and the underlying mechanisms. Firstly, the effect of Stokes number (St) on the particle distribution in flow of Mach 1.01 (referred to as high-Mach-number case in this study) is investigated as a necessary supplementation for the previous studies in incompressible and weakly compressible flows. It turns out that heavy particles with Stokes number close to unity exhibit the strongest preferential concentration, which is in agreement with the observation in incompressible flow. All types of heavy particles have a tendency to accumulate in high-density regions of the background flow. While all kinds of particles dominantly collect in low-vorticity regions, intermediate and large particles (St = 1 and St = 5) are also found to collect in high-vorticity regions behind the randomly formed shocklets. Secondly, the impact of turbulent Mach number (Mt) (or the compressibility) of the carrier flow on the spatial distribution of the particles with St = 1 is discussed using the simulated compressible flows with Mt being 0.22, 0.68, and 1.01, respectively. In low-Mach-number flow, particles tend to concentrate in regions of low vorticity due to the centrifuge effect of vortices and particle concentration decreases monotonically with the increasing vorticity magnitude. As Mach number increases, the degree of particle clustering is slightly weakened in low-vorticity regions but is enhanced in high-vorticity regions, which
Isotropic blackbody cosmic microwave background radiation as evidence for a homogeneous universe.
Clifton, Timothy; Clarkson, Chris; Bull, Philip
2012-08-01
The question of whether the Universe is spatially homogeneous and isotropic on the largest scales is of fundamental importance to cosmology but has not yet been answered decisively. Surprisingly, neither an isotropic primary cosmic microwave background (CMB) nor combined observations of luminosity distances and galaxy number counts are sufficient to establish such a result. The inclusion of the Sunyaev-Zel'dovich effect in CMB observations, however, dramatically improves this situation. We show that even a solitary observer who sees an isotropic blackbody CMB can conclude that the Universe is homogeneous and isotropic in their causal past when the Sunyaev-Zel'dovich effect is present. Critically, however, the CMB must either be viewed for an extended period of time, or CMB photons that have scattered more than once must be detected. This result provides a theoretical underpinning for testing the cosmological principle with observations of the CMB alone. PMID:23006164
Turbulent Diffusion in Non-Homogeneous Environments
NASA Astrophysics Data System (ADS)
Diez, M.; Redondo, J. M.; Mahjoub, O. B.; Sekula, E.
2012-04-01
Many experimental studies have been devoted to the understanding of non-homogeneous turbulent dynamics. Activity in this area intensified when the basic Kolmogorov self-similar theory was extended to two-dimensional or quasi 2D turbulent flows such as those appearing in the environment, that seem to control mixing [1,2]. The statistical description and the dynamics of these geophysical flows depend strongly on the distribution of long lived organized (coherent) structures. These flows show a complex topology, but may be subdivided in terms of strongly elliptical domains (high vorticity regions), strong hyperbolic domains (deformation cells with high energy condensations) and the background turbulent field of moderate elliptic and hyperbolic characteristics. It is of fundamental importance to investigate the different influence of these topological diverse regions. Relevant geometrical information of different areas is also given by the maximum fractal dimension, which is related to the energy spectrum of the flow. Using all the available information it is possible to investigate the spatial variability of the horizontal eddy diffusivity K(x,y). This information would be very important when trying to model numerically the behaviour in time of the oil spills [3,4] There is a strong dependence of horizontal eddy diffusivities with the Wave Reynolds number as well as with the wind stress measured as the friction velocity from wind profiles measured at the coastline. Natural sea surface oily slicks of diverse origin (plankton, algae or natural emissions and seeps of oil) form complicated structures in the sea surface due to the effects of both multiscale turbulence and Langmuir circulation. It is then possible to use the topological and scaling analysis to discriminate the different physical sea surface processes. We can relate higher orden moments of the Lagrangian velocity to effective diffusivity in spite of the need to calibrate the different regions determining the
Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating
NASA Astrophysics Data System (ADS)
Mitchell-Thomas, R. C.; Quevedo-Teruel, O.; Sambles, J. R.; Hibbins, A. P.
2016-08-01
The field of transformation optics owes a lot of its fame to the concept of cloaking. While some experimental progress has been made towards free-space cloaking in three dimensions, the material properties required are inherently extremely difficult to achieve. The approximations that then have to be made to allow fabrication produce unsatisfactory device performance. In contrast, when surface wave systems are the focus, it has been shown that a route distinct from those used to design free-space cloaks can be taken. This results in very simple solutions that take advantage of the ability to incorporate surface curvature. Here, we provide a demonstration in the microwave regime of cloaking a bump in a surface. The distortion of the shape of the surface wave fronts due to the curvature is corrected with a suitable refractive index profile. The surface wave cloak is fabricated from a metallic backed homogeneous dielectric waveguide of varying thickness, and exhibits omnidirectional operation.
Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating
Mitchell-Thomas, R. C.; Quevedo-Teruel, O.; Sambles, J. R.; Hibbins, A. P.
2016-01-01
The field of transformation optics owes a lot of its fame to the concept of cloaking. While some experimental progress has been made towards free-space cloaking in three dimensions, the material properties required are inherently extremely difficult to achieve. The approximations that then have to be made to allow fabrication produce unsatisfactory device performance. In contrast, when surface wave systems are the focus, it has been shown that a route distinct from those used to design free-space cloaks can be taken. This results in very simple solutions that take advantage of the ability to incorporate surface curvature. Here, we provide a demonstration in the microwave regime of cloaking a bump in a surface. The distortion of the shape of the surface wave fronts due to the curvature is corrected with a suitable refractive index profile. The surface wave cloak is fabricated from a metallic backed homogeneous dielectric waveguide of varying thickness, and exhibits omnidirectional operation. PMID:27492929
Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating.
Mitchell-Thomas, R C; Quevedo-Teruel, O; Sambles, J R; Hibbins, A P
2016-01-01
The field of transformation optics owes a lot of its fame to the concept of cloaking. While some experimental progress has been made towards free-space cloaking in three dimensions, the material properties required are inherently extremely difficult to achieve. The approximations that then have to be made to allow fabrication produce unsatisfactory device performance. In contrast, when surface wave systems are the focus, it has been shown that a route distinct from those used to design free-space cloaks can be taken. This results in very simple solutions that take advantage of the ability to incorporate surface curvature. Here, we provide a demonstration in the microwave regime of cloaking a bump in a surface. The distortion of the shape of the surface wave fronts due to the curvature is corrected with a suitable refractive index profile. The surface wave cloak is fabricated from a metallic backed homogeneous dielectric waveguide of varying thickness, and exhibits omnidirectional operation. PMID:27492929
Symmetries and the approach to statistical equilibrium in isotropic turbulence
NASA Astrophysics Data System (ADS)
Clark, Timothy T.; Zemach, Charles
1998-11-01
The relaxation in time of an arbitrary isotropic turbulent state to a state of statistical equilibrium is identified as a transition to a state which is invariant under a symmetry group. We deduce the allowed self-similar forms and time-decay laws for equilibrium states by applying Lie-group methods (a) to a family of scaling symmetries, for the limit of high Reynolds number, as well as (b) to a unique scaling symmetry, for nonzero viscosity or nonzero hyperviscosity. This explains why a diverse collection of turbulence models, going back half a century, arrived at the same time-decay laws, either through derivations embedded in the mechanics of a particular model, or through numerical computation. Because the models treat the same dynamical variables having the same physical dimensions, they are subject to the same scaling invariances and hence to the same time-decay laws, independent of the eccentricities of their different formulations. We show in turn, by physical argument, by an explicitly solvable analytical model, and by numerical computation in more sophisticated models, that the physical mechanism which drives (this is distinct from the mathematical circumstance which allows) the relaxation to equilibrium is the cascade of turbulence energy toward higher wave numbers, with the rate of cascade approaching zero in the low wave-number limit and approaching infinity in the high wave-number limit. Only the low-wave-number properties of the initial state can influence the equilibrium state. This supplies the physical basis, beyond simple dimensional analysis, for quantitative estimates of relaxation times. These relaxation times are estimated to be as large as hundreds or more times the initial dominant-eddy cycle times, and are determined by the large-eddy cycle times. This mode of analysis, applied to a viscous turbulent system in a wind tunnel with typical initial laboratory parameters, shows that the time necessary to reach the final stage of decay is
Large-deviation statistics of vorticity stretching in isotropic turbulence
NASA Astrophysics Data System (ADS)
Johnson, Perry L.; Meneveau, Charles
2016-03-01
A key feature of three-dimensional fluid turbulence is the stretching and realignment of vorticity by the action of the strain rate. It is shown in this paper, using the cumulant-generating function, that the cumulative vorticity stretching along a Lagrangian path in isotropic turbulence obeys a large deviation principle. As a result, the relevant statistics can be described by the vorticity stretching Cramér function. This function is computed from a direct numerical simulation data set at a Taylor-scale Reynolds number of Reλ=433 and compared to those of the finite-time Lyapunov exponents (FTLE) for material deformation. As expected, the mean cumulative vorticity stretching is slightly less than that of the most-stretched material line (largest FTLE), due to the vorticity's preferential alignment with the second-largest eigenvalue of strain rate and the material line's preferential alignment with the largest eigenvalue. However, the vorticity stretching tends to be significantly larger than the second-largest FTLE, and the Cramér functions reveal that the statistics of vorticity stretching fluctuations are more similar to those of the largest FTLE. In an attempt to relate the vorticity stretching statistics to the vorticity magnitude probability density function in statistically stationary conditions, a model Kramers-Moyal equation is constructed using the statistics encoded in the Cramér function. The model predicts a stretched-exponential tail for the vorticity magnitude probability density function, with good agreement for the exponent but significant difference (35%) in the prefactor.
Carroll, Jonathan J.; Frank, Adam; Blackman, Eric G.
2010-10-10
Feedback from protostellar outflows can influence the nature of turbulence in star-forming regions even if they are not the primary source of velocity dispersion for all scales of molecular clouds. For the rate and power expected in star-forming regions, we previously (Carroll et al.) demonstrated that outflows could drive supersonic turbulence at levels consistent with the scaling relations from Matzner although with a steeper velocity power spectrum than expected for an isotropically driven supersonic turbulent cascade. Here, we perform higher resolution simulations and combine simulations of outflow driven turbulence with those of isotropically forced turbulence. We find that the presence of outflows within an ambient isotropically driven turbulent environment produces a knee in the velocity power spectrum at the outflow scale and a steeper slope at sub-outflow scales than for a purely isotropically forced case. We also find that the presence of outflows flattens the density spectrum at large scales effectively reducing the formation of large-scale turbulent density structures. These effects are qualitatively independent of resolution. We have also carried out Principal Component Analysis (PCA) for synthetic data from our simulations. We find that PCA as a tool for identifying the driving scale of turbulence has a misleading bias toward low amplitude large-scale velocity structures even when they are not necessarily the dominant energy containing scales. This bias is absent for isotropically forced turbulence but manifests strongly for collimated outflow driven turbulence.
Energy transfer and dissipation in forced isotropic turbulence.
McComb, W D; Berera, A; Yoffe, S R; Linkmann, M F
2015-04-01
A model for the Reynolds-number dependence of the dimensionless dissipation rate C(ɛ) was derived from the dimensionless Kármán-Howarth equation, resulting in C(ɛ)=C(ɛ,∞)+C/R(L)+O(1/R(L)(2)), where R(L) is the integral scale Reynolds number. The coefficients C and C(ɛ,∞) arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNSs) of forced isotropic turbulence for integral scale Reynolds numbers up to R(L)=5875 (R(λ)=435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law R(L)(n) with exponent value n=-1.000±0.009 and that this decay of C(ɛ) was actually due to the increase in the Taylor surrogate U(3)/L. The model equation was fitted to data from the DNS, which resulted in the value C=18.9±1.3 and in an asymptotic value for C(ɛ) in the infinite Reynolds-number limit of C(ɛ,∞)=0.468±0.006. PMID:25974586
Interacting scales and energy transfer in isotropic turbulence
NASA Technical Reports Server (NTRS)
Zhou, YE
1993-01-01
The dependence of the energy transfer process on the disparity of the interacting scales is investigated in the inertial and far-dissipation ranges of isotropic turbulence. The strategy for generating the simulated flow fields and the choice of a disparity parameter to characterize the scaling of the interactions is discussed. The inertial range is found to be dominated by relatively local interactions, in agreement with the Kolmogorov assumption. The far-dissipation is found to be dominated by relatively non-local interactions, supporting the classical notion that the far-dissipation range is slaved to the Kolmogorov scales. The measured energy transfer is compared with the classical models of Heisenberg, Obukhov, and the more detailed analysis of Tennekes and Lumley. The energy transfer statistics measured in the numerically simulated flows are found to be nearly self-similar for wave numbers in the inertial range. Using the self-similar form measured within the limited scale range of the simulation, an 'ideal' energy transfer function and the corresponding energy flux rate for an inertial range of infinite extent are constructed. From this flux rate, the Kolmogorov constant is calculated to be 1.5, in excellent agreement with experiments.
Testing a similarity theory for isotropic turbulence on DNS data.
NASA Astrophysics Data System (ADS)
Melander, Mogens; Fabijonas, Bruce
2006-11-01
Using direct numerical simulations, we consider the issue of self-similarity in 3D incompressible isotropic turbulence. The starting point for our investigation is a similarity theory we have developed on the basis of high Reynolds number shell model calculations. Like Kolmogorov's 1941 theory, our theory calls for similarity across all scales in the inertial range. Unlike K41, our theory does not fail on account of intermittency, but is developed to blossom in that environment. To observe self-similarity, it is essential that the correct variables are used, otherwise one sees only intermittency. The correct variables are reasonably easy to spot for the shell model, but they are more difficult to identify for the full Navier-Stokes equations. Moreover, one has to overcome the fact that the DNS has lower Reynolds numbers than in the shell model simulations so that the inertial range is shorter. Using the technique ESS, we clear this obstacle with only a minor modification to the theory. The DNS data then collapse on the theoretical pdf at all scales.
Energy transfer and dissipation in forced isotropic turbulence
NASA Astrophysics Data System (ADS)
McComb, W. D.; Berera, A.; Yoffe, S. R.; Linkmann, M. F.
2015-04-01
A model for the Reynolds-number dependence of the dimensionless dissipation rate Cɛ was derived from the dimensionless Kármán-Howarth equation, resulting in Cɛ=Cɛ ,∞+C /RL+O (1 /RL2) , where RL is the integral scale Reynolds number. The coefficients C and Cɛ ,∞ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNSs) of forced isotropic turbulence for integral scale Reynolds numbers up to RL=5875 (Rλ=435 ), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law RLn with exponent value n =-1.000 ±0.009 and that this decay of Cɛ was actually due to the increase in the Taylor surrogate U3/L . The model equation was fitted to data from the DNS, which resulted in the value C =18.9 ±1.3 and in an asymptotic value for Cɛ in the infinite Reynolds-number limit of Cɛ ,∞=0.468 ±0.006 .
Passive scalar convective-diffusive subrange for low Prandtl numbers in isotropic turbulence
NASA Astrophysics Data System (ADS)
Briard, A.; Gomez, T.
2015-01-01
In this Rapid Communication, we study the behavior of a strongly diffusive passive scalar field T submitted to a freely decaying, homogeneous and isotropic turbulence with eddy-damped quasinormal Markovian simulations. We present a new subrange located between the k-17 /3 inertial-diffusive subrange and the Kolmogorov wave number kη. This subrange is generated by small-scale convection linked to kη that balances diffusion effects. Thus, we build a typical length scale kCD -1 based on convection and diffusion and give an expression for the shape of the passive scalar spectrum in this subrange ET˜√{Pr}k-11 /3 using physical arguments. This result unifies two different theories coming from Batchelor [G. K. Batchelor, J. Fluid. Mech. 5, 113 (1959), 10.1017/S002211205900009X] and Chasnov [J. Chasnov et al., Phys. Fluids A 1, 1698 (1989), 10.1063/1.857535] and explains results previously obtained experimentally.
NASA Astrophysics Data System (ADS)
Liu, Xing-Xiang; Alù, Andrea
2011-06-01
In this work, we discuss the homogenization of a metamaterial geometry composed of periodic arrays of densely packed subwavelength magnetodielectric spheres, in order to study whether a local quasi-isotropic homogenization model may accurately describe its wave interaction in its negative-index or zero-index operation. We analyze and compare the electromagnetic response of these arrays with their retrieved metamaterial model, for frequency regimes in which positive or negative values of effective index of refraction are expected. We pay special attention to the effects of array truncation and complex forms of excitation, showing that it is possible to realize quasi-isotropic negative-index or zero-index metamaterials with negligible spatial dispersion effects in certain frequency bands. We then apply these concepts to specific configurations of interest for metamaterial devices, showing that, despite their finite size and complex operation, their response is consistent with the one associated with their homogenized local description.
Homogeneous turbulence subjected to mean flow with elliptic streamlines
NASA Technical Reports Server (NTRS)
Blaisdell, G. A.; Shariff, K.
1994-01-01
Direct numerical simulations are performed for homogeneous turbulence with a mean flow having elliptic streamlines. This flow combines the effects of rotation and strain on the turbulence. Qualitative comparisons are made with linear theory for cases with high Rossby number. The nonlinear transfer process is monitored using a generalized skewness. In general, rotation turns off the nonlinear cascade; however, for moderate ellipticities and rotation rates the nonlinear cascade is turned off and then reestablished. Turbulence statistics of interest in turbulence modeling are calculated, including full Reynolds stress budgets.
Repeated cascade theory of homogeneous turbulence.
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1973-01-01
The problem of turbulent spectrum engenders two coupled hierarchies: one originates from the development of stress, leading to a transfer function, and the other from the development of an eddy viscosity. In order to incorporate physical roles among scales, the turbulent velocity fluctuation is decomposed into a series of ranks in the increasing order of randomness, contributing successively to energy or stress, eddy viscosity, relaxation frequency, and higher-rank frequencies in the memory chain. As a result, the first hierarchy mentioned above becomes closed at the quadrupole correlation. The second hierarchy governs the eddy viscosities of different ranks, related to relaxation frequencies of such ranks, in the form of a memory chain. It is cut off by an implicit viscous mechanism. For zero wind gradient, the spectrum in the inertial subrange recovers the Kolmogoroff k to the minus 5/3 law with a numerical constant 1.58, in good agreement with experiments. For a strong wind gradient, the spectrum in the production subrange has a k to the minus 1 law.
Broken Ergodicity in Two-Dimensional Homogeneous Magnetohydrodynamic Turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2010-01-01
Two-dimensional (2-D) homogeneous magnetohydrodynamic (MHD) turbulence has many of the same qualitative features as three-dimensional (3-D) homogeneous MHD turbulence.The se features include several ideal invariants, along with the phenomenon of broken ergodicity. Broken ergodicity appears when certain modes act like random variables with mean values that are large compared to their standard deviations, indicating a coherent structure or dynamo.Recently, the origin of broken ergodicity in 3-D MHD turbulence that is manifest in the lowest wavenumbers was explained. Here, a detailed description of the origins of broken ergodicity in 2-D MHD turbulence is presented. It will be seen that broken ergodicity in ideal 2-D MHD turbulence can be manifest in the lowest wavenumbers of a finite numerical model for certain initial conditions or in the highest wavenumbers for another set of initial conditions.T he origins of broken ergodicity in ideal 2-D homogeneous MHD turbulence are found through an eigen analysis of the covariance matrices of the modal probability density functions.It will also be shown that when the lowest wavenumber magnetic field becomes quasi-stationary, the higher wavenumber modes can propagate as Alfven waves on these almost static large-scale magnetic structures
NASA Technical Reports Server (NTRS)
Squires, Kyle D.; Eaton, John K.
1991-01-01
Direct numerical simulation is used to study dispersion in decaying isotropic turbulence and homogeneous shear flow. Both Lagrangian and Eulerian data are presented allowing direct comparison, but at fairly low Reynolds number. The quantities presented include properties of the dispersion tensor, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The Lagrangian time microscale is found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame.
Non-isotropic turbulence effects on spray combustion
NASA Technical Reports Server (NTRS)
Kim, Y. M.; Shang, H. M.; Chen, C. P.
1991-01-01
A numerical model for the prediction of local properties of statistically stationary spray-combusting flows is evaluated by comparison with experimental data. To appraise the relative performance of turbulence models, computations were carried out by the k-epsilon model and the algebraic stress model. The present numerical results show the qualitative agreement with experimental data. In terms of overall local flow properties, the algebraic stress model improves a degree of conformity to the experimental data due to its ability to introduce the nonisotropic turbulence effects. Two swirl numbers are considered to investigate the influence of swirl on the droplet evaporation and trajectories, and the effects of droplet/turbulence interactions in flow properties. It is found that the large swirl produces a higher evaporationn rate, and more intensive turbulent mixing and burning. The discrepancies observed in the results are attributed mainly to uncertainties in the initial spray size and velocity distributions, the droplet/wall impingement interaction, the combustion model with the fast chemistry and the turbulence models dealing with the strong streamline curvature and complex interactions between the dispersed droplets and the continuous gas-phase flows.
Network Structure of Two-Dimensional Homogeneous Turbulence
NASA Astrophysics Data System (ADS)
Taira, Kunihiko; Nair, Aditya; Brunton, Steven
2015-11-01
The network structure of two-dimensional incompressible homogeneous turbulence is characterized by highlighting the vortical interactions in the flow field. By analyzing the degree distribution of the turbulence network, it is observed that turbulence has an underlying scale-free network that describes how vortical structures are interconnected. In the network-theoretic framework, we can identify strong vortices that serve as hubs that are strongly connected to other vortical hubs. Smaller and weaker eddies are found to be predominantly influenced by the neighboring hubs. These observations complement previous knowledge of turbulence based on vortex dynamics. The time evolution of the fluid flow network shows that the scale-free property is achieved when turbulence is sustained but is not observed when the flow reaches a laminar regime through dissipation. The finding that turbulence has a scale-free interaction network enables us to identify the type of perturbations that turbulence is resilient against. These insights from network analysis enable us to examine how the behavior of turbulent flows can be modified. This work was supported by the US Army Research Office (Grant W911NF-14-1-0386) and the US Air Force Office of Scientific Research (Grant FA9550-13-1-0183).
Cross-helicity in rotating homogeneous shear-stratified turbulence.
Pieri, A B; Godeferd, F S; Cambon, C; Dubrulle, B; Thalabard, S
2014-03-21
We consider homogeneous shear-stratified turbulence in a rotating frame, that exhibits complex nonlinear dynamics. Since the analysis of relative orientation between coupled fluctuating fields helps us to understand turbulence dynamics, we focus on the alignment properties of both the velocity and gravity fields with the potential vorticity gradient. With the help of statistical mechanics, we define a vector field which plays a role in the analogous so-called cross-helicity in magnetohydrodynamics. High-resolution direct numerical simulations of developed homogeneous baroclinic turbulence are performed, and a detailed analysis of probability density functions for cross-helicity is provided. A net preference for positive cross-helicity is shown to be related to a new alignment mechanism. We argue that the analysis of cross-helicity is crucial for understanding the dynamics of buoyancy driven flows. PMID:24702376
NASA Technical Reports Server (NTRS)
Han, Jongil; Lin, Yuh-Lang; Arya, S. Pal; Proctor, Fred H.
1999-01-01
The effects of ambient turbulence on decay and descent of aircraft wake vortices are studied using a validated, three-dimensional: large-eddy simulation model. Numerical simulations are performed in order to isolate the effect of ambient turbulence on the wake vortex decay rate within a neutrally-stratified atmosphere. Simulations are conducted for a range of turbulence intensities, by injecting wake vortex pairs into an approximately homogeneous and isotropic turbulence field. The decay rate of the vortex circulation increases clearly with increasing ambient turbulence level, which is consistent with field observations. Based on the results from the numerical simulations, simple decay models are proposed as functions of dimensionless ambient turbulence intensity (eta) and dimensionless time (T) for the circulation averaged over a range of radial distances. With good agreement with the numerical results, a Gaussian type of vortex decay model is proposed for weak turbulence: while an exponential type of Tortex decay model can be applied for strong turbulence. A relationship for the vortex descent based on above vortex decay model is also proposed. Although the proposed models are based on simulations assuming neutral stratification, the model predictions are compared to Lidar vortex measurements observed during stable, neutral, and unstable atmospheric conditions. In the neutral and unstable atmosphere, the model predictions appear to be in reasonable agreement with the observational data, while in the stably-stratified atmosphere, they largely underestimate the observed circulation decay with consistent overestimation of the observed vortex descent. The underestimation of vortex decay during stably-stratified conditions suggests that stratification has an important influence on vortex decay when ambient levels of turbulence are weak.
Sweeping and straining effects in sound generation by high Reynolds number isotropic turbulence
NASA Technical Reports Server (NTRS)
Zhou, YE; Rubinstein, Robert
1995-01-01
The sound radiated by isotropic turbulence is computed using inertial range scaling expressions for the relevant two time and two point correlations. The result depends on whether the decay of Eulerian time correlations is dominated by large scale sweeping or by local straining: the straining hypothesis leads to an expression for total acoustic power, whereas the sweeping hypothesis leads to a more recent result.
Energy transfer in isotropic turbulence at low Reynolds numbers
NASA Technical Reports Server (NTRS)
Domaradzki, J. A.; Rogallo, R. S.
1988-01-01
Detailed measurements were made of energy transfer among the scales of motion in incompressible turbulent fields at low Reynolds numbers generated by direct numerical simulation. It was observed that although the transfer resulted from triad interactions that were non-local in k space, the energy always transferred locally. The results are consistent with the notion of non-uniform advection of small weak eddies by larger and stronger ones, similar to transfer processes in the far dissipation range at high Reynolds numbers.
Suppression of turbulent energy cascade due to phase separation in homogenous binary mixture fluid
NASA Astrophysics Data System (ADS)
Takagi, Youhei; Okamoto, Sachiya
2015-11-01
When a multi-component fluid mixture becomes themophysically unstable state by quenching from well-melting condition, phase separation due to spinodal decomposition occurs, and a self-organized structure is formed. During phase separation, free energy is consumed for the structure formation. In our previous report, the phase separation in homogenous turbulence was numerically simulated and the coarsening process of phase separation was discussed. In this study, we extended our numerical model to a high Schmidt number fluid corresponding to actual polymer solution. The governing equations were continuity, Navier-Stokes, and Chan-Hiliard equations as same as our previous report. The flow filed was an isotropic homogenous turbulence, and the dimensionless parameters in the Chan-Hilliard equation were estimated based on the thermophysical condition of binary mixture. From the numerical results, it was found that turbulent energy cascade was drastically suppressed in the inertial subrange by phase separation for the high Schmidt number flow. By using the identification of turbulent and phase separation structure, we discussed the relation between total energy balance and the structures formation processes. This study is financially supported by the Grand-in-Aid for Young Scientists (B) (No. T26820045) from the Ministry of Education, Cul-ture, Sports, Science and Technology of Japan.
Spectral multigrid methods for the solution of homogeneous turbulence problems
NASA Technical Reports Server (NTRS)
Erlebacher, G.; Zang, T. A.; Hussaini, M. Y.
1987-01-01
New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.
Decay Power Law in, High Intensity, Isotropic Turbulent Flow
NASA Astrophysics Data System (ADS)
Koster, Timothy; Puga, Alejandro; Larue, John
2014-11-01
In the study reported here, isotropy is determined using the measure proposed by George (1992), where isotropy corresponds to those downstream positions where the product of the Taylor Reynolds number and the skewness of the velocity derivative is a constant. Straight forward approach can be used which is based on the observation of Batchelor (1953), that the square of the Talor micorscale is linearly related to downstream distance relative to the virtual origin. The fact that the decay of downstream velocity variance is described by a power law is shown to imply power law behavior for various other parameters such as the dissipation, the integral length scale, the Taylor microscale, the Kolmogorov microscale and the Taylor Reynolds number and that there is an algebraic relationship between the various power law exponents. Results are presented for mean velocities of 6 and 8 m/s for the downstream decay of the parameters listed in the preceding. The corresponding values of the Taylor Reynolds number at the start of the isotropic region are 290 and 400, and the variance decay exponent and virtual origin are found to be respectively -1.707 and -1.298 and -27.95 and -5.757. The exponents in the decay law for the other parameters are found to be within +/- 3% of the expected values. University of California Irvine Research Funds.
The radiated noise from isotropic turbulence and heated jets
NASA Technical Reports Server (NTRS)
Lilley, G. M.
1995-01-01
Our understanding of aerodynamic noise has its foundations in the work of Sir James Lighthill (1952), which was the first major advance in acoustics since the pioneering work of Lord Rayleigh in the last century. The combination of Lighthill's theory of aerodynamic noise as applied to turbulent flows and the experimental growing database from the early 1950's was quickly exploited by various jet propulsion engine designers in reducing the noise of jet engines at takeoff and landing to levels marginally acceptable to communities living in the neighborhoods of airports. The success in this noise containment led to the rapid growth of fast economical subsonic civil transport aircraft worldwide throughout the 1960's and has continued to the present day. One important factor in this success story has been the improvements in the engine cycle that have led to both reductions in specific fuel consumption and noise. The second is the introduction of Noise Certification, which specifies the maximum noise levels at takeoff and landing that all aircraft must meet before they can be entered on the Civil Aircraft Register. The growing interest in the development of a new supersonic civil transport to replace 'Concorde' in the early years of the next century has led to a resurgence of interest in the more challenging problem of predicting the noise of hot supersonic jets and developing means of aircraft noise reduction at takeoff and landing to meet the standards now accepted for subsonic Noise Certification. The prediction of aircraft noise to the accuracy required to meet Noise Certification requirements has necessitated reliance upon experimental measurements and empirically derived laws based on the available experimental data bases. These laws have their foundation in the results from Lighthill's theory, but in the case of jet noise, where the noise is generated in the turbulent mixing region with the external ambient fluid, the complexity of the turbulent motion has
NASA Astrophysics Data System (ADS)
Asinari, P.
2011-03-01
Boltzmann equation is one the most powerful paradigms for explaining transport phenomena in fluids. Since early fifties, it received a lot of attention due to aerodynamic requirements for high altitude vehicles, vacuum technology requirements and nowadays, micro-electro-mechanical systems (MEMs). Because of the intrinsic mathematical complexity of the problem, Boltzmann himself started his work by considering first the case when the distribution function does not depend on space (homogeneous case), but only on time and the magnitude of the molecular velocity (isotropic collisional integral). The interest with regards to the homogeneous isotropic Boltzmann equation goes beyond simple dilute gases. In the so-called econophysics, a Boltzmann type model is sometimes introduced for studying the distribution of wealth in a simple market. Another recent application of the homogeneous isotropic Boltzmann equation is given by opinion formation modeling in quantitative sociology, also called socio-dynamics or sociophysics. The present work [1] aims to improve the deterministic method for solving homogenous isotropic Boltzmann equation proposed by Aristov [2] by two ideas: (a) the homogeneous isotropic problem is reformulated first in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium).
Optical propagation through a homogeneous turbulent shear flow
NASA Technical Reports Server (NTRS)
Truman, C. Randall; Lee, Moon J.
1988-01-01
Effects of organized turbulent structures on the propagation of an optical beam in a homogeneous shear flow were studied. A passive-scalar field in a computed turbulent shear flow is used to represent index-of-refraction fluctuations, and phase errors induced in a coherent optical beam by turbulent fluctuations are computed. The organized vortical structures produce a scalar distribution with elongated regions of intense fluctuations which have an inclination with respect to the mean flow similar to that of the characteristic hairpin eddies. It is found that r.m.s. phase error is minimized by propagating approximately normal to the inclined vortical structures. Two-point correlations of vorticity and scalar fluctuation suggest that the regions of intense scalar fluctuation are produced primarily by the hairpin eddies.
Optimal thermalization in a shell model of homogeneous turbulence
NASA Astrophysics Data System (ADS)
Thalabard, Simon; Turkington, Bruce
2016-04-01
We investigate the turbulence-induced dissipation of the large scales in a statistically homogeneous flow using an ‘optimal closure,’ which one of us (BT) has recently exposed in the context of Hamiltonian dynamics. This statistical closure employs a Gaussian model for the turbulent scales, with corresponding vanishing third cumulant, and yet it captures an intrinsic damping. The key to this apparent paradox lies in a clear distinction between true ensemble averages and their proxies, most easily grasped when one works directly with the Liouville equation rather than the cumulant hierarchy. We focus on a simple problem for which the optimal closure can be fully and exactly worked out: the relaxation arbitrarily far-from-equilibrium of a single energy shell towards Gibbs equilibrium in an inviscid shell model of 3D turbulence. The predictions of the optimal closure are validated against DNS and contrasted with those derived from EDQNM closure.
NASA Astrophysics Data System (ADS)
Rutily, B.; Bergeat, J.
1994-12-01
The exact solution of the transfer equation (TE) in a homogeneous plane-parallel medium of any optical extent (i.e., infinite, semi-infinite, or finite) is derived in the case of isotropic local scattering. The sources are not necessarily isotropic. We start from our recent study of the Schwarzschild-Milne (SM) integral equation as derived from the TE with appropriate boundary conditions. Using the Laplace transform on the range of the optical depth variable, the solution of the TE is obtained as the transform, by an introduced logical-operator, of the solution of the SM equation. The latter is then expressed in terms of the sources by means of the Green distribution of the SM equation. We are thus led to calculate the transform of this distribution by the logical-operator, which is a fundamental auxiliary function of plane-parallel media. This transform, namely Gamma, is thoroughly studied in the present article. The transform of the Gamma-function by the logical-operator, i.e., the bi-transform of the Green distribution, yields the solution of the TE in terms of the specified sources. It is thus the Green function of the problem. This function is studied in detail hereafter and written in terms of the Gamma-function by means of simple algebraic formulae. Analytical and numerical studies of the auxiliary functions introduced here and in a former article are required before a numerical evaluation of our solution can be obtained.
Infinity of geodesics in a homogeneous and isotropic expanding space-time
NASA Astrophysics Data System (ADS)
Adda, Fayçal Ben; Porchon, Hélène
2016-03-01
In this paper, we construct a discrete simulation of an expanding homogeneous and isotropic space-time that expands via expansion of its basic elements to figure out properties and characteristics of such a space-time and derive conclusions. We prove that in such an expanding space-time, the geodesics are curved and more precisely, they fluctuate on the boundaries of the expanding basic elements. The non-existence of privileged expansion direction leads to the existence of an infinity of fluctuating geodesics between any two locations in this space-time, that provides a prediction of polarization in geometric optics, and a prediction of an earlier acceleration of the expansion as for the cosmic inflation model. This simulation is a case study and an example of space-time with variable topology using the principle of variation of topology via a transformation that creates holes.
NASA Astrophysics Data System (ADS)
Zito, Gianluigi; Rusciano, Giulia; Pesce, Giuseppe; Dochshanov, Alden; Sasso, Antonio
2015-04-01
Label-free chemical imaging of live cell membranes can shed light on the molecular basis of cell membrane functionalities and their alterations under membrane-related diseases. In principle, this can be done by surface-enhanced Raman scattering (SERS) in confocal microscopy, but requires engineering plasmonic architectures with a spatially invariant SERS enhancement factor G(x, y) = G. To this end, we exploit a self-assembled isotropic nanostructure with characteristics of homogeneity typical of the so-called near-hyperuniform disorder. The resulting highly dense, homogeneous and isotropic random pattern consists of clusters of silver nanoparticles with limited size dispersion. This nanostructure brings together several advantages: very large hot spot density (~104 μm-2), superior spatial reproducibility (SD < 1% over 2500 μm2) and single-molecule sensitivity (Gav ~ 109), all on a centimeter scale transparent active area. We are able to reconstruct the label-free SERS-based chemical map of live cell membranes with confocal resolution. In particular, SERS imaging is here demonstrated on red blood cells in vitro in order to use the Raman-resonant heme of the cell as a contrast medium to prove spectroscopic detection of membrane molecules. Numerical simulations also clarify the SERS characteristics of the substrate in terms of electromagnetic enhancement and distance sensitivity range consistently with the experiments. The large SERS-active area is intended for multi-cellular imaging on the same substrate, which is important for spectroscopic comparative analysis of complex organisms like cells. This opens new routes for in situ quantitative surface analysis and dynamic probing of living cells exposed to membrane-targeting drugs.Label-free chemical imaging of live cell membranes can shed light on the molecular basis of cell membrane functionalities and their alterations under membrane-related diseases. In principle, this can be done by surface-enhanced Raman
Spectral expansions of homogeneous and isotropic tensor-valued random fields
NASA Astrophysics Data System (ADS)
Malyarenko, Anatoliy; Ostoja-Starzewski, Martin
2016-06-01
We establish spectral expansions of tensor-valued homogeneous and isotropic random fields in terms of stochastic integrals with respect to orthogonal scattered random measures previously known only for the case of tensor rank 0. The fields under consideration take values in the 3-dimensional Euclidean space {E^3} and in the space {S^2(E^3)} of symmetric rank 2 tensors over {E^3}. We find a link between the theory of random fields and the theory of finite-dimensional convex compact sets. These random fields furnish stepping-stone for models of rank 1 and rank 2 tensor-valued fields in continuum physics, such as displacement, velocity, stress, strain, providing appropriate conditions (such as the governing equation or positive-definiteness) are imposed.
NASA Astrophysics Data System (ADS)
Wei, Qi; Cheng, Ying; Liu, Xiaojun
2012-12-01
Based on the effective medium theory, we propose a practical implementation of a cylindrical acoustic cloak with a concentric alternating multilayered structure of homogeneous isotropic materials, which can perfectly mimic the ideal radius-dependent and anisotropic ordinary lens cloak. The proposal exhibits near-ideal cloaking performance such as low-scattering and shadow-reducing in a wide frequency range, thus it can hide an object from the detection of acoustic waves. The acoustic wave can pass through the cloaking shell with an unchanged wavefront shape, which endues the cloaked object with duplex communication ability. More simulations on the acoustic far-field scattering patterns and the total scattering cross-section are performed to investigate the layer number and the frequency dependence of the cloaking effect, and the results show that the thinner layers exhibit a better cloaking effect. The proposal may significantly facilitate the experimental demonstration of the acoustic cloak.
NASA Astrophysics Data System (ADS)
Cheng, Ying; Liu, XiaoJun
2008-11-01
It was qualitatively demonstrated through finite-element full-wave simulations that acoustic cloak can be constructed by using concentric multilayered structure with alternating homogeneous isotropic materials [Y. Cheng et al., Appl. Phys. Lett. 92, 151913 (2008)]. Here we present a sequential in-depth analysis of the proposed cloak by means of the multiple-scattering algorithms. Calculated pressure fields demonstrate that the cloak possesses low-reflection and wavefront-bending properties. The scattering patterns further characterize the directional cloaking performance in the far field, which is consistent with the pressure fields. The mechanism of the cloaking is ascribed to a specific multiple-scattering process determined by the microscopic material distribution and structural details of the cloak. We also discuss the behavior of the multilayered cloak as a function of wavelength.
Coherent Vortex Simulations of linearly forced homogeneous turbulence
NASA Astrophysics Data System (ADS)
Vasilyev, Oleg V.; Goldstein, Daniel E.; de Stefano, Giuliano
2007-11-01
This is the first of two talks on the wavelet based eddy capturing computational methodology that is capable of identifying and tracking on an adaptive mesh energetic coherent vortical structures in a turbulent flow field. This talk focuses on Coherent Vortex Simulations (CVS) approach, where the velocity field is decomposed into two parts: a coherent, inhomogeneous, non-Gaussian component and an incoherent, homogeneous, Gaussian component. This separation of coherent and incoherent components is achieved by wavelet thresholding, which can be viewed as a non-linear filter that depends on each flow realization. The essence of the CVS approach is to solve for the coherent non-Gaussian component of a turbulent flow field. It has been shown previously that second generation bi-orthogonal wavelet threshold filtering is able to decompose a turbulent velocity field such that the total resulting SGS dissipation is approximately zero. The results of Coherent Vortex Simulations of linearly forced incompressible 3D homogeneous turbulence for different Reynolds numbers demonstrated that CVS with no SGS model is capable to recover not only low order statistics, but also energy and, more importantly, enstrophy spectra up to the dissipative wavenumber range.
Zito, Gianluigi; Rusciano, Giulia; Pesce, Giuseppe; Dochshanov, Alden; Sasso, Antonio
2015-05-14
Label-free chemical imaging of live cell membranes can shed light on the molecular basis of cell membrane functionalities and their alterations under membrane-related diseases. In principle, this can be done by surface-enhanced Raman scattering (SERS) in confocal microscopy, but requires engineering plasmonic architectures with a spatially invariant SERS enhancement factor G(x, y) = G. To this end, we exploit a self-assembled isotropic nanostructure with characteristics of homogeneity typical of the so-called near-hyperuniform disorder. The resulting highly dense, homogeneous and isotropic random pattern consists of clusters of silver nanoparticles with limited size dispersion. This nanostructure brings together several advantages: very large hot spot density (∼10(4) μm(-2)), superior spatial reproducibility (SD < 1% over 2500 μm(2)) and single-molecule sensitivity (Gav ∼ 10(9)), all on a centimeter scale transparent active area. We are able to reconstruct the label-free SERS-based chemical map of live cell membranes with confocal resolution. In particular, SERS imaging is here demonstrated on red blood cells in vitro in order to use the Raman-resonant heme of the cell as a contrast medium to prove spectroscopic detection of membrane molecules. Numerical simulations also clarify the SERS characteristics of the substrate in terms of electromagnetic enhancement and distance sensitivity range consistently with the experiments. The large SERS-active area is intended for multi-cellular imaging on the same substrate, which is important for spectroscopic comparative analysis of complex organisms like cells. This opens new routes for in situ quantitative surface analysis and dynamic probing of living cells exposed to membrane-targeting drugs. PMID:25898990
NASA Astrophysics Data System (ADS)
Grappin, Roland; Müller, Wolf-Christian; Verdini, Andrea
2015-04-01
Standard phenomenologies of MHD turbulence generally neglect deviations from kinetic-magnetic energies equipartition. However, solar wind turbulence commonly shows a magnetic excess (or positive residual energy) in the inertial range, with a definite power-law. We report here direct MHD simulation results showing a magnetic excess, both in homogeneous and expanding turbulence, with the latter taking into account the radial flow (expanding box model or EBM). We show that the results on magnetic excess, both scaling laws and amplitude, can be interpreted as resulting from the competition between the nonlinear stretching of the magnetic field by the velocity field and the relaxation to equipartition by the linear propagation of Alfvén waves. We generalize in this way earlier results on homogeneous MHD turbulence.
NASA Astrophysics Data System (ADS)
Farhat, Mohamed; Guenneau, Sebastien; Enoch, Stefan
2012-01-01
A cylindrical cloak is designed to control the bending waves propagating in isotropic thin plates. This is achieved through homogenization of a multiply perforated coating of isotropic homogeneous elastic material, which greatly simplifies the design of the multilayered cloak we proposed [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.024301 103, 024301 (2009)]. We first derive the homogenized biharmonic equation, which involves an anisotropic Young's modulus and an isotropic mass density. We then numerically show that a clamped obstacle is cloaked over a finite range of frequencies for an acoustic source located a couple of wavelengths away from its surrounding cloak. The reduced backward and forward scattering is confirmed by both the profile of the total field computed along a line passing through the source and the center of the cloak (near field confirmation), and the computation of the scattered far field.
Distortion of homogeneous turbulence by axisymmetric strain and dilatation
NASA Technical Reports Server (NTRS)
Lee, Moon Joo
1989-01-01
Rapid distortion theory is applied to study distortion of homogeneous turbulence subject to two different axisymmetric strain modes: the axisymmetric contraction (AC, nozzle-type flow), and the axisymmetric expansion (AE, diffuser-type flow). The paper explores the differences in effects of the two axisymmetric strain modes on the anisotropy of correlations and structures of turbulence; examines the effect of dilatation on the distortion of turbulence; and provides a theoretical background for turbulence model development. It is found that velocity and vorticity fluctuations are enhanced more efficiently by contraction than by expansion; contraction produces much higher anisotropy in velocity and vorticity than expansion; root-mean-square pressure is slightly reduced during contraction, whereas it increases rapidly during expansion; and vortical structures of rodlike shape develop in a contraction flow, while disklike structures develop in an expansion flow. A simple model that reflects the dependence of turbulence evolution on structural parameters such as the Reynolds-stress anisotropy and total strain is proposed, and is shown to outperform all other models for all cases examined, regardless of the mean strain rate.
NASA Technical Reports Server (NTRS)
Deissler, Robert G.
1996-01-01
Background material on Fourier analysis and on the spectral form of the continuum equations, both averaged and unaveraged, are given. The equations are applied to a number of cases of homogeneous turbulence with and without mean gradients. Spectral transfer of turbulent activity between scales of motion is studied in some detail. The effects of mean shear, heat transfer, normal strain, and buoyancy are included in the analyses.
NASA Astrophysics Data System (ADS)
Chouippe, Agathe; Uhlmann, Markus
2015-12-01
We consider the case of finite-size spherical particles which are settling under gravity in a homogeneous turbulent background flow. Turbulence is forced with the aid of the random forcing method of Eswaran and Pope ["An examination of forcing in direct numerical simulations of turbulence," Comput. Fluids 16(3), 257-278 (1988)], while the solid particles are represented with an immersed-boundary method. The forcing scheme is used to generate isotropic turbulence in vertically elongated boxes in order to warrant better decorrelation of the Lagrangian signals in the direction of gravity. Since only a limited number of Fourier modes are forced, it is possible to evaluate the forcing field directly in physical space, thereby avoiding full-size transforms. The budget of box-averaged kinetic energy is derived from the forced momentum equations. Medium-sized simulations for dilute suspensions at low Taylor-scale Reynolds number Reλ = 65, small density ratio ρp/ρf = 1.5, and for two Galileo numbers Ga = 0 and 120 are carried out over long time intervals in order to exclude the possibility of slow divergence. It is shown that the results at zero gravity are fully consistent with previous experimental measurements and available numerical reference data. Specific features of the finite-gravity case are discussed with respect to a reduction of the average settling velocity, the acceleration statistics, and the Lagrangian auto-correlations.
Voigt waves in homogenized particulate composites based on isotropic dielectric components
NASA Astrophysics Data System (ADS)
Mackay, Tom G.
2011-10-01
Homogenized composite materials (HCMs) can support a singular form of optical propagation, known as Voigt wave propagation, while their component materials do not. In essence, Voigt waves represent coalescent degenerate eigenmodes of the corresponding propagation matrix. Crucially, the existence of Voigt waves stems from the non-Hermitian nature of this propagation matrix, which in turn is a manifestation of the dissipative nature of the HCM. This phenomenon was investigated for biaxial HCMs arising from nondissipative isotropic dielectric component materials. The biaxiality of these HCMs stems from the oriented spheroidal shapes of the particles which make up the component materials. An extended version of the Bruggeman homogenization formalism was used to investigate the influence of component particle orientations, shapes and sizes, as well as volume fractions of the component materials, upon Voigt wave propagation. Our numerical studies revealed that the directions in which Voigt waves propagate are highly sensitive to the orientations of the component particles and to the volume fractions of the component materials, but less sensitive to the shapes of the component particles and less sensitive still to the sizes of the component particles. Furthermore, whether or not an HCM supports Voigt wave propagation at all is critically dependent upon the sizes of the component particles and, in certain cases, upon the volume fractions of the component materials.
How isotropic are turbulent flows generated by using periodic conditions in a cube?
NASA Astrophysics Data System (ADS)
Qin, Z. C.; Fang, L.; Fang, J.
2016-03-01
In numerical simulations, "isotropic" turbulent flows are always generated by using periodic conditions. We show that these periodic conditions mathematically lead to large-scale anisotropy which can be about 10% of the mean values, and thus prevent existing post-processing results from being accurate. A decomposition method by employing spherical harmonics is then proposed to distinguish this scale-dependent anisotropy effect from others and to minimize the related post-processing error.
Asymptotic Sensitivity of Homogeneous Turbulent Shear Flow to the
NASA Astrophysics Data System (ADS)
Isaza, Juan; Warhaft, Zellman; Collins, Lance
2007-11-01
Our recent numerical studies of homogeneous turbulent shear flow suggest the dynamics of the large and small scales are sensitive to the initial value of the shear parameter. In particular for initial values of S^* = S k /ɛ>=10, we find that the asymptotic state of the turbulence depends upon this parameter. Rapid distortion theory (RDT) predicts the dependence of both large- and small-scale statistics on S^* reasonably well, but the theory is applicable only for relatively short times (S t < 2). Direct numerical simulation (DNS) has a somewhat longer window, but it too eventually fails when the integral length scale becomes too large. Motivated by this earlier work, we performed experimental measurements of large- and small-scale velocity statistics in homogeneous turbulent shear flow in a wind tunnel. We are able to vary the initial shear parameter over the relevant range and observe the aforementioned asymptotic statistics. The experimental results will be presented, including detailed comparisons with earlier DNS and RDT.
NASA Astrophysics Data System (ADS)
Joly, A.; Moulin, F.; Violeau, D.; Astruc, D.
2012-10-01
The prediction of solid bodies transport (such as algae, debris, sediment grains, or corrosion deposits) is a necessary requirement in many industrial or environmental processes. The physical processes involved cover a wide range of processes, from tidal flow to turbulent eddies and particle drag. A stochastic model was therefore developed to link the different scales of the physical processes where it was assumed that the particles are dilute enough that they do not affect the flow or the motion of other particles while being large enough that each particle does not follow exactly the fluid motions (i.e., macro-particles). The stochastic model is built in such a way that it uses Reynolds-averaged fluid properties to predict trajectories of individual particles. This model was then tested using experimental measurements obtained for isotropic particles released in semi-homogeneous turbulence. The turbulent flow was generated using a pair of oscillating grids and was characterized using particle image velocimetry measurements. The trajectories of the particles were measured using a pair of high resolution cameras. The comparison between the experimental data and different numerical models gives satisfactory results.
NASA Technical Reports Server (NTRS)
Ling, S. C.; Saad, A.
1977-01-01
The energetic isotropic turbulence generated by a waterfall of low head was found to be developed in part through the unstable two-phase flow of entrained air bubbles. The resulting turbulent field had a turbulent Reynolds number in excess of 20,000 and maintained a self-similar structure throughout the decay period studied. The present study may provide some insight into the structure of turbulence produced by breaking waves over the ocean.
Solving dynamical equations in general homogeneous isotropic cosmologies with a scalaron
NASA Astrophysics Data System (ADS)
Filippov, A. T.
2016-07-01
We consider gauge-dependent dynamical equations describing homogeneous isotropic cosmologies coupled to a scalar field ψ (scalaron). For flat cosmologies (k = 0), we analyze the gauge-independent equation describing the differential χ(α) ≡ ψ (a) of the map of the metric a to the scalaron field ψ, which is the main mathematical characteristic of a cosmology and locally defines its portrait in the so-called a version. In the more customary ψ version, the similar equation for the differential of the inverse map bar χ (ψ ) ≡ χ ^{ - 1} (α ) is solved in an asymptotic approximation for arbitrary potentials v(ψ). In the flat case, bar χ (ψ ) and χ-1(α) satisfy first-order differential equations depending only on the logarithmic derivative of the potential, v(ψ)/v(ψ). If an analytic solution for one of the χ functions is known, then we can find all characteristics of the cosmological model. In the α version, the full dynamical system is explicitly integrable for k ≠ 0 with any potential v(α) ≡ v[ψ(α)] replacing v(ψ). Until one of the maps, which themselves depend on the potentials, is calculated, no sort of analytic relation between these potentials can be found. Nevertheless, such relations can be found in asymptotic regions or by perturbation theory. If instead of a potential we specify a cosmological portrait, then we can reconstruct the corresponding potential. The main subject here is the mathematical structure of isotropic cosmologies. We also briefly present basic applications to a more rigorous treatment of inflation models in the framework of the α version of the isotropic scalaron cosmology. In particular, we construct an inflationary perturbation expansion for χ. If the conditions for inflation to arise are satisfied, i.e., if v > 0, k = 0, χ2 < 6, and χ(α) satisfies a certain boundary condition as α→-∞, then the expansion is invariant under scaling the potential, and its first terms give the standard inflationary
Numerical Experiments on Homogeneous Strained Turbulence Subjected to Coriolis Force
NASA Technical Reports Server (NTRS)
Shariff, K.; Blaisdell, G. A.; Abid, R.; Speziale, C. G.; Rai, Man Mohan (Technical Monitor)
1995-01-01
Homogeneous turbulent flows with various combinations of strain-rate, rotation rate and coriolis force capture some important aspects of more complex flows with streamline curvature and rotation. Presently, a situation is considered in which as a box of turbulence rotates, strain axes rotate with it. This is to be contrasted with the elliptic streamline flow in which the strain axes are fixed in an inertial frame. The elliptic flow is known to exhibit (inviscid) growth of turbulent energy and one might expect even more rapid growth with the strain-axes following the box. Instead, it is found that the sign of the Reynolds shear stress is reversed leading to a negative production term for turbulent energy. Partial understanding of the phenomenon is obtained from a consideration of the rotation of inertial waves relative to the strain axes as well as the "pressure-less" RDT argument put forward by Cambon etal. [J. Fluid Mech, 278, 175]. Some comparisons with the predictions of second-order closure models will be presented.
Pumping velocity in homogeneous helical turbulence with shear
NASA Astrophysics Data System (ADS)
Rogachevskii, Igor; Kleeorin, Nathan; Käpylä, Petri J.; Brandenburg, Axel
2011-11-01
Using different analytical methods (the quasilinear approach, the path-integral technique, and the tau-relaxation approximation) we develop a comprehensive mean-field theory for a pumping effect of the mean magnetic field in homogeneous nonrotating helical turbulence with imposed large-scale shear. The effective pumping velocity is proportional to the product of α effect and large-scale vorticity associated with the shear, and causes a separation of the toroidal and poloidal components of the mean magnetic field along the direction of the mean vorticity. We also perform direct numerical simulations of sheared turbulence in different ranges of hydrodynamic and magnetic Reynolds numbers and use a kinematic test-field method to determine the effective pumping velocity. The results of the numerical simulations are in agreement with the theoretical predictions.
The role of wall confinement on the decay rate of an initially isotropic turbulent field
NASA Astrophysics Data System (ADS)
Dowling, David R.; Movahed, Pooya; Johnsen, Eric
2014-11-01
The problem of freely decaying isotropic turbulence has been the subject of intensive research during the past few decades due to its importance for modeling purposes. While isotropy and periodic boundary conditions assumptions simplify the analysis, large-scale anisotropy (e.g., caused by rotation, shear, acceleration or walls) is in practice present in most turbulent flows and affects flow dynamics across different scales, as well as the kinetic energy decay. We investigate the role of wall confinement and viscous dissipation on the decay rate of an initially isotropic field for confining volumes of different aspect ratios. We first generate an isotropic velocity field in a cube with periodic boundary conditions. Next, using this field, we change the boundary conditions to no-slip walls on all sides. These walls restrict the initial field to a confined geometry and also provide an additional viscous dissipation mechanism. The problem is considered for confining volumes of different aspect ratios by adjusting the initial field. The change in confining volume introduces an additional length scale to the problem. Direct numerical simulation of the proposed set-up is used to verify the scaling arguments for the decay rate of kinetic energy. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant Number ACI-1053575.
Scale-by-scale energy fluxes in anisotropic non-homogeneous turbulence behind a square cylinder
NASA Astrophysics Data System (ADS)
Alves Portela, Felipe; Papadakis, George; Vassilicos, John Christos
2015-11-01
The turbulent wake behind a square section cylinder is studied by means of high resolution direct numerical simulations using an in-house finite volume code. The Reynolds number based on the cylinder side is 3900. Single- and two-point statistics are collected in the lee of the cylinder for over 30 shedding periods, allowing for an extensive description of the development of the turbulence. The power spectrum in the frequency domain of velocity fluctuations displays a near -5/3 power law in the near wake, where the turbulence is neither isotropic nor homogeneous. In the same region of the flow, two-point statistics reveal a direct cascade of fluctuating kinetic energy down the scales as a result of the combined effect of linear and non-linear interactions. For scales aligned with the mean flow the non-linear interactions dominate the cascade. Conversely, for scales normal to the mean flow the cascade is dominated by the linear interactions while the non-linear term is mostly responsible for redistributing energy to different orientations. The authors acknowledge support form the EU through the FP7 Marie Curie MULTISOLVE project (grant agreement No. 317269).
On Lagrangian and Eulerian Acceleration in Rotating and Sheared Homogeneous Turbulence
NASA Astrophysics Data System (ADS)
Jacobitz, Frank; Schneider, Kai; Bos, Wouter; Farge, Marie
2013-11-01
The Lagrangian and Eulerian acceleration properties of turbulence are of importance for problems ranging from fundamental theoretical considerations to modeling of dispersion processes. The acceleration statistics of rotating and sheared homogeneous turbulence are studied here using direct numerical simulations. The study focusses in particular on the influence of the Coriolis to shear rate ratio and also on the scale dependence of the statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian acceleration show a strong and similar influence on the rotation ratio. The flatness further quantifies this influence and yields values close to three for strong rotation. For moderate and vanishing rotation, the flatness of the Eulerian acceleration is larger than that of the Lagrangian acceleration, contrary to previous results for isotropic turbulence. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian acceleration increases as scale decreases. For strong rotation, the Eulerian acceleration is more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation.
Scaling laws for homogeneous turbulent shear flows in a rotating frame
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Mhuiris, Nessan Macgiolla
1988-01-01
The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri=-2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.
On the dynamics of small-scale vorticity in isotropic turbulence
NASA Technical Reports Server (NTRS)
Jimenez, Javier; Wray, A. A.
1994-01-01
It was previously shown that the strong vorticity in isotropic turbulence is organized into tubular vortices ('worms') whose properties were characterized through the use of full numerical simulations at several Reynolds numbers. At the time most of the observations were kinematic, and several scaling laws were discovered for which there was no theoretical explanation. In the meantime, further analysis of the same fields yielded new information on the generation of the vortices, and it was realized that even if they had to be formed by stretching, they were at any given moment actually compressed at many points of their axes. This apparent contradiction was partially explained by postulating axial inertial waves induced by the nonuniformity of the vortex cores, which helped to 'spread' the axial strain and allowed the vortices to remain compact even if not uniformly stretched. The existence of such solutions was recently proved numerically. The present report discusses a set of new numerical simulations of isotropic turbulence, and a reanalysis of the old ones, in an effort to prove or disprove the presence of these waves in actual turbulent flows and to understand the dynamics, as opposed to the kinematics, of the vortices.
The isotropic nature of the background turbulence spectra in the solar wind
NASA Astrophysics Data System (ADS)
Wang, X.; Tu, C. Y.; He, J.; Marsch, E.; Wang, L.
2014-12-01
At the high-frequency end of the inertial range, the solar wind turbulence power spectrum was recently found to be anisotropic with respect to the direction of local magnetic field, as an evidence for the presence of a "critical balance" style turbulence cascade. However, we find that the spectral anisotropy seems to result from intermittent structures. The following two independent studies corroborate this statement by showing that the power spectra of the background turbulence, in which there are no intermittent structures, have an isotropic nature. In Study 1, we remove the wavelet coefficients of the local intermittency with large partial variance increment (PVI), and find the spectral indices of the magnetic field are 1.63±0.02, independent of the angle θRB between the direction of the local background magnetic field and the radial direction. In Study 2, we make a statistical study on the magnetic field spectral indices obtained by using Fast Fourier Transform on 40 time series, in which no intermittent structures appear. We find that for the time series with 0o<θRB <6o, the probability distribution of the observed spectral indices peaks at -1.7, while the -2 index predicted by the "critical balance" theory rarely appears. For the time series with 84 o <θRB <90 o, the probability distribution of the indices peaks at -1.5. Considering the uncertainty of the statistics, these results show that the background-turbulence spectra are nearly isotropic with respect to θRB, which may be consistent with some explanations based on hydrodynamic turbulence theory.
Numerical simulations of non-homogeneous viscoelastic turbulent channel flow
NASA Astrophysics Data System (ADS)
Housiadas, Kostas; Beris, Antony
2004-11-01
The effect of the polymer mixing in turbulent channel flow is studied through numerical simulations, using a spectral technique. In particular, we simulate injection of polymeric material through a slit very close to the wall and parallel to it in pre-established Newtonian turbulent flow. The governing equations consist of the mass conservation, the modified Navier-Stokes equation (in order to take into account the polymer extra-stress), the evolution equation for the conformation tensor and an advection-diffusion equation for the polymer concentration. The injection process is simulated by dividing the computational domain in three different regions: (a) the entrance region where the polymer is introduced (b) the developing region where the polymer is allowed to convect freely interacting/modifying the turbulent flow and (c) the recovering region where we use a reacting sink to force the removal of the polymer from the solvent in order to re-establish the inlet conditions. A fully spectral method is used in order to solve the set of governing equations similar to that developed for homogenous viscoelastic turbulent DNS (Housiadas & Beris, Phys. Fluids, 15, (2003)). Although a significantly improved numerical algorithm has been successfully used before (Housiadas & Beris, to appear in J. Non-Newt. Fluid Mech. (2004)) a further improved version of that algorithm is presented in this work. The new algorithm has enabled us to extend the simulations for much wider range of viscoelasticity parameter values as well as for many viscoelastic models like the FENE-P, Giesekus, Oldroyd-B and the modified Giesekus/FENE-P model. Results for illustrative sets of parameter values are going to be presented.
Fang, L; Zhang, Y J; Fang, J; Zhu, Y
2016-08-01
We show by direct numerical simulations (DNSs) that in different types of isotropic turbulence, the fourth-order statistical invariants have approximately a linear relation, which can be represented by a straight line in the phase plane, passing two extreme states: the Gaussian state and the restricted Euler state. Also, each DNS case corresponds to an equilibrium region that is roughly Reynolds-dependent. In addition, both the time reversal and the compressibility effect lead to nonequilibrium transition processes in this phase plane. This observation adds a new restriction on the mean-field theory. PMID:27627399
NASA Astrophysics Data System (ADS)
Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil
2012-10-01
We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.
NASA Astrophysics Data System (ADS)
Asinari, Pietro
2010-10-01
The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains extremely challenging from the computational point of view, in particular by deterministic methods (free of stochastic noise). This work aims to improve a deterministic direct method recently proposed [V.V. Aristov, Kluwer Academic Publishers, 2001] for solving the HIBE with a generic collisional kernel and, in particular, for taking care of the late dynamics of the relaxation towards the equilibrium. Essentially (a) the original problem is reformulated in terms of particle kinetic energy (exact particle number and energy conservation during microscopic collisions) and (b) the computation of the relaxation rates is improved by the DVM-like correction, where DVM stands for Discrete Velocity Model (ensuring that the macroscopic conservation laws are exactly satisfied). Both these corrections make possible to derive very accurate reference solutions for this test case. Moreover this work aims to distribute an open-source program (called HOMISBOLTZ), which can be redistributed and/or modified for dealing with different applications, under the terms of the GNU General Public License. The program has been purposely designed in order to be minimal, not only with regards to the reduced number of lines (less than 1000), but also with regards to the coding style (as simple as possible). Program summaryProgram title: HOMISBOLTZ Catalogue identifier: AEGN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 23 340 No. of bytes in distributed program, including test data, etc.: 7 635 236 Distribution format: tar
NASA Technical Reports Server (NTRS)
Bardino, J.; Ferziger, J. H.; Reynolds, W. C.
1983-01-01
The physical bases of large eddy simulation and subgrid modeling are studied. A subgrid scale similarity model is developed that can account for system rotation. Large eddy simulations of homogeneous shear flows with system rotation were carried out. Apparently contradictory experimental results were explained. The main effect of rotation is to increase the transverse length scales in the rotation direction, and thereby decrease the rates of dissipation. Experimental results are shown to be affected by conditions at the turbulence producing grid, which make the initial states a function of the rotation rate. A two equation model is proposed that accounts for effects of rotation and shows good agreement with experimental results. In addition, a Reynolds stress model is developed that represents the turbulence structure of homogeneous shear flows very well and can account also for the effects of system rotation.
The upper atmosphere of Uranus - A critical test of isotropic turbulence models
NASA Technical Reports Server (NTRS)
French, R. G.; Elliot, J. L.; Sicardy, B.; Nicholson, P.; Matthews, K.
1982-01-01
Observations of the August 15, 1980, Uranus occultation of KM 12, obtained from Cerro Tololo InterAmerican Observatory, European Southern Observatory, and Cerro Las Campanas Observatory, are used to compare the atmospheric structure at points separated by approximately 140 km along the planetary limb. The results reveal striking, but by no means perfect correlation of the light curves, ruling out isotropic turbulence as the cause of the light curve spikes. The atmosphere is strongly layered, and any acceptable turbulence model must accommodate the axial ratios of greater than about 60 which are observed. The mean temperature of the atmosphere is 150 plus or minus 15 K for the region near number density 10 to the 14th per cu cm. Derived temperature variations of vertical scale approximately 130 km and amplitude plus or minus 5 K are in agreement for all stations, and correlated spikes correspond to low-amplitude temperature variations with a vertical scale of several kilometers.
Thermoelectric effects in decaying homogeneous magneto-gas turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1991-01-01
In the formulation of compressible MHD (i.e., magneto-gas dynamics), a 'generalized Ohm's law is required. In particular, an electron pressure term and a 'Hall effect' term may appear as non-negligible additions to the Ohm's law that is conventionally used for incompressible MHD. In 'high-beta' (i.e., relatively low magnetic energy) situations, the Hall term may be neglected (at least initially) but, as it turns out, the electron pressure term cannot be neglected. Here, three-dimensional, high-beta, homogeneous, decaying, magneto-gas turbulence is examined with regard to this additional term. Through numerical simulation, it is found that 'thermoelectric effects' are produced that significantly alter the evolution of the magnetic field and electric current strengths.
Numerical simulation of a compressible homogeneous, turbulent shear flow
NASA Astrophysics Data System (ADS)
Feiereisen, W. J.; Reynolds, W. C.; Ferziger, J. H.
1981-03-01
A direct, low Reynolds number, numerical simulation was performed on a homogeneous turbulent shear flow. The full compressible Navier-Stokes equations were used in a simulation on the ILLIAC IV computer with a 64,000 mesh. The flow fields generated by the code are used as an experimental data base, to examine the behavior of the Reynols stresses in this simple, compressible flow. The variation of the structure of the stresses and their dynamic equations as the character of the flow changed is emphasized. The structure of the tress tensor is more heavily dependent on the shear number and less on the fluctuating Mach number. The pressure-strain correlation tensor in the dynamic uations is directly calculated in this simulation. These correlations are decomposed into several parts, as contrasted with the traditional incompressible decomposition into two parts. The performance of existing models for the conventional terms is examined, and a model is proposed for the 'mean fluctuating' part.
Modulation of isotropic turbulence by deformable droplets of Taylor lengthscale size
NASA Astrophysics Data System (ADS)
Dodd, Michael; Ferrante, Antonino
2014-11-01
We investigate the effects of finite-size deformable droplets on decaying isotropic turbulence via direct numerical simulation (DNS). DNS is performed using the two-fluid pressure-correction method by Dodd and Ferrante [J. Comput. Phys. 273, 416 (2014)] coupled with the volume of fluid method by Baraldi et al. [Comput. & Fluids 96, 322 (2014)]. We fully-resolve the flow around and inside 3130 droplets of Taylor lengthscale size, resulting in a droplet volume fraction of 0.05. The initial Taylor lengthscale Reynolds number is Reλ0 = 75 , and the computational mesh has 10243 grid points. We analyze the effects on turbulence modulation of varying the droplet- to carrier-fluid viscosity ratio (1 <=μd /μc <= 100) and the droplet Weber number based on the r.m.s velocity of turbulence (0 . 1 <=Werms <= 5). We discuss how varying these parameters affects the turbulence kinetic energy budget, and explain the physical mechanisms for such modulation. This work was supported by the National Science Foundation CAREER Award, Grant Number OCI-1054591.
Zonal Flows from Spontaneous Symmetry Breaking of Homogeneous Turbulence
NASA Astrophysics Data System (ADS)
Parker, Jeffrey; Krommes, John
2013-10-01
To study how zonal flows (ZF) arise, we examine one of the simplest possible models, the stochastically forced Hasegawa-Mima equation, which displays the bifurcation of steady ZFs from a state of homogeneous turbulence; thus a statistical treatment is required. Here an approach is adopted in which the ZFs are treated as mean fields that spontaneously break the background symmetry. The resulting inhomogeneous ensemble is treated self-consistently without assuming weak inhomogeneity. Closed statistical equations are obtained by ignoring the drift-wave self-interactions while fully retaining the drift-wave-ZF nonlinearities. We show that from the statistical point of view ZF generation can be understood as pattern formation. This leads to the surprising result that in a saturated turbulent state the ZF wavelength is not unique; a continuous band of ZF scales is allowed. Only those within a smaller sub-band are linearly stable. That stability is analyzed and the stability diagram in parameter space is calculated and successfully compared with simulations. The stability concept provides a way of interpreting the merging of zonal jets, a phenomenon commonly observed in observations and numerical studies. Work supported by U.S DOE Contract No DE-AC02-09CH11466 and by an NSF Graduate Research Fellowship.
On the asymptotic similarity of rotating homogeneous turbulence
NASA Technical Reports Server (NTRS)
Squires, K. D.; Chasnov, J. R.; Mansour, N. N.
1994-01-01
Asymptotic similarity states at large Reynolds numbers and small Rossby numbers in rotating homogeneous turbulence are investigated using the database obtained from large-eddy simulations of the incompressible Navier-Stokes equations. Previous work has shown that the turbulence kinetic energy and integral length scales are accurately described by simple scaling laws based on the low wavenumbers part of the three-dimensional energy spectrum. The primary interest of the present study is to search for spectrum similarity in the asymptotic state. Four independent energy spectra are defined. It is shown that rescaling of these energy spectra in the asymptotic regime will collapse three out of the four spectra. The spectrum which does not collapse is a function only of the vertical wavenumber and corresponds to two-component motions in the plane normal to the rotation axis. Detailed investigation of the cause of this anomalous behavior reveals the existence of a strong reverse cascade of energy from small-to-large scales of the two-dimensional, two-component motions. This feature of the rotating flow is presumably linked to the lack of a complete similarity state, though further study of this issue is required.
Anisotropic Structure of Rotating Homogeneous Turbulence at High Reynolds Numbers
NASA Technical Reports Server (NTRS)
Cambon, Claude; Mansour, Nagi N.; Squires, Kyle D.; Rai, Man Mohan (Technical Monitor)
1995-01-01
Large eddy simulation is used to investigate the development of anisotropies and the evolution towards a quasi two-dimensional state in rotating homogeneous turbulence at high Reynolds number. The present study demonstrates the existence of two transitions in the development of anisotropy. The first transition marks the onset of anisotropy and occurs when a macro-Rossby number (based on a longitudinal integral lengthscale) has decreased to near unity while the second transition occurs when a micro-Rossby number (defined in this work as the ratio of the rms fluctuating vorticity to background vorticity) has decreased to unity. The anisotropy marked by the first transition corresponds to a reduction in dimensionality while the second transition corresponds to a polarization of the flow, i.e., relative dominance of the velocity components in the plane normal to the rotation axis. Polarization is reflected by emergence of anisotropy measures based on the two-dimensional component of the turbulence. Investigation of the vorticity structure shows that the second transition is also characterized by an increasing tendency for alignment between the fluctuating vorticity vector and the background angular velocity vector with a preference for corrotative vorticity.
Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field
NASA Astrophysics Data System (ADS)
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.; Rowlands, G.; Vyas, S.
2016-08-01
In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R=(b/{B}0)({{\\ell }}\\parallel /{{\\ell }}\\perp ) for rms magnetic fluctuation b, large-scale mean field {{\\boldsymbol{B}}}0, and coherence scales parallel ({{\\ell }}\\parallel ) and perpendicular ({{\\ell }}\\perp ) to {{\\boldsymbol{B}}}0. Here we use a nonperturbative analytic framework based on Corrsin’s hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B 0 with finite b and isotropic fluctuations with {{\\ell }}\\parallel /{{\\ell }}\\perp =1, instead of the well-studied route of varying {{\\ell }}\\parallel /{{\\ell }}\\perp for b \\ll {B}0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with b z = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B 0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with b z = 0, when different routes to R\\to ∞ are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.
Effect of freestream isotropic turbulence on heat transfer from a sphere
NASA Astrophysics Data System (ADS)
Bagchi, Prosenjit; Kottam, Kirit
2008-07-01
We consider direct numerical simulation (DNS) based on pseudospectral methods to study the heat transfer around a stationary sphere held at a constant temperature and subject to an ambient turbulent velocity and temperature condition. The sphere Reynolds number is in the range of 63-400, and the sphere diameter (d) varies from one to eight times the Kolmogorov scale (η). The ambient turbulent field is isotropic, and the Taylor microscale Reynolds number Rλ varies from 38 to 240. Results from two sets of DNS are presented. In the first set, the ambient velocity field is turbulent, but the ambient temperature is held constant. In the second set of simulations, both the ambient velocity and the temperature fields are turbulent. These two sets of simulations allow us to isolate the role of freestream velocity fluctuations and temperature fluctuations in modifying the mean and time-dependent heat transfer from the sphere. The mean Nusselt number is observed to be independent of Rλ. It is shown that the freestream turbulence does not have any significant effect on the mean Nusselt number, and the available correlations for a steady and uniform ambient can predict the mean Nusselt number under the turbulent ambient condition. The instantaneous Nusselt number, however, can differ significantly from the mean, and can be negative in case of large temperature fluctuation in the far field. The instantaneous Nusselt number obtained from the DNS is analyzed and compared with the analytical expression for the unsteady thermal response of a sphere. It is shown that the thermal added-mass effect is small for d /η≈1 but introduces spurious oscillation at higher d. The thermal history effect is shown to be insignificant for all d /η. Properties of the thermal wake in the presence of the turbulent velocity and temperature fields are studied. The mean thermal wake is observed to be shorter in streamwise direction and wider in crossflow direction in a turbulent ambient than that
NASA Astrophysics Data System (ADS)
Chiadini, Francesco; Fiumara, Vincenzo; Scaglione, Antonio; Lakhtakia, Akhlesh
2015-01-01
Multiple p- and s-polarized compound surface-plasmon-polariton (SPP) waves at a fixed frequency can be guided by a structure consisting of a metal layer sandwiched between a homogeneous isotropic dielectric (HID) material and a periodic multilayered isotropic dielectric (PMLID) material. For any thickness of the metal layer, at least one compound SPP wave must exist. It possesses the p-polarization state, and is strongly bound to the metal/HID interface when the metal thickness is large but to both metal/dielectric interfaces when the metal thickness is small. When the metal layer vanishes, this compound SPP wave transmutes into a Tamm wave. Additional compound SPP waves exist, depending on the thickness of the metal layer, the relative permittivity of the HID material, and the period and composition of the PMLID material. Some of these are p-polarized, the others are s-polarized. All of them differ in phase speed, attenuation rate, and field profile, even though all are excitable at the same frequency. The multiplicity and dependence of the number of compound SPP waves on the relative permittivity of the HID material when the metal layer is thin could be useful for optical sensing applications and intrachip plasmonic optical communication.
Particle dispersion in homogeneous turbulence using the one-dimensional turbulence model
Sun, Guangyuan; Lignell, David O.; Hewson, John C.; Gin, Craig R.
2014-10-09
Lagrangian particle dispersion is studied using the one-dimensional turbulence (ODT) model in homogeneous decaying turbulence configurations. The ODT model has been widely and successfully applied to a number of reacting and nonreacting flow configurations, but only limited application has been made to multiphase flows. We present a version of the particle implementation and interaction with the stochastic and instantaneous ODT eddy events. The model is characterized by comparison to experimental data of particle dispersion for a range of intrinsic particle time scales and body forces. Particle dispersion, velocity, and integral time scale results are presented. Moreover, the particle implementation introduces a single model parameter β p , and sensitivity to this parameter and behavior of the model are discussed. Good agreement is found with experimental data and the ODT model is able to capture the particle inertial and trajectory crossing effects. Our results serve as a validation case of the multiphase implementations of ODT for extensions to other flow configurations.
Particle dispersion in homogeneous turbulence using the one-dimensional turbulence model
Sun, Guangyuan Lignell, David O.; Hewson, John C.; Gin, Craig R.
2014-10-15
Lagrangian particle dispersion is studied using the one-dimensional turbulence (ODT) model in homogeneous decaying turbulence configurations. The ODT model has been widely and successfully applied to a number of reacting and nonreacting flow configurations, but only limited application has been made to multiphase flows. Here, we present a version of the particle implementation and interaction with the stochastic and instantaneous ODT eddy events. The model is characterized by comparison to experimental data of particle dispersion for a range of intrinsic particle time scales and body forces. Particle dispersion, velocity, and integral time scale results are presented. The particle implementation introduces a single model parameter β{sub p}, and sensitivity to this parameter and behavior of the model are discussed. Good agreement is found with experimental data and the ODT model is able to capture the particle inertial and trajectory crossing effects. These results serve as a validation case of the multiphase implementations of ODT for extensions to other flow configurations.
NASA Astrophysics Data System (ADS)
Borgas, Michael S.; Yeung, P. K.
2004-03-01
A new model for Lagrangian particle-pair separation in turbulent flows is developed and compared with data from direct numerical simulations (DNS) of isotropic turbulence. The model formulation emphasizes (i) non-Gaussian behaviour in Eulerian and Lagrangian statistics, (ii) the occurrence of large separation velocities, (iii) the role of straining and streaming flow structure as recognized in kinematic simulations of turbulence, and (iv) the role of conditionally averaged accelerations in stochastic modelling of turbulent relative dispersion. Previous stochastic models of relative dispersion have produced unrealistic behaviour, particularly in the dissipation subrange where viscous effects are important, which have led to questions on the adequacy of stochastic modelling. However, this failure can now be recognized as inadequate detail in formulation, which is explained and rectified in this paper. The model is quasi-one-dimensional in nature, and is focused on the statistics of particle-pair separation distance and its rate of change, referred to as the separation speed. Detailed comparisons are presented at several Reynolds numbers using the DNS database reported in a companion paper (Part 1). Up to fourth-order moments for these quantities are examined, as well as the separation-distance probability density function, which is discussed in the context of recent claims of Richardson scaling in the literature. The model is able to account for the spatial representation of straining regions as well as incompressibility of the flow, and is shown to reproduce strong non-Gaussianity and intermittency in the Lagrangian separation statistics observed in DNS. Comparisons with recent physical experiments are also remarkably consistent. This work demonstrates that stochastic models when properly formulated are effective and efficient representations of the dispersion process and this general class of models therefore possess great utility for calculations of both one
Pressure-strain-rate events in homogeneous turbulent shear flow
NASA Technical Reports Server (NTRS)
Brasseur, James G.; Lee, Moon J.
1988-01-01
A detailed study of the intercomponent energy transfer processes by the pressure-strain-rate in homogeneous turbulent shear flow is presented. Probability density functions (pdf's) and contour plots of the rapid and slow pressure-strain-rate show that the energy transfer processes are extremely peaky, with high-magnitude events dominating low-magnitude fluctuations, as reflected by very high flatness factors of the pressure-strain-rate. A concept of the energy transfer class was applied to investigate details of the direction as well as magnitude of the energy transfer processes. In incompressible flow, six disjoint energy transfer classes exist. Examination of contours in instantaneous fields, pdf's and weighted pdf's of the pressure-strain-rate indicates that in the low magnitude regions all six classes play an important role, but in the high magnitude regions four classes of transfer processes, dominate. The contribution to the average slow pressure-strain-rate from the high magnitude fluctuations is only 50 percent or less. The relative significance of high and low magnitude transfer events is discussed.
Forward and backward in time dispersion of fluid and inertial particles in isotropic turbulence
NASA Astrophysics Data System (ADS)
Bragg, Andrew D.; Ireland, Peter J.; Collins, Lance R.
2016-01-01
In this paper, we investigate both theoretically and numerically the Forward-In-Time (FIT) and Backward-In-Time (BIT) dispersion of fluid and inertial particle-pairs in isotropic turbulence. Fluid particles are known to separate faster BIT than FIT in three-dimensional turbulence, and we find that inertial particles do the same. However, we find that the irreversibility in the inertial particle dispersion is in general much stronger than that for fluid particles. For example, the ratio of the BIT to FIT mean-square separation can be up to an order of magnitude larger for the inertial particles than for the fluid particles. We also find that for both the inertial and fluid particles, the irreversibility becomes stronger as the scale of their separation decreases. Regarding the physical mechanism for the irreversibility, we argue that whereas the irreversibility of fluid particle-pair dispersion can be understood in terms of a directional bias arising from the energy transfer process in turbulence, inertial particles experience an additional source of irreversibility arising from the non-local contribution to their velocity dynamics, a contribution that vanishes in the limit St → 0, where St is the particle Stokes number. For each given initial (final, in the BIT case) separation, r0, there is an optimum value of St for which the dispersion irreversibility is strongest, as such particles are optimally affected by both sources of irreversibility. We derive analytical expressions for the BIT, mean-square separation of inertial particles and compare the predictions with numerical data obtained from a Reλ ≈ 582 (where Reλ is the Taylor Reynolds number) Direct Numerical Simulation (DNS) of particle-laden isotropic turbulent flow. The small-time theory, which in the dissipation range is valid for times ≤max[Stτη, τη] (where τη is the Kolmogorov time scale), is in excellent agreement with the DNS. The theory for long-times is in good agreement with the DNS
He, G.; Doolen, G.D.; Chen, S.
1999-12-01
The longitudinal structure function (LSF) and the transverse structure function (TSF) in isotropic turbulence are calculated using a vortex model. The vortex model is composed of the Rankine and Burgers vortices which have the exponential distributions in the vortex Reynolds number and vortex radii. This model exhibits a power law in the inertial range and satisfies the minimal condition of isotropy that the second-order exponent of the LSF in the inertial range is equal to that of the TSF. Also observed are differences between longitudinal and transverse structure functions caused by intermittency. These differences are related to their scaling differences which have been previously observed in experiments and numerical simulations. {copyright} {ital 1999 American Institute of Physics.}
Isotropic boundary adapted wavelets for coherent vorticity extraction in turbulent channel flows
NASA Astrophysics Data System (ADS)
Farge, Marie; Sakurai, Teluo; Yoshimatsu, Katsunori; Schneider, Kai; Morishita, Koji; Ishihara, Takashi
2015-11-01
We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze DNS data of turbulent channel flow computed at a friction-velocity based Reynolds number of 395 and investigate the role of coherent vorticity. Thresholding of the wavelet coefficients allows to split the flow into two parts, coherent and incoherent vorticity. The statistics of the former, i.e., energy and enstrophy spectra, are close to the ones of the total flow, and moreover the nonlinear energy budgets are well preserved. The remaining incoherent part, represented by the large majority of the weak wavelet coefficients, corresponds to a structureless, i.e., noise-like, background flow and exhibits an almost equi-distribution of energy.
NASA Astrophysics Data System (ADS)
Goto, Susumu; Kida, Shigeo
1999-07-01
The Lagrangian direct-interaction approximation developed previously by the present authors [S. Kida and S. Goto, J. Fluid Mech. 345, 307 (1997)] is applied to a passive scalar field in isotropic turbulence. We examine the behavior of solutions to the resultant closure equations for the correlation function of the scalar field for arbitrary values of the Schmidt number, and show systematically that the solutions are completely consistent with the phenomenological theories on the scalar spectral function by Obukhov (1949), Corrsin (1951), Batchelor et al. (1959), and Batchelor (1959). The universal forms of the function in the statistically stationary state are obtained by solving the closure equations numerically in the whole wave number range for each case of moderate, extremely large, and small values of the Schmidt number.
NASA Astrophysics Data System (ADS)
Gotoh, Toshiyuki
2012-11-01
Spectrum of passive scalar variance at very high Schmidt number up to 1000 in isotropic steady turbulence has been studied by using very high resolution DNS. Gaussian random force and scalar source which are isotropic and white in time are applied at low wavenumber band. Since the Schmidt number is very large, the system was integrated for 72 large eddy turn over time for the system to forgot the initial state. It is found that the scalar spectrum attains the asymptotic k-1 spectrum in the viscous-convective range and the constant CB is found to be 5.7 which is larger than 4.9 obtained by DNS under the uniform mean scalar gradient. Reasons for the difference are inferred as the Reynolds number effect, anisotropy, difference in the scalar injection, duration of time average, and the universality of the constant is discussed. The constant CB is also compared with the prediction by the Lagrangian statistical theory for the passive scalar. The scalar spectrum in the far diffusive range is found to be exponential, which is consistent with the Kraichnan's spectrum. However, the Kraichnan spectrum was derived under the assumption that the velocity field is white in time, therefore theoretical explanation of the agreement needs to be explored. Grant-in-Aid for Scientific Research No. 21360082, Ministry of Education, Culture, Sports, Science and Technology of Japan.
Large fluctuations of the nonlinearities in isotropic turbulence. Anisotropic filtering analysis
NASA Astrophysics Data System (ADS)
Tordella, D.; Di Savino, S.; Sitzia, L.
2014-09-01
Using a Navier-Stokes isotropic turbulent field numerically simulated in a box with a discretization of 10243 (Biferale et al., 2005), we show that the probability of having a stretching-tilting larger than a few times the local enstrophy is low. By using an anisotropic kind of filter in the Fourier space, where wavenumbers that have at least one component below a threshold or inside a range are removed, we analyze these survival statistics when the large, the small inertial or the small inertial and dissipation scales are filtered out. By considering a flow obtained by randomizing the phases of the Fourier modes, and applying our filtering techniques, we identified clearly the properties attributable to turbulence. It can be observed that, in the unfiltered isotropic Navier-Stokes field, the probability of the ratio (|ωṡ∇U|/|) being higher than a given threshold is higher than in the fields where the large scales were filtered out. At the same time, it is lower than in the fields where the small inertial and dissipation range of scales is filtered out. This is basically due to the suppression of compact structures in the ranges that have been filtered in different ways. The partial removal of the background of filaments and sheets does not have a first order effect on these statistics. These results are discussed in the light of a hypothesized relation between vortical filaments, sheets and blobs in physical space and in Fourier space. The study in fact can be viewed as a kind of test for this idea and tries to highlight its limits. We conclude that a qualitative relation in physical space and in Fourier space can be supposed to exist for blobs only. That is for the near isotropic structures which are sufficiently described by a single spatial scale and do not suffer from the disambiguation problem as filaments and sheets do. Information is also given on the filtering effect on statistics concerning the inclination of the strain rate tensor eigenvectors with
NASA Astrophysics Data System (ADS)
Suriyawichitseranee, A.; Grigoriev, Yu. N.; Meleshko, S. V.
2015-03-01
The paper is devoted to group analysis of the spatially homogeneous and isotropic Boltzmann equation with a source term. In fact, the Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. Using a particular class of solutions, the determining equation for the admitted Lie group is reduced to a partial differential equation for the source function. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation is given. All invariant solutions of this equation are also presented in the paper.
NASA Astrophysics Data System (ADS)
Xu, Tao; Zhu, Xue-Feng; Liang, Bin; Li, Yong; Zou, Xin-Ye; Cheng, Jian-Chun
2012-07-01
We have designed a cylindrical multilayered structure to reduce scattering for an acoustic sensor while allowing it to receive external information. The proposed structure consists of two alternately arranged complementary media with homogeneous isotropic single-negative parameters. Numerical results show that the acoustic scattering from the sensor is suppressed considerably when the number of bilayers is large enough and the thickness of each bilayer is much smaller than the incident wavelength. This may be particularly significant for practical applications where acoustic measurements would otherwise be disturbed by the insertion of sensors.
NASA Astrophysics Data System (ADS)
Collins, Lance; Bragg, Andrew; Ireland, Peter
2014-11-01
In this talk, we consider the physical mechanism for the clustering of inertial particles in the inertial range of turbulence. By comparisons with DNS data we demonstrate that the mechanism in the theory of Zaichik et al. (Phys. Fluids 19, 113308, 2007) quantitatively describes the clustering of particles in the inertial range. We then analyze the theory for isotropic turbulence in the limit Reλ --> ∞ . For arbitrary St (Stokes number), there exists a separation in the inertial range beyond which Str << 1 , where Str is the Stokes number based on the eddy turnover timescale at separation r. The inertial-range clustering in this limit can be understood to be due to the preferential sampling of the coarse-grained velocity gradient tensor at that scale. At smaller separations, there may be transitions to Str ~ 1 , where a path history symmetry breaking effect dominates the clustering mechanism, and in some cases Str >> 1 , which implies ballistic behavior and a flat RDF. The scaling for each of these regimes is derived and compared to DNS, where applicable. Finally, we compare the results with the ``sweep-stick'' mechanism by Coleman and Vassilicos (Phys. Fluids 21, 113301, 2009) and discuss the similarities and differences between the two theories.
Long-time behavior of material-surface curvature in isotropic turbulence
NASA Technical Reports Server (NTRS)
Girimaji, S. S.
1992-01-01
The behavior at large times of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. The main objectives are: to study the asymptotic behavior of the pdf curvature as a function of initial curvature and shape; and to establish whether the curvature of an initially plane material element goes to a stationary probability distribution. The evidence available in the literature about the asymptotic curvature-pdf of initially flat surfaces is ambiguous, and the conjecture is that it is quasi-stationary. In this work several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times the moments of the logarithm of curvature are independent of the initial pdf of curvature. This, it is argued, supports the view that the curvature attains a stationary distribution at long times. It is also shown that, irrespective of initial shape or curvature, the shape of any material element at long times is cylindrical with a high probability.
Dynamic and Thermal Turbulent Time Scale Modelling for Homogeneous Shear Flows
NASA Technical Reports Server (NTRS)
Schwab, John R.; Lakshminarayana, Budugur
1994-01-01
A new turbulence model, based upon dynamic and thermal turbulent time scale transport equations, is developed and applied to homogeneous shear flows with constant velocity and temperature gradients. The new model comprises transport equations for k, the turbulent kinetic energy; tau, the dynamic time scale; k(sub theta), the fluctuating temperature variance; and tau(sub theta), the thermal time scale. It offers conceptually parallel modeling of the dynamic and thermal turbulence at the two equation level, and eliminates the customary prescription of an empirical turbulent Prandtl number, Pr(sub t), thus permitting a more generalized prediction capability for turbulent heat transfer in complex flows and geometries. The new model also incorporates constitutive relations, based upon invariant theory, that allow the effects of nonequilibrium to modify the primary coefficients for the turbulent shear stress and heat flux. Predictions of the new model, along with those from two other similar models, are compared with experimental data for decaying homogeneous dynamic and thermal turbulence, homogeneous turbulence with constant temperature gradient, and homogeneous turbulence with constant temperature gradient and constant velocity gradient. The new model offers improvement in agreement with the data for most cases considered in this work, although it was no better than the other models for several cases where all the models performed poorly.
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
NASA Astrophysics Data System (ADS)
Johnson, Perry L.; Meneveau, Charles
2015-08-01
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ1 : λ2 : λ3 is shown to be about 4:1:-5, compared to about 8:3:-11 when using only the strain-rate tensor for calculating fluid volume deformations. The results
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
Johnson, Perry L. Meneveau, Charles
2015-08-15
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume
Pawar, Shashikant S; Arakeri, Jaywant H
2016-08-01
Frequency spectra obtained from the measurements of light intensity and angle of arrival (AOA) of parallel laser light propagating through the axially homogeneous, axisymmetric buoyancy-driven turbulent flow at high Rayleigh numbers in a long (length-to-diameter ratio of about 10) vertical tube are reported. The flow is driven by an unstable density difference created across the tube ends using brine and fresh water. The highest Rayleigh number is about 8×10^{9}. The aim of the present work is to find whether the conventional Obukhov-Corrsin scaling or Bolgiano-Obukhov (BO) scaling is obtained for the intensity and AOA spectra in the case of light propagation in a buoyancy-driven turbulent medium. Theoretical relations for the frequency spectra of log amplitude and AOA fluctuations developed for homogeneous isotropic turbulent media are modified for the buoyancy-driven flow in the present case to obtain the asymptotic scalings for the high and low frequency ranges. For low frequencies, the spectra of intensity and vertical AOA fluctuations obtained from measurements follow BO scaling, while scaling for the spectra of horizontal AOA fluctuations shows a small departure from BO scaling. PMID:27505375
NASA Astrophysics Data System (ADS)
Roussel, O.; Schneider, K.; Farge, M.
A comparison between two different ways of extracting coherent vortices in three-dimensional (3D) homogeneous isotropic turbulence is performed, using either orthogonal or biorthogonal wavelets. The method is based on a wavelet decomposition of the vorticity field and a subsequent thresholding of the wavelet coefficients. The coherent vorticity is reconstructed from a few strong wavelet coefficients, while the incoherent vorticity is reconstructed from the remaining weak coefficients. The choice of the threshold, which has no adjustable parameters, is motivated for the orthogonal case from the denoising theory. Using only 3 % of the coefficients we show that both decompositions, that is orthogonal and biorthogonal, extract the coherent vortices. They contain most of the energy (around 99 % in both cases) and retain 74 % and 68 % of the enstrophy in the orthogonal and biorthogonal cases, respectively. The incoherent background flow for the orthogonal decomposition, which corresponds to 97 % of the wavelet coefficients, is structureless, decorrelated, and has a Gaussian velocity probability distribution function (PDF). In contrast, for the biorthogonal decomposition, the background flow exhibits quasi-two-dimensional (2D) structures and yields an exponential velocity PDF. Moreover, the biorthogonal decomposition loses 3.7% of both enstrophy and helicity, while they are conserved by the orthogonal decomposition.
Bounded energy states in homogeneous turbulent shear flow - An alternative view
NASA Technical Reports Server (NTRS)
Bernard, P. S.; Speziale, C. G.
1992-01-01
The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if a residual vortex stretching term is maintained in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are presented for a k-epsilon model modified to account for net vortex stretching.
Particle dispersion in homogeneous turbulence using the one-dimensional turbulence model
Sun, Guangyuan; Lignell, David O.; Hewson, John C.; Gin, Craig R.
2014-10-09
Lagrangian particle dispersion is studied using the one-dimensional turbulence (ODT) model in homogeneous decaying turbulence configurations. The ODT model has been widely and successfully applied to a number of reacting and nonreacting flow configurations, but only limited application has been made to multiphase flows. We present a version of the particle implementation and interaction with the stochastic and instantaneous ODT eddy events. The model is characterized by comparison to experimental data of particle dispersion for a range of intrinsic particle time scales and body forces. Particle dispersion, velocity, and integral time scale results are presented. Moreover, the particle implementation introducesmore » a single model parameter β p , and sensitivity to this parameter and behavior of the model are discussed. Good agreement is found with experimental data and the ODT model is able to capture the particle inertial and trajectory crossing effects. Our results serve as a validation case of the multiphase implementations of ODT for extensions to other flow configurations.« less
MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD
Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P.; Subedi, P.; Matthaeus, W. H.; Chuychai, P. E-mail: david.ruf@mahidol.ac.th E-mail: pat.wongpan@postgrad.otago.ac.nz E-mail: prasub@udel.edu
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
Magnetic Field Line Random Walk in Isotropic Turbulence with Zero Mean Field
NASA Astrophysics Data System (ADS)
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B 0)(l∥/l) for rms magnetic fluctuation b, large-scale mean field B 0, and parallel and perpendicular coherence scales l∥ and l, respectively. Here we examine the FLRW when R → ∞ by taking B 0 → 0 for finite bz (fluctuation component along B 0), which differs from the well-studied route with bz = 0 or bz Lt B 0 as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B 0 = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k -1 or k -2 moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B 0 → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
Power and Nonpower Laws of Passive Scalar Moments Convected by Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Gotoh, Toshiyuki; Watanabe, Takeshi
2015-09-01
The scaling behavior of the moments of two passive scalars that are excited by two different methods and simultaneously convected by the same isotropic steady turbulence at Rλ=805 and Sc=0.72 is studied by using direct numerical simulation with N =40963 grid points. The passive scalar θ is excited by a random source that is Gaussian and white in time, and the passive scalar q is excited by the mean uniform scalar gradient. In the inertial convective range, the n th-order moments of the scalar increment δ θ (r ) do not obey a simple power law, but have the local scaling exponents ξnθ+βnlog (r /r*) with βn>0 . In contrast, the local scaling exponents of q have well-developed plateaus and saturate with increasing order. The power law of passive scalar moments is not trivial. The universality of passive scalars is found not in the moments, but in the normalized moments.
Power and nonpower laws of passive scalar moments convected by isotropic turbulence.
Gotoh, Toshiyuki; Watanabe, Takeshi
2015-09-11
The scaling behavior of the moments of two passive scalars that are excited by two different methods and simultaneously convected by the same isotropic steady turbulence at R_{λ}=805 and Sc=0.72 is studied by using direct numerical simulation with N=4096^{3} grid points. The passive scalar θ is excited by a random source that is Gaussian and white in time, and the passive scalar q is excited by the mean uniform scalar gradient. In the inertial convective range, the nth-order moments of the scalar increment δθ(r) do not obey a simple power law, but have the local scaling exponents ξ_{n}^{θ}+β_{n}log(r/r_{*}) with β_{n}>0. In contrast, the local scaling exponents of q have well-developed plateaus and saturate with increasing order. The power law of passive scalar moments is not trivial. The universality of passive scalars is found not in the moments, but in the normalized moments. PMID:26406833
A Stochastic Model for the Relative Motion of High Stokes Number Particles in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Dhariwal, Rohit; Rani, Sarma; Koch, Donald
2014-11-01
In the current study, a novel analytical closure for the diffusion current in the PDF equation is presented that is applicable to high-inertia particle pairs with Stokes numbers Str >> 1 . Here Str is a Stokes number based on the time-scale τr of eddies whose size scales with pair separation r. Using this closure, Langevin equations were solved to evolve particle-pair relative velocities and separations in stationary isotropic turbulence. The Langevin equation approach enables the simulation of the full PDF of pair relative motion, instead of only the first few moments of the PDF as is the case in a moments-based approach. Accordingly, PDFs Ω (U | r) and Ω (Ur | r) are computed for various separations r, where the former is the PDF of relative velocity U and the latter is the PDF of the radial component of relative velocity Ur, both conditioned upon the separation r. Consistent with the DNS study of Sundaram & Collins, the Langevin simulations capture the transition of Ω (U | r) from being Gaussian at integral-scale separations to an exponential PDF at Kolmogorov-scale separations. The radial distribution functions (RDFs) computed from these simulations also show reasonable quantitative agreement with those from the DNS of Fevrier et al.
NASA Astrophysics Data System (ADS)
Meneveau, Charles; Yang, Yunke; Perlman, Eric; Wan, Minpin; Burns, Randal; Szalay, Alex; Chen, Shiyi; Eyink, Gregory
2008-11-01
A public database system archiving a direct numerical simulation (DNS) data set of isotropic, forced turbulence is used for studying basic turbulence dynamics. The data set consists of the DNS output on 1024-cubed spatial points and 1024 time-samples spanning about one large-scale turn-over timescale. This complete space-time history of turbulence is accessible to users remotely through an interface that is based on the Web-services model (see http://turbulence.pha.jhu.edu). Users may write and execute analysis programs on their host computers, while the programs make subroutine-like calls that request desired parts of the data over the network. The architecture of the database is briefly explained, as are some of the new functions such as Lagrangian particle tracking and spatial box-filtering. These tools are used to evaluate and compare subgrid stresses and models.
NASA Astrophysics Data System (ADS)
Ireland, Peter J.; Bragg, Andrew D.; Collins, Lance R.
2016-06-01
In this study, we analyze the statistics of both individual inertial particles and inertial particle pairs in direct numerical simulations of homogeneous isotropic turbulence in the absence of gravity. The effect of the Taylor microscale Reynolds number $R_\\lambda$ on the particle statistics is examined over the largest range to date (from $R_\\lambda = 88-597$). We first explore the effect of preferential sampling on the single-particle statistics, and use our understanding of preferential sampling to provide a physical explanation for many of the trends in the particle velocity gradients, kinetic energies, and accelerations at low $St$. As $St$ increases, inertial filtering effects become more important, causing the particle kinetic energies and accelerations to decrease. We then consider particle-pair statistics, and focus our attention on the relative velocities and radial distribution functions (RDFs) of the particles. The relative velocity statistics indicate that preferential-sampling effects are important for $St \\lesssim 0.1$ and that path-history/non-local effects become increasingly important for $St \\gtrsim 0.2$. The lower-order relative velocity statistics are only weakly sensitive to changes in Reynolds number at low $St$. We find that the RDFs peak near $St$ of order unity, that they exhibit power-law scaling for low and intermediate $St$, and that they are largely independent of Reynolds number for low and intermediate $St$. We also observe that at large $St$, changes in the RDF are related to changes the scaling exponents of the relative velocity variances. The particle collision kernel is found to be largely insensitive to the flow Reynolds number, suggesting that relatively low-Reynolds-number simulations may be able to capture much of the relevant physics of droplet collisions and growth in the adiabatic cores of atmospheric clouds.
Flow structure interaction between a flexible cantilever beam and isotropic turbulence
NASA Astrophysics Data System (ADS)
Vogel, Andrew; Morvan, Thomas; Goushcha, Oleg; Andreopoulos, Yiannis; Elvin, Niell
2015-11-01
In the present experimental work we consider the degree of distortion of isotropy and homogeneity of grid turbulence caused by the presence of a thin flexible cantilever beam immersed in the flow aligned in the longitudinal direction. Beams of various rigidities and lengths were used in the experiments. Piezoelectric patches were attached to the beams which provided an output voltage proportional to the strain and therefore proportional to the beam's deflection. The experiments were carried out in a large scale wind tunnel and hot-wires were used to measure turbulence intensity in the vicinity of the beams for various values of the ratio of aerodynamic loading to beam's rigidity. It was found that the flow field distortion depends on the rigidity of the beam. For very rigid beams this distortion is of the order of the boundary layer thickness developing over the beam while for very flexible beams the distorted region is of the order of the beam's tip deflection. Analysis of the time-dependent signals indicated some correlation between the frequency of beam's vibration and flow structures detected. Supported by NSF Grant: CBET #1033117.
Numerical Simulation of Turbulent Propane-Air Combustion with Non-Homogeneous Reactants
NASA Astrophysics Data System (ADS)
Haworth, D.; Cuenot, B.; Poinsot, T.; Blint, R.
1998-11-01
Two-dimensional numerical simulations of turbulent propane-air combustion have been performed including complex chemistry and realistic molecular transport. The aerothermochemical conditions simulated (reactant temperature and pressure, turbulence rms velocity and integral length scale) correspond to conditions at the time of ignition in an automotive gasoline direct-injection reciprocating IC engine at low speed and light load. Both stoichiometric homogeneous reactants and non-homogeneous reactants with fuel-based equivalence ratios ranging from zero to four have been simulated. In the case of non-homogeneous reactants, a primary premixed flame (defined based on disappearance of the propane fuel) is followed by a secondary heat-release zone that is dominated by CO kinetics and turbulent mixing. Beyond a few flame thicknesses behind the primary flame, any remaining fuel has been broken down into carbon monoxide and hydrogen. Quantitative information relevant for modeling turbulent flame propagation through nonhomogeneous reactants has been extracted.
Intermittency in non-homogeneous Wake and Jet Turbulence
NASA Astrophysics Data System (ADS)
Mahjoub, O. B.; Sekula, E.; Redondo, J. M.
2010-05-01
The scale to scale transfer and the structure functions are calculated and from these the intermittency parametres [1[3]. The estimates of turbulent diffusivity could also be measured. Some two point correlations and time lag calculations are used to investigate the local mixedness [4,5] and the temporal and spatial integral length scales obtained from both Lagrangian and Eulerian correlations and functions. We compare these results with both theoretical and experimental ones in the Laboratory with a wind tunnel at the wake of a grid or cillinder with and withoutand a near Wall. The a theoretical description of how to simulate intermittency following the model of Babiano et al. (1996) and the role of locality in higher order exponents is applied to the different flows. The information about turbulent jets is needed in several configurations providing basic information about the turbulent free jet, the circular jet and the turbulent wall jet. The experimental measurements of turbulent velocity is based on Acoustic Doppler Velocimeter measurements of the jet centerline and off centered radial positions in the tank at several distances from the wall. Spectral and structure function analysis are useful to determine the flow mixing ability using also flow visualization [6,7]. Results of experiments include the velocity distribution, entrainment angle of the jets, jet and wake average and fluctuating velocity, PDF's, Skewness and Kurthosis, velocity and vorticity standard deviation, boundary layers function and turbulence intensity . Different range of Wake and Jet flows show a maximum of turbulent intensity at a certain distance from the wall as it breaks the flow simmetry and adds large scale vorticity in the different experiments, these efects are also believed to occur in Geo-Astrophysical flows. [1] Babiano, A. (2002), On Particle dispersion processes in two-dimensional turbulence. In Turbulent mixing in geophysical flows. Eds. Linden P.F. and Redondo J.M., p. 2
Analysis of subgrid models using direct and large-eddy simulations of isotropic turbulence
NASA Astrophysics Data System (ADS)
Menon, S.; Yeung, P. K.
1994-12-01
Direct and large eddy simulations of forced and decaying isotropic turbulence have been performed using a pseudospectral and a finite-difference code. Subgrid models that include a one-equation subgrid kinetic energy model with and without a stochastic backscatter forcing term and a new scale similarity model have been analyzed in both Fourier space and physical space. The Fourier space analysis showed that the energy transfer across the cutoff wavenumber k(sub c) is dominated by local interaction. The correlation between the exact and the modeled (by a spectral eddy viscosity) nonlinear terms and the subgrid energy transfer in physical space was found to be quite low. In physical space, a similar correlation analysis was carried out using top hat filtering. Results show that the subgrid stress and the energy flux predicted by the subgrid models correlates very well with the exact data. The scale similarity model showed very high correlation for reasonable grid resolution. However, with decrease in grid resolution, the scale similarity model became more uncorrelated, when compared to the kinetic energy subgrid model. The subgrid models were then used for large-eddy simulations for a range of Reynolds number. It was determined that the dissipation was modeled poorly and that the correlation with the exact results was quite low for all the models. In general, for coarse grid resolution, the scale similarity model consistently showed very low correlation while the kinetic energy model showed a relatively higher correlation. These results suggest that to use the scale similarity model relatively fine grid resolution may be required, whereas, the kinetic energy model could be used even in coarse grid.
NASA Astrophysics Data System (ADS)
Sekimoto, Atsushi; Dong, Siwei; Jiménez, Javier
2016-03-01
Statistically stationary and homogeneous shear turbulence (SS-HST) is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, long-term simulations of HST are "minimal" in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, Lz, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (Lx ≳ 2Lz, Ly ≳ Lz) to prevent other directions to be constrained as well. It is also found that very long boxes, Lx ≳ 2Ly, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wall-bounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ˜20S-1, and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general.
Turbulent equipartition and homogenization of plasma angular momentum.
Gürcan, O D; Diamond, P H; Hahm, T S
2008-04-01
A physical model of turbulent equipartition (TEP) of plasma angular momentum is developed. We show that using a simple, model insensitive ansatz of conservation of total angular momentum, a TEP pinch of angular momentum can be obtained. We note that this term corresponds to a part of the pinch velocity previously calculated using quasilinear gyrokinetic theory. We observe that the nondiffusive TEP flux is inward, and therefore may explain the peakedness of the rotation profiles observed in certain experiments. Similar expressions for linear toroidal momentum and flow are computed and it is noted that there is an additional effect due the radial profile of moment of inertia density. PMID:18517961
Rubinstein, Robert; Kurien, Susan; Cambon, Claude
2015-06-22
The representation theory of the rotation group is applied to construct a series expansion of the correlation tensor in homogeneous anisotropic turbulence. The resolution of angular dependence is the main analytical difficulty posed by anisotropic turbulence; representation theory parametrises this dependence by a tensor analogue of the standard spherical harmonics expansion of a scalar. As a result, the series expansion is formulated in terms of explicitly constructed tensor bases with scalar coefficients determined by angular moments of the correlation tensor.
NASA Astrophysics Data System (ADS)
Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Grundestam, O.; Johansson, A. V.
2016-02-01
A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper
Critical assessment of Reynolds stress turbulence models using homogeneous flows
NASA Technical Reports Server (NTRS)
Shabbir, Aamir; Shih, Tsan-Hsing
1992-01-01
In modeling the rapid part of the pressure correlation term in the Reynolds stress transport equations, extensive use has been made of its exact properties which were first suggested by Rotta. These, for example, have been employed in obtaining the widely used Launder, Reece and Rodi (LRR) model. Some recent proposals have dropped one of these properties to obtain new models. We demonstrate, by computing some simple homogeneous flows, that doing so does not lead to any significant improvements over the LRR model and it is not the right direction in improving the performance of existing models. The reason for this, in our opinion, is that violation of one of the exact properties can not bring in any new physics into the model. We compute thirteen homogeneous flows using LRR (with a recalibrated rapid term constant), IP and SSG models. The flows computed include the flow through axisymmetric contraction; axisymmetric expansion; distortion by plane strain; and homogeneous shear flows with and without rotation. Results show that for most general representation for a model linear in the anisotropic tensor, performs either better or as good as the other two models of the same level.
Bounded energy states in homogeneous turbulent shear flow: An alternative view
NASA Technical Reports Server (NTRS)
Bernard, Peter S.; Speziale, Charles G.
1990-01-01
The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if vortex stretching is accounted for in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are present for a k-epsilon model modified to account for vortex stretching. The calculations indicate an initial exponential time growth of the turbulent kinetic energy and dissipation rate for elapsed times that are as large as those considered in any of the previously conducted physical or numerical experiments on homogeneous shear flow. However, vortex stretching eventually takes over and forces a production-equals-dissipation equilibrium with bounded energy states. The validity of this result is further supported by an independent theoretical argument. It is concluded that the generally accepted structural equilibrium for homogeneous shear flow with unbounded component energies is in need of re-examination.
Anisotropic structure of homogeneous turbulence subjected to uniform rotation
NASA Technical Reports Server (NTRS)
Cambon, C.; Mansour, N. N.; Squires, K. D.
1994-01-01
Large-eddy simulation results are used to investigate the development of anisotropies and the possible transition towards a quasi two-dimensional state in rotating turbulence at high Reynolds number. The present study demonstrates the existence of two transitions that are identified by two Rossby numbers. The first transition marks the onset of anisotropic effects and corresponds to a macro Rossby number Ro(sup L) (based on a longitudinal integral length scale) near unity. A second transition can be defined in terms of a lower bound of micro-Rossby number Ro(sup w) also near unity (defined in this work as the ratio of the rms fluctuating vorticity to background vorticity) and corresponds to a continued development of anisotropy but with an increasing emergence of those indicators based on the pure two-dimensional component of the flow, e.g., integral length scales measured along the rotation axis. Investigation of the vorticity structure shows that the second transition is also characterized by an increasing tendency for alignment between the fluctuating vorticity vector and the basic angular velocity vector with a preference for corotative vorticity.
Gomez, T; Sagaut, P; Schilling, O; Zhou, Y
2006-07-05
A spectral subggrid-scale eddy viscosity and magnetic resisitivity model based on the eddy-damped quasi-normal Markovian (EDQNM) spectral kinetic and magnetic energy transfer presented in [12] is used in large-eddy simulation (LES) of large kinetic and magnetic Reynold number magneto-hydrodynamic (MHD) turbulence. The proposed model is assessed via a posteri tests on three-dimensional, incompressible, isotropic, non-helical, freely-decaying MHD turbulence at asymptotically large Reynolds numbers. Using LES with an initial condition characterized by an Alfv{acute e}n ratio of kinetic to magnetic energy {tau}{sub A} equal to unity, it is shown that at the kinetic energy spectrum E{sub K}(k) and magnetic energy spectrum E{sub M}(k) exhibit Kolmogorov -5/3 inertial subrange scalings in the LES, consistent with the EDQNM model.
Is the Alfven-wave propagation effect important for energy decay in homogeneous MHD turbulence?
Hossain, Murshed; Gray, Perry C.; Pontius, Duane H. Jr.; Matthaeus, William H.; Oughton, Sean
1996-07-20
We investigate the role of three-point decorrelation due to Alfven wave propagation in three-dimensional incompressible homogeneous MHD turbulence. By comparing numerical simulations with theoretical expectations, we have studied how this effect influences the decay of turbulent energy caused by both an external mean magnetic field and the fluctuating turbulent field. Decay is initially suppressed by a mean magnetic field, as expected, but the effect soon saturates. The decay rate does not scale with mean magnetic field for higher values. The disagreement with theoretical predictions can be accounted for by anisotropic spectral transfer. Thus, phenomenological models for energy decay that include decorrelation due to Alfvenic propagation are not substantiated. This work complements our detailed study of various models of energy decay in homogeneous MHD [Hossain et al., 1995].
A Lagrangian PDF Model for the Scalar Dissipation in Homogeneous Turbulence
NASA Astrophysics Data System (ADS)
Fox, Rodney O.
1996-11-01
The scalar dissipation is a key quantity in the description of turbulent mixing. The spectral relaxation model (SRM) was developed to account for the effect of the evolution of the scalar spectrum on the mean scalar dissipation < ɛ_φ >, and it successfully predicts the observed (DNS, grid turbulence) dependence on Re, Sc (>= 1), and the initial scalar spectrum without recourse to fitting parameters. In this work, we present a Lagrangian PDF version (LSRM) for the PDF of ɛ_φ conditioned on the turbulent vortex stretching history of Kolmogorov-scale fluid particles. In homogeneous turbulence, the LSRM is coupled to a Lagrangian PDF model for the turbulent dissipation (ɛ) which strongly influences the statistics of ɛ_φ. Closure of scalar molecular dissipation term (< Γ nabla^2 φ | φ, ɛ^*_φ, ɛ^* >) is carried out using the Fokker-Planck model that was developed earlier for the joint scalar, scalar gradient PDF following fluid particles with the identical vortex stretching histories. Model predictions for inert scalar mixing in homogeneous turbulence with and without a uniform mean scalar gradient are compared to DNS data. In particular, the effect of the mean scalar gradient on the correlation between ɛ_φ and ɛ (i.e. local anisotropy) is examined, as well as the effect of the initial scalar spectrum and small-scale random vortex stretching on non-Gaussian behavior of the scalar PDF.
Reynolds stress calculations of homogeneous turbulent shear flow with bounded energy states
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Abid, R.
1992-01-01
Reynolds stress calculations of homogeneous turbulent shear flow are conducted with a second-order closure model modified to account for non-equilibrium vortex stretching in the dissipation rate transport equation, as recently proposed by Bernard and Speziale. As with the earlier reported k-epsilon model calculations incorporating this vortex stretching effect, a production-equals-dissipation equilibrium is obtained with bounded turbulent kinetic energy and dissipation. However, this equilibrium is not achieved until the dimensionless time greater than 60, an elapsed time that is at least twice as large as any of those considered in previous numerical and physical experiments on homogeneous shear flow. Direct quantitative comparisons between the model predictions and the results of experiments are quite favorable. In particular, it is shown that the inclusion of this non-equilibrium vortex stretching effect has the capability of explaining the significant range of production to dissipation ratios observed in experiments.
Reynolds stress calculations of homogeneous turbulent shear flow with bounded energy states
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Abid, R.
1993-01-01
Reynolds stress calculations of homogeneous turbulent shear flow are conducted with a second-order closure model modified to account for nonequilibrium vortex stretching in the dissipation rate transport equation as recently proposed by Bernard and Speziale (1992). As with the earlier reported K-epsilon model calculations incorporating this vortex stretching effect, a production-equals-dissipation equilibrium is obtained with bounded turbulent kinetic energy and dissipation. However, this equilibrium is now not achieved until the dimensionless time St greater than 60 - an elapsed time that is at least twice as large as any of those considered in previous numerical and physical experiments on homogeneous shear flow. Direct quantitative comparisons between the model predictions and the results of experiments are quite favorable. In particular, it is shown that the inclusion of this nonequilibrium vortex stretching effect has the capability of explaining the significant range of production to dissipation ratios observed in experiments.
NASA Technical Reports Server (NTRS)
Bennett, Floyd V.; Yntema, Robert T.
1959-01-01
Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.
NASA Astrophysics Data System (ADS)
Kassinos, S. C.; Reynolds, W. C.; Langer, C. A.
2002-11-01
Reynolds-averaged two equation turbulence models carry transport equations for two turbulence scales. The kinetic energy (k) equation provides a solid foundation for the energy scale. The exact transport equation for the energy dissipation rate (ɛ) is not useful as the basis for the second scale because ɛ is determined by large-scale turbulent interactions not represented in this equation. The transport equation for the large-scale enstrophy does provide a solid basis for modeling the evolution of the large-scale enstrophy, which together with k determines the spectral energy transfer that ultimately leads to dissipation by the small-scale motions. Here we close this equation using the new structure tensors and use it with our structure-based turbulence models (SBM) for homogeneous turbulence that is strained and sheared in fixed or rotating frames. Model predictions are in excellent agreement with results from large-scale Direct Numerical Simulations (DNS) that we are conducting for the ASCI program at Stanford. For shear in a rotating frame, of particular interest is the ratio of production over dissipation (P/ɛ) in the final equilibrium, and the dependence of this ratio on the ratio of frame rotation rate to shear rate (Ω^f/Γ). SBM predictions are in excellent agreement with DNS results; the traditional pair of the k and ɛ scale equations leads to wrong behavior for P/ɛ with Ω^f/Γ.
NASA Astrophysics Data System (ADS)
Tóth-Katona, Tibor; Gleeson, James T.
2004-01-01
Fluctuations of the injected electric power during electroconvection (EHC) of liquid crystals are reported in both the conductive and the dielectric regime of convection. The amplitude and the frequency of the fluctuations, as well as the probability density functions have been compared in these two regimes and substantial differences have been found both in defect turbulence of EHC and at the DSM1→DSM2 transition.
NASA Astrophysics Data System (ADS)
Donzis, Diego; Yakhot, Victor; Sreenivasan, K. R.
2015-11-01
Most approaches to understand turbulence have sought universal behavior believed to manifest at high Reynolds numbers (Rλ). However, recent theory and simulations suggest that universal characteristics, such as the non-trivial anomalous scaling exponents of moments of velocity gradients, emerge even at very low Rλ at which no inertial range exists. Furthermore, with decreasing Reynolds numbers, a transition occurs from fully intermittent turbulence to (approximately) Gaussian behavior at an apparently universal critical Rλ. A potential implication of these observations is that significant information concerning the inertial range (e.g. scaling exponents) is already manifest in the dissipation range at very low Rλ. Thus, high Rλ properties can be studied with well-resolved low-Rλ simulations instead of marginally resolved high-Reynolds flows. The focus of this talk is to explore signatures of universality at high-Reynolds numbers in the dissipation range of highly resolved DNS (kmax η ~ O (20)) for Rλ up to 90, and decaying simulations close to the critical Rλ. In addition to statistics of velocity gradients and dissipation we explore evidence of Beltramization as suggested in past theoretical work.
Numerical Simulations of Homogeneous Turbulence Using Lagrangian-Averaged Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Mohseni, Kamran; Shkoller, Steve; Kosovic, Branko; Marsden, Jerrold E.; Carati, Daniele; Wray, Alan; Rogallo, Robert
2000-01-01
The Lagrangian-averaged Navier-Stokes (LANS) equations are numerically evaluated as a turbulence closure. They are derived from a novel Lagrangian averaging procedure on the space of all volume-preserving maps and can be viewed as a numerical algorithm which removes the energy content from the small scales (smaller than some a priori fixed spatial scale alpha) using a dispersive rather than dissipative mechanism, thus maintaining the crucial features of the large scale flow. We examine the modeling capabilities of the LANS equations for decaying homogeneous turbulence, ascertain their ability to track the energy spectrum of fully resolved direct numerical simulations (DNS), compare the relative energy decay rates, and compare LANS with well-accepted large eddy simulation (LES) models.
An analysis of RNG based turbulence models for homogeneous shear flow
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Gatski, Thomas B.; Fitzmaurice, Nessan
1991-01-01
In a recent paper, the authors compared the performance of a variety of turbulence models including the k-epsilon model and the second-order closure model based on Renormalization Group (RNG) Methods. The performance of these RNG models in homogeneous turbulent shear flow was found to be quite poor, apparently due to the value of the constant C(sub epsilon1) in the modeled dissipation rate equation which was substantially lower than its traditional value. However, recently a correction has been made in the RNG based calculation of C(sub epsilon1). It is shown that with the new value of C(sub epsilon1), the performance of the RNG k-epsilon model is substantially improved. On the other hand, while the predictions of the revised RNG second-order closure model are better, some lingering problems still remain which can be easily remedied by the addition of higher order terms.
Local structure of intercomponent energy transfer in homogeneous turbulent shear flow
NASA Technical Reports Server (NTRS)
Brasseur, James G.; Lee, Moon J.
1987-01-01
Intercomponent energy transfer by pressure-strain-rate was investigated for homogeneous turbulent shear flow. The rapid and slow parts of turbulent pressure (decomposed according to the influence of the mean deformation rate) are found to be uncorrelated; this finding provides strong justification for current modeling procedure in which the pressure-strain-rate term is split into the corresponding parts. Issues pertinent to scales involved in the intercomponent energy transfer are addressed in comparison with those for the Reynolds-stress and vorticity fields. A physical picture of the energy transfer process is described from a detailed study of instantaneous events of high transfer regions. It was found that the most significant intercomponent energy transfer events are highly localized in space and are imbedded within a region of concentrated vorticity.
Navier-Stokes Simulation of Homogeneous Turbulence on the CYBER 205
NASA Technical Reports Server (NTRS)
Wu, C. T.; Ferziger, J. H.; Chapman, D. R.; Rogallo, R. S.
1984-01-01
A computer code which solves the Navier-Stokes equations for three dimensional, time-dependent, homogenous turbulence has been written for the CYBER 205. The code has options for both 64-bit and 32-bit arithmetic. With 32-bit computation, mesh sizes up to 64 (3) are contained within core of a 2 million 64-bit word memory. Computer speed timing runs were made for various vector lengths up to 6144. With this code, speeds a little over 100 Mflops have been achieved on a 2-pipe CYBER 205. Several problems encountered in the coding are discussed.
NASA Astrophysics Data System (ADS)
Mamatsashvili, George; Dong, Siwei; Khujadze, George; Chagelishvili, George; Jiménez, Javier; Foysi, Holger
2016-04-01
We performed direct numerical simulations of homogeneous shear turbulence to study the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows. For this purpose, we analyzed the turbulence dynamics in Fourier/wavenumber/spectral space based on the simulation data for the domain aspect ratio 1 : 1 : 1. Specifically, we examined the interplay of linear transient growth of Fourier harmonics and nonlinear processes. The transient growth of harmonics is strongly anisotropic in spectral space. This, in turn, leads to anisotropy of nonlinear processes in spectral space and, as a result, the main nonlinear process appears to be not a direct/inverse, but rather a transverse/angular redistribution of harmonics in Fourier space referred to as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by the interplay of the linear transient, or nonmodal growth and the transverse cascade. This course of events reliably exemplifies the wellknown bypass scenario of subcritical turbulence in spectrally stable shear flows. These processes mainly operate at large length scales, comparable to the box size. Consequently, the central, small wavenumber area of Fourier space (the size of which is determined below) is crucial in the self-sustenance and is labeled the vital area. Outside the vital area, the transient growth and the transverse cascade are of secondary importance - Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. The number of harmonics actively participating in the self-sustaining process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) is quite large - it is equal to 36 for the considered box aspect ratio - and obviously cannot be described by low-order models.
NASA Technical Reports Server (NTRS)
Goldstein, M. L.; Klimas, A. J.; Sandri, G.
1975-01-01
The Fokker-Planck coefficient for pitch-angle scattering, appropriate for cosmic rays in homogeneous stationary magnetic turbulence is computed without making any specific assumptions concerning the statistical symmetries of the random field. The Fokker-Planck coefficient obtained can be used to compute the parallel diffusion coefficient for high-energy cosmic rays propagating in the presence of strong turbulence, or for low-energy cosmic rays in the presence of weak turbulence. Because of the generality of magnetic turbulence allowed for in the analysis, special interplanetary magnetic field features, such as discontinuities or particular wave modes, can be included rigorously.
NASA Astrophysics Data System (ADS)
Ireland, Peter J.; Bragg, Andrew D.; Collins, Lance R.
2016-06-01
In Part I of this study, we analyzed the motion of inertial particles in isotropic turbulence in the absence of gravity using direct numerical simulation (DNS). Here, in Part II, we introduce gravity and study its effect over a wide range of flow Reynolds numbers, Froude numbers, and particle Stokes numbers. We see that gravity causes particles to sample the flow more uniformly and reduces the time particles can spend interacting with the underlying turbulence. We also find that gravity tends to increase inertial particle accelerations, and we introduce a model to explain that effect. We then analyze the particle relative velocities and radial distribution functions (RDFs), which are generally seen to be independent of Reynolds number for low and moderate Kolmogorov-scale Stokes numbers $St$. We see that gravity causes particle relative velocities to decrease, and that the relative velocities have higher scaling exponents with gravity. We observe that gravity has a non-trivial effect on clustering, acting to decrease clustering at low $St$ and to increase clustering at high $St$. By considering the effect of gravity on the clustering mechanisms described in the theory of Zaichik & Alipchenkov (New J. Phys., 11:103018, 2009), we provide an explanation for this non-trivial effect of gravity. We also show that when the effects of gravity are accounted for in the theory of Zaichik & Alipchenkov, the results compare favorably with DNS. The relative velocities and RDFs exhibit considerable anisotropy at small separations, and this anisotropy is quantified using spherical harmonic functions. We use the relative velocities and the RDFs to compute the particle collision kernels, and find that the collision kernel remains as it was for the case without gravity, namely nearly independent of Reynolds number for low and moderate $St$.
Rotational motion of elongated particles in isotropic turbulent flow: statistical perspective
NASA Astrophysics Data System (ADS)
Zhao, Lihao; Andersson, Helge; Variano, Evan
2014-11-01
We consider the rotational motion of non-spherical particles in turbulent flow, comparing the statistics of particles' angular velocity to the corresponding quantities computed in the fluid phase. We use numerical (DNS) and laboratory measurements for particles that are both larger and smaller than the Kolmogorov lengthscale. The particles are spheroids or rods, with aspect ratios between 1 and 10. We will discuss the subtleties of defining a meaningful Stokes number for these particles, focusing on the effect of asphericity and the fact that our interest is in rotation and not translation. Comparing the probability density function of angular velocity between fluid and particle phase indicates that the angular velocity of particles has a narrower distribution than that of the fluid phase, and that. particles do respond to extreme events in the fluid phase. The first four moments of the PDFs are analyzed, and these show that the ``filtering'' effect is very similar between DNS and lab experiments, despite differences in particle sizes and mass. We propose a nondimensional curve for predicting the magnitude of the filtering effect, and discuss the implications of this curve for the definition of Stokes number, as discussed earlier. This work has been supported by grants from the Peder Sather Center for Advanced Study at UC Berkeley and from the Research Council of Norway (Contract No. 213917/F20).
NASA Astrophysics Data System (ADS)
Jin, Guodong; He, Guo-Wei
2015-11-01
Clustering and intermittency in radial relative velocity (RRV) of heavy particles of same size settling in turbulent flows can be remarkably changed due to gravity. Clustering is monotonically reduced at Stokes number less than 1 under gravity due to the disability of the centrifugal mechanism, however it is non-monotonically enhanced at Stokes number greater than 1 due to the multiplicative amplification in the case that the proposed effective Kubo number is less than 1. Although gravity causes monotonical reduction in the rms of RRV of particles at a given Stokes number with decreasing Froude number, the variation tendency in the tails of standardized PDF of RRV versus Froude number is obviously different: the tails become narrower at a small Stokes number, while they become broader at a large Stokes number. The mechanism of this variation stems from the compromise between the following two competing factors. The mitigation of correlation of particle positions and the regions of high strain rate which are more intermittent reduces the intermittency in RRV at small Stokes numbers, while the significant reduction in the backward-in-time relative separations will make particle pairs see small-scale structures, leading to a higher intermittency in RRV at large Stokes numbers. NSAF of China (grant number U1230126); NSFC (grant numbers 11072247 and 11232011).
NASA Astrophysics Data System (ADS)
Dong, Siwei; Sekimoto, Atsushi; Jiménez, Javier
2013-11-01
The rough independence of the logarithmic layer (LL) of wall-bounded turbulence from the details of the buffer and outer layers, suggests that the interaction of the turbulent fluctuations with the mean shear may be mimicked by statistically-stationary homogeneous shear turbulence (SS-HST) in a finite box. We study SS-HST in boxes for which the statistics best agree with those of the LL. Both flows share similar Corrsin shear parameters, and Reynolds-stress and vorticity anisotropies. Two-point correlation functions show that u and w are constrained by the simulation box and are respectively shorter and narrower for SS-HST than for the LL, but v and the vorticity are roughly of the same size in both flows when Reλ is similar. The transient bursting of v in both flows is quite similar to the linear Orr mechanism, with time scales that are of the same order in both flows. In both cases, a streamwise velocity streak forms and breaks down quasi periodically, and the break down is accompanied by an enhanced flux of momentum, in the form of large-scale ejections and sweeps. Funded by the ERC Multiflow program and CSC.
Early turbulent mixing as the origin of chemical homogeneity in open star clusters.
Feng, Yi; Krumholz, Mark R
2014-09-25
The abundances of elements in stars are critical clues to stars' origins. Observed star-to-star variations in logarithmic abundance within an open star cluster--a gravitationally bound ensemble of stars in the Galactic plane--are typically only about 0.01 to 0.05 over many elements, which is noticeably smaller than the variation of about 0.06 to 0.3 seen in the interstellar medium from which the stars form. It is unknown why star clusters are so homogenous, and whether homogeneity should also prevail in regions of lower star formation efficiency that do not produce bound clusters. Here we report simulations that trace the mixing of chemical elements as star-forming clouds assemble and collapse. We show that turbulent mixing during cloud assembly naturally produces a stellar abundance scatter at least five times smaller than that in the gas, which is sufficient to explain the observed chemical homogeneity of stars. Moreover, mixing occurs very early, so that regions with star formation efficiencies of about 10 per cent are nearly as well mixed as those with formation efficiencies of about 50 per cent. This implies that even regions that do not form bound clusters are likely to be well mixed, and improves the prospects of using 'chemical tagging' to reconstruct (via their unique chemical signatures, or tags) star clusters whose constituent stars have become unbound from one another and spread across the Galactic disk. PMID:25174709
NASA Technical Reports Server (NTRS)
Kumar, P.; Patel, S. R.
1974-01-01
A method is described for studying theoretically the concentration fluctuations of a dilute contaminate undergoing a first-order chemical reaction. The method is based on Deissler's (1958) theory for homogeneous turbulence for times before the final period, and it follows the approach used by Loeffler and Deissler (1961) to study temperature fluctuations in homogeneous turbulence. Four-point correlation equations are obtained; it is assumed that terms containing fifth-order correlation are very small in comparison with those containing fourth-order correlations, and can therefore be neglected. A spectrum equation is obtained in a form which can be solved numerically, yielding the decay law for the concentration fluctuations in homogeneous turbulence for the period much before the final period of decay.
Numerical simulation of a compressible homogeneous, turbulent shear flow. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Feiereisen, W. J.; Reynolds, W. C.; Ferziger, J. H.
1981-01-01
A direct, low Reynolds number, numerical simulation was performed on a homogeneous turbulent shear flow. The full compressible Navier-Stokes equations were used in a simulation on the ILLIAC IV computer with a 64,000 mesh. The flow fields generated by the code are used as an experimental data base, to examine the behavior of the Reynols stresses in this simple, compressible flow. The variation of the structure of the stresses and their dynamic equations as the character of the flow changed is emphasized. The structure of the tress tensor is more heavily dependent on the shear number and less on the fluctuating Mach number. The pressure-strain correlation tensor in the dynamic uations is directly calculated in this simulation. These correlations are decomposed into several parts, as contrasted with the traditional incompressible decomposition into two parts. The performance of existing models for the conventional terms is examined, and a model is proposed for the 'mean fluctuating' part.
NASA Astrophysics Data System (ADS)
Pawar, Shashikant S.; Arakeri, Jaywant H.
2016-06-01
Kinetic energy and scalar spectra from the measurements in high Rayleigh number axially homogeneous buoyancy driven turbulent flow are presented. Kinetic energy and concentration (scalar) spectra are obtained from the experiments wherein density difference is created using brine and fresh water and temperature spectra are obtained from the experiments in which heat is used. Scaling of the frequency spectra of lateral and longitudinal velocity near the tube axis is closer to the Kolmogorov-Obukhov scaling, while the scalar spectra show some evidence of dual scaling, Bolgiano-Obukhov scaling followed by Obukhov-Corrsin scaling. These scalings are also observed in the corresponding second order spatial structure functions of velocity and concentration fluctuations.
Two regimes of flux scaling in axially homogeneous turbulent convection in vertical tube
NASA Astrophysics Data System (ADS)
Pawar, Shashikant S.; Arakeri, Jaywant H.
2016-08-01
From experiments of axially homogeneous turbulent convection in a vertical tube using heat (Prandtl number Pr≃6 ) and brine (Pr≃600 ) we show that at sufficiently high Rayleigh numbers (Rag), the Nusselt number Nug˜(RagPr)1/2, which corresponds to the so-called ultimate regime scaling. In heat experiments below certain Rag,however,there is transition to a new regime, Nug˜(RagPr)0.3. This transition also seems to exist in earlier reported data for Pr=1 and Pr≃600 , at different Rag. However, the transition occurs at a single Grashof number, Grgc≃1.6 ×105 , and unified flux scalings for Pr≥1 , Nug/Pr˜Grg0.3, and Nug/Pr˜Grg1/2 can be given for the two regimes.
NASA Astrophysics Data System (ADS)
Grigoriev, Yurii N.; Meleshko, Sergey V.; Suriyawichitseranee, Amornrat
2015-06-01
Group analysis of the spatially homogeneous and molecular energy dependent Boltzmann equations with source term is carried out. The Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The correspondent determining equation of the admitted Lie group is reduced to a partial differential equation for the admitted source. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation with respect to a source function is given. The representation of invariant solutions and corresponding reduced equations for all obtained source functions are also presented.
NASA Technical Reports Server (NTRS)
Madnia, C. K.; Frankel, S. H.; Givi, P.
1992-01-01
Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing
NASA Astrophysics Data System (ADS)
Chiadini, Francesco; Fiumara, Vincenzo; Scaglione, Antonio; Lakhtakia, Akhlesh
2016-03-01
Multiple compound surface plasmon-polariton (SPP) waves can be guided by a structure consisting of a sufficiently thick layer of metal sandwiched between a homogeneous isotropic dielectric (HID) material and a dielectric structurally chiral material (SCM). The compound SPP waves are strongly bound to both metal/dielectric interfaces when the thickness of the metal layer is comparable to the skin depth but just to one of the two interfaces when the thickness is much larger. The compound SPP waves differ in phase speed, attenuation rate, and field profile, even though all are excitable at the same frequency. Some compound SPP waves are not greatly affected by the choice of the direction of propagation in the transverse plane but others are, depending on metal thickness. For fixed metal thickness, the number of compound SPP waves depends on the relative permittivity of the HID material, which can be useful for sensing applications.
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Lumley, John L.
1991-01-01
Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.
All-speed Roe scheme for the large eddy simulation of homogeneous decaying turbulence
NASA Astrophysics Data System (ADS)
Li, Xue-song; Li, Xin-liang
2016-01-01
As a type of shock-capturing scheme, the traditional Roe scheme fails in large eddy simulation (LES) because it cannot reproduce important turbulent characteristics, such as the famous k-5/3 spectral law, as a consequence of the large numerical dissipation. In this work, the Roe scheme is divided into five parts, namely, ξ, δUp, δpp, δUu, and δpu, which denote basic upwind dissipation, pressure difference-driven modification of interface fluxes, pressure difference-driven modification of pressure, velocity difference-driven modification of interface fluxes, and velocity difference-driven modification of pressure, respectively. Then, the role of each part in the LES of homogeneous decaying turbulence with a low Mach number is investigated. Results show that the parts δUu, δpp, and δUp have little effect on LES. Such minimal effect is integral to computational stability, especially for δUp. The large numerical dissipation is due to ξ and δpu, each of which features a larger dissipation than the sub-grid scale model. On the basis of these conditions, an improved all-speed Roe scheme for LES is proposed. This scheme can provide satisfactory LES results even for coarse grid resolutions with usually adopted second-order reconstructions for the finite volume method.
NASA Astrophysics Data System (ADS)
Yoshimatsu, Katsunori; Schneider, Kai; Okamoto, Naoya; Kawahara, Yasuhiro; Farge, Marie
2011-09-01
Scale-dependent and geometrical statistics of three-dimensional incompressible homogeneous magnetohydrodynamic turbulence without mean magnetic field are examined by means of the orthogonal wavelet decomposition. The flow is computed by direct numerical simulation with a Fourier spectral method at resolution 5123 and a unit magnetic Prandtl number. Scale-dependent second and higher order statistics of the velocity and magnetic fields allow to quantify their intermittency in terms of spatial fluctuations of the energy spectra, the flatness, and the probability distribution functions at different scales. Different scale-dependent relative helicities, e.g., kinetic, cross, and magnetic relative helicities, yield geometrical information on alignment between the different scale-dependent fields. At each scale, the alignment between the velocity and magnetic field is found to be more pronounced than the other alignments considered here, i.e., the scale-dependent alignment between the velocity and vorticity, the scale-dependent alignment between the magnetic field and its vector potential, and the scale-dependent alignment between the magnetic field and the current density. Finally, statistical scale-dependent analyses of both Eulerian and Lagrangian accelerations and the corresponding time-derivatives of the magnetic field are performed. It is found that the Lagrangian acceleration does not exhibit substantially stronger intermittency compared to the Eulerian acceleration, in contrast to hydrodynamic turbulence where the Lagrangian acceleration shows much stronger intermittency than the Eulerian acceleration. The Eulerian time-derivative of the magnetic field is more intermittent than the Lagrangian time-derivative of the magnetic field.
NASA Technical Reports Server (NTRS)
Goldstein, M. L.; Klimas, A. J.; Sandri, G.
1974-01-01
The Fokker-Planck coefficient for pitch angle scattering, appropriate for cosmic rays in homogeneous, stationary, magnetic turbulence, is computed from first principles. No assumptions are made concerning any special statistical symmetries the random field may have. This result can be used to compute the parallel diffusion coefficient for high energy cosmic rays moving in strong turbulence, or low energy cosmic rays moving in weak turbulence. Becuase of the generality of the magnetic turbulence which is allowed in this calculation, special interplanetary magnetic field features such as discontinuities, or particular wave modes, can be included rigorously. The reduction of this results to previously available expressions for the pitch angle scattering coefficient in random field models with special symmetries is discussed. The general existance of a Dirac delta function in the pitch angle scattering coefficient is demonstrated. It is proved that this delta function is the Fokker-Planck prediction for pitch angle scattering due to mirroring in the magnetic field.
NASA Astrophysics Data System (ADS)
Belcaid, Aicha; Le Palec, Georges; Draoui, Abdeslam
2015-12-01
This paper investigates a numerical and experimental study about horizontal round turbulent forced plume injected into a static homogeneous environment. Helium-air plume is an example of non-Boussinesq forced plume in which a low-density binary gas mixture is injected into a high density ambient of air. Since the domain temperature is assumed to be constant, the density of the mixture is a function of the concentration only. Numerical model is based on the finite volume method and reports on an application of standard k-ɛ model for steady flow with densimetric Froude numbers of 30-300 and Reynolds numbers of 2000-6000. The basic features of the model are: the conservation of mass, momentum and concentration. The boundaries of plume body, the centerline trajectory, the radius plume and the centerline mixture density are determined. It is found that the plume spreading and behavior depend on the ratio between buoyancy flux and momentum, i.e. Froude number. Laboratory experiments have been conducted for photographic observations of plumes trajectories for different mixture (helium-air) densities with different velocities and injection nozzle diameters. Numerical results are described and compared with the experiments and good agreement has been achieved.
Masterlark, Timothy
2003-01-01
Dislocation models can simulate static deformation caused by slip along a fault. These models usually take the form of a dislocation embedded in a homogeneous, isotropic, Poisson-solid half-space (HIPSHS). However, the widely accepted HIPSHS assumptions poorly approximate subduction zone systems of converging oceanic and continental crust. This study uses three-dimensional finite element models (FEMs) that allow for any combination (including none) of the HIPSHS assumptions to compute synthetic Green's functions for displacement. Using the 1995 Mw = 8.0 Jalisco-Colima, Mexico, subduction zone earthquake and associated measurements from a nearby GPS array as an example, FEM-generated synthetic Green's functions are combined with standard linear inverse methods to estimate dislocation distributions along the subduction interface. Loading a forward HIPSHS model with dislocation distributions, estimated from FEMs that sequentially relax the HIPSHS assumptions, yields the sensitivity of predicted displacements to each of the HIPSHS assumptions. For the subduction zone models tested and the specific field situation considered, sensitivities to the individual Poisson-solid, isotropy, and homogeneity assumptions can be substantially greater than GPS. measurement uncertainties. Forward modeling quantifies stress coupling between the Mw = 8.0 earthquake and a nearby Mw = 6.3 earthquake that occurred 63 days later. Coulomb stress changes predicted from static HIPSHS models cannot account for the 63-day lag time between events. Alternatively, an FEM that includes a poroelastic oceanic crust, which allows for postseismic pore fluid pressure recovery, can account for the lag time. The pore fluid pressure recovery rate puts an upper limit of 10-17 m2 on the bulk permeability of the oceanic crust. Copyright 2003 by the American Geophysical Union.
Cascade modeling of single and two-phase turbulence
NASA Astrophysics Data System (ADS)
Bolotnov, Igor A.
The analysis of turbulent two-phase flows requires closure models in order to perform reliable computational multiphase fluid dynamics (CFMD) analyses. A turbulence cascade model, which tracks the evolution of the turbulent kinetic energy between the various eddy sizes, has been developed for the analysis of the single and bubbly two-phase turbulence. Various flows are considered including the decay of isotropic grid-induced turbulence, uniform shear flow and turbulent channel flow. The model has been developed using a "building block" approach by moving from modeling of simpler turbulent flows (i.e., homogeneous, isotropic decay) to more involved turbulent flows (i.e., non-homogeneous channel flow). The spectral cascade-transport model's performance has been assessed against a number of experimental and direct numerical simulation (DNS) results.
Homogeneous and isotropic big rips?
Giovannini, Massimo
2005-10-15
We investigate the way big rips are approached in a fully inhomogeneous description of the space-time geometry. If the pressure and energy densities are connected by a (supernegative) barotropic index, the spatial gradients and the anisotropic expansion decay as the big rip is approached. This behavior is contrasted with the usual big-bang singularities. A similar analysis is performed in the case of sudden (quiescent) singularities and it is argued that the spatial gradients may well be non-negligible in the vicinity of pressure singularities.
NASA Technical Reports Server (NTRS)
Cambon, C.; Coleman, G. N.; Mansour, N. N.
1992-01-01
The effect of rapid mean compression on compressible turbulence at a range of turbulent Mach numbers is investigated. Rapid distortion theory (RDT) and direct numerical simulation results for the case of axial (one-dimensional) compression are used to illustrate the existence of two distinct rapid compression regimes. These regimes are set by the relationships between the timescales of the mean distortion, the turbulence, and the speed of sound. A general RDT formulation is developed and is proposed as a means of improving turbulence models for compressible flows.
Suppression of turbulent resistivity in turbulent Couette flow
NASA Astrophysics Data System (ADS)
Si, Jiahe; Colgate, Stirling A.; Sonnenfeld, Richard G.; Nornberg, Mark D.; Li, Hui; Colgate, Arthur S.; Westpfahl, David J.; Romero, Van D.; Martinic, Joe
2015-07-01
Turbulent transport in rapidly rotating shear flow very efficiently transports angular momentum, a critical feature of instabilities responsible both for the dynamics of accretion disks and the turbulent power dissipation in a centrifuge. Turbulent mixing can efficiently transport other quantities like heat and even magnetic flux by enhanced diffusion. This enhancement is particularly evident in homogeneous, isotropic turbulent flows of liquid metals. In the New Mexico dynamo experiment, the effective resistivity is measured using both differential rotation and pulsed magnetic field decay to demonstrate that at very high Reynolds number rotating shear flow can be described entirely by mean flow induction with very little contribution from correlated velocity fluctuations.
Suppression of turbulent resistivity in turbulent Couette flow
Si, Jiahe Sonnenfeld, Richard G.; Colgate, Arthur S.; Westpfahl, David J.; Romero, Van D.; Martinic, Joe; Colgate, Stirling A.; Li, Hui; Nornberg, Mark D.
2015-07-15
Turbulent transport in rapidly rotating shear flow very efficiently transports angular momentum, a critical feature of instabilities responsible both for the dynamics of accretion disks and the turbulent power dissipation in a centrifuge. Turbulent mixing can efficiently transport other quantities like heat and even magnetic flux by enhanced diffusion. This enhancement is particularly evident in homogeneous, isotropic turbulent flows of liquid metals. In the New Mexico dynamo experiment, the effective resistivity is measured using both differential rotation and pulsed magnetic field decay to demonstrate that at very high Reynolds number rotating shear flow can be described entirely by mean flow induction with very little contribution from correlated velocity fluctuations.
Gaussian Multiplicative Chaos for Symmetric Isotropic Matrices
NASA Astrophysics Data System (ADS)
Chevillard, Laurent; Rhodes, Rémi; Vargas, Vincent
2013-02-01
Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.
A nonlinear theory of cosmic ray pitch angle diffusion in homogeneous magnetostatic turbulence
NASA Technical Reports Server (NTRS)
Goldstein, M. L.
1975-01-01
A plasma strong turbulence, weak coupling, theory is applied to the problem of cosmic ray pitch angle scattering in magnetostatic turbulence. The theory used is a rigorous generalization of Weinstock's resonance-broadening theory and contains no ad hoc approximations. A detailed calculation is presented for a model of slab turbulence with an exponential correlation function. The results agree well with numerical simulations. The rigidity dependence of the pitch angle scattering coefficient differs from that found by previous researchers. The differences result from an inadequate treatment of particle trajectories near 90 deg pitch angle in earlier work.
NASA Astrophysics Data System (ADS)
Nejadmalayeri, Alireza; Vezolainen, Alexei; Vasilyev, Oleg V.
2011-11-01
With the recent development of parallel adaptive wavelet collocation method, adaptive numerical simulations of high Reynolds number turbulent flows have become feasible. The integration of turbulence modeling of different fidelity with adaptive wavelet methods results in a hierarchical approach for modeling and simulating turbulent flows in which all or most energetic parts of coherent eddies are dynamically resolved on self-adaptive computational grids, while modeling the effect of the unresolved incoherent or less energetic modes. This talk is the first attempt to estimate how spatial modes of both Coherent Vortex Simulations (CVS) and Stochastic Coherent Adaptive Large Eddy Simulations (SCALES) scale with Reynolds number. The computational complexity studies for both CVS and SCALES of linearly forced homogeneous turbulence are performed at effective non-adaptive resolutions of 2563, 5123, 10243, and 20483 corresponding to approximate Reλ of 70, 120, 190, 320. The details of the simulations are discussed and the results of compression achieved by CVS and SCALES as well as scalability studies of the parallel algorithm for the aforementioned Taylor micro-scale Reynolds numbers are presented. This work was supported by NSF under grant No. CBET-0756046.
2015-01-01
High-throughput production of nanoparticles (NPs) with controlled quality is critical for their clinical translation into effective nanomedicines for diagnostics and therapeutics. Here we report a simple and versatile coaxial turbulent jet mixer that can synthesize a variety of NPs at high throughput up to 3 kg/d, while maintaining the advantages of homogeneity, reproducibility, and tunability that are normally accessible only in specialized microscale mixing devices. The device fabrication does not require specialized machining and is easy to operate. As one example, we show reproducible, high-throughput formulation of siRNA-polyelectrolyte polyplex NPs that exhibit effective gene knockdown but exhibit significant dependence on batch size when formulated using conventional methods. The coaxial turbulent jet mixer can accelerate the development of nanomedicines by providing a robust and versatile platform for preparation of NPs at throughputs suitable for in vivo studies, clinical trials, and industrial-scale production. PMID:24824296
Mamatsashvili, G; Khujadze, G; Chagelishvili, G; Dong, S; Jiménez, J; Foysi, H
2016-08-01
To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space is the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wave number area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance: Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies
Turbulent solutions of equations of fluid motion
NASA Technical Reports Server (NTRS)
Deissler, R. G.
1985-01-01
Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence, such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations the initially nonrandom flow develops into an apparently random turbulence. The cases considered include turbulence that is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.
NASA Technical Reports Server (NTRS)
Kerr, R. A.
1983-01-01
In a three dimensional simulation higher order derivative correlations, including skewness and flatness factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. The equations are forced to maintain steady state turbulence and collect statistics. It is found that the scalar derivative flatness increases much faster with Reynolds number than the velocity derivative flatness, and the velocity and mixed derivative skewness do not increase with Reynolds number. Separate exponents are found for the various fourth order velocity derivative correlations, with the vorticity flatness exponent the largest. Three dimensional graphics show strong alignment between the vorticity, rate of strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short minus 5/3 spectral regime is observed.
Similarity states of homogeneous stably-stratified turbulence at infinite Froude number
NASA Technical Reports Server (NTRS)
Chasnov, Jeffrey R.
1993-01-01
We present evidence of similarity states which may develop inhomogeneous stably-stratified flows if a dimensionless group in addition to the Reynolds number, the so-called Froude number, is sufficiently large. Here, we define the Froude number as the ratio of the internal wave time-scale to the turbulence time-scale. We examine three different similarity states which may develop depending on the initial conditions of the velocity and density fields. Theoretical arguments and results of large-eddy simulations will be presented. We will conclude this report with some speculative thoughts on similarity states which may develop in stably-stratified turbulence at arbitrary Froude number as well as our future research plans in this area.
Evolution of a confined turbulent jet in a long cylindrical cavity: Homogeneous fluids
NASA Astrophysics Data System (ADS)
Voropayev, S. I.; Sanchez, X.; Nath, C.; Webb, S.; Fernando, H. J. S.
2011-11-01
The flow induced in a long cylinder by an axially discharging round turbulent jet was investigated experimentally with applications to crude oil storage in the U.S. strategic petroleum reserves (SPR). It was found that the flow does not reach a true steady state, but vacillates periodically. Digital video recordings and particle image velocimetry were used to map the flow structures and velocity/vorticity fields, from which the frequency of jet switching, jet stopping distance, mean flow, turbulence characteristics, and the influence of end-wall boundary conditions were inferred. The results were parameterized using the characteristic length D and velocity J1/2/D scales based on the jet kinematic momentum flux J and cylinder width D. The scaling laws so developed could be used to extrapolate laboratory observations to SPR flows.
Development and Application of AN Improved Subgrid Model for Homogeneous Turbulence
NASA Astrophysics Data System (ADS)
Chasnov, Jeffrey Robert
1990-01-01
As most of the fluids in nature are in turbulent motion, a considerable effort has been devoted to understanding turbulence using experimental, analytical, and numerical methods. With recent advances in computer technology, numerical simulations are currently on the leading edge of turbulence research. However, it will not be possible to resolve the entire spectrum of eddies in a high Reynolds number flow, even with the fastest foreseen computers. A more promising approach consists of explicitly simulating only the largest eddies of the flow, while employing an analytical subgrid model to simulate the effects of the smallest eddies. Previous subgrid models using an eddy viscosity have simulated the net subgrid scale energy transfer only as an energy transfer from the resolved scales to the unresolved subgrid scales. Two objections may be raised to the eddy viscosity model: first, physically, the energy transfer from the subgrid scales to the resolved scales is poorly represented, and; second, any physical effects which do not result in an energy transfer are omitted. A subgrid model that addresses these two objections is developed. First, only the energy transfer from the resolved to the subgrid scales is modeled as an eddy viscosity, whereas the energy transfer from the subgrid to the resolved scales is modeled as a stochastic force. Second, a new effect that does not result in an immediate energy transfer is modeled: the random sweeping of the smallest resolved eddies by the largest. Both the eddy viscosity and the stochastic force of the improved subgrid model are computed from an analytical model and from a direct numerical simulation. The simulation is found to validate the analytical model. The subgrid model is then applied to study: (1) the Kolmogorov inertial subrange; (2) the local and non-local energy fluxes across a given wavenumber, and; (3) the spectrum of a passive scalar field in the inertial-diffusive subrange. Future applications of the improved
Bumblebee Flight in Heavy Turbulence
NASA Astrophysics Data System (ADS)
Engels, T.; Kolomenskiy, D.; Schneider, K.; Lehmann, F.-O.; Sesterhenn, J.
2016-01-01
High-resolution numerical simulations of a tethered model bumblebee in forward flight are performed superimposing homogeneous isotropic turbulent fluctuations to the uniform inflow. Despite tremendous variation in turbulence intensity, between 17% and 99% with respect to the mean flow, we do not find significant changes in cycle-averaged aerodynamic forces, moments, or flight power when averaged over realizations, compared to laminar inflow conditions. The variance of aerodynamic measures, however, significantly increases with increasing turbulence intensity, which may explain flight instabilities observed in freely flying bees.
Particle Settling in Low Energy Turbulence
NASA Astrophysics Data System (ADS)
Allen, Rachel; MacVean, Lissa; Tse, Ian; Mazzaro, Laura; Stacey, Mark; Variano, Evan
2014-11-01
Particle settling velocities can be altered by turbulence. In turbulence, dense particles may get trapped in convergent flow regions, and falling particles may be swept towards the downward side of turbulent eddies, resulting in enhanced settling velocities. The degree of velocity enhancement may depend on the Stokes number, the Rouse number, and the turbulent Reynolds number. In a homogeneous, isotropic turbulence tank, we tested the effects of particle size and type, suspended sediment concentration, and level of turbulence on the settling velocities of particles typically found in muddy estuaries. Two Acoustic Doppler Velocimeters (ADVs), separated vertically, measured turbulent velocities and suspended sediment concentrations, which yield condition dependent settling velocities, via ∂/á C ñ ∂ t = -∂/∂ z (ws á C ñ + á w ' C ' ñ) . These results are pertinent to fine sediment transport in estuaries, where high concentrations of suspended material are transported and impacted by low energy turbulence.
Analysis of Multipoint-Multitime Correlations and Diffusion in Decaying Homogeneous Turbulence
NASA Technical Reports Server (NTRS)
Deissler, Robert G.
1961-01-01
Two-point, two-time correlation equations are obtained by considering the Navier-Stokes equations for two points in a fluid at two time. By neglecting the triple correlations in the equations, a solution is obtained for the final period of decay. The analysis is extended to earlier times by considering three points at three different times. The set of equations is made determinate by neglecting the quadruple correlations in comparison with the triple correlations. The diffusion of particles from a source in a decaying turbulent field is calculated approximately by assuming that the velocity fluctuations are small.
Three-dimensional vortex dynamics in superfluid /sup 4/He: Homogeneous superfluid turbulence
Schwarz, K.W.
1988-08-01
The behavior of a tangle of quantized vortex lines subject to uniform superfluid and normal-fluid driving velocities is investigated. The dynamical equation of the quantized vortices in the local approximation is supplemented by the assumption that when two such singularities cross, they undergo a reconnection. The properties of the dynamical equation, when combined with the assumption of homogeneity, imply numerous scaling relations, which are in fact observed experimentally. The primitive dynamical rules are utilized to perform extensive numerical simulations of the vortex tangle, using not only periodic, but also smooth-wall and rough-wall boundary conditions. All lead to the same homogeneous vortex-tangle state, although the case of periodic boundary conditions requires an additional trick to eliminate artificial features. The quantitative results obtained from these simulations are found to be in excellent absolute agreement with a large variety of experiments, including recent studies of the vortex-tangle anisotropy.
NASA Astrophysics Data System (ADS)
Dhariwal, Rohit; Rani, Sarma; Koch, Donald
2015-11-01
In an earlier work, Rani, Dhariwal, and Koch (JFM, Vol. 756, 2014) developed an analytical closure for the diffusion current in the PDF transport equation describing the relative motion of high-Stokes-number particle pairs in isotropic turbulence. In this study, an improved closure was developed for the diffusion coefficient, such that the motion of the particle-pair center of mass is taken into account. Using the earlier and the new analytical closures, Langevin simulations of pair relative motion were performed for four particle Stokes numbers, Stη = 10 , 20 , 40 , 80 and at two Taylor micro-scale Reynolds numbers Reλ = 76 , 131 . Detailed comparisons of the analytical model predictions with those of DNS were undertaken. It is seen that the pair relative motion statistics obtained from the improved theory show excellent agreement with the DNS statistics. The radial distribution functions (RDFs), and relative velocity PDFs obtained from the improved-closure-based Langevin simulations are found to be in very good agreement with those from DNS. It was found that the RDFs and relative velocity RMS increased with Reλ for all Stη . The collision kernel also increased strongly with Reλ , since it depended on the RDF and the radial relative velocities.
NASA Astrophysics Data System (ADS)
Yoshimatsu, Katsunori; Kondo, Yuji; Schneider, Kai; Okamoto, Naoya; Hagiwara, Hiroyuki; Farge, Marie
2009-08-01
A method for extracting coherent vorticity sheets and current sheets out of three-dimensional homogeneous magnetohydrodynamic (MHD) turbulence is proposed, which is based on the orthogonal wavelet decomposition of the vorticity and current density fields. Thresholding the wavelet coefficients allows both fields to be split into coherent and incoherent parts. The fields to be analyzed are obtained by direct numerical simulation (DNS) of forced incompressible MHD turbulence without mean magnetic field, using a classical Fourier spectral method at a resolution of 5123. Coherent vorticity sheets and current sheets are extracted from the DNS data at a given time instant. It is found that the coherent vorticity and current density preserve both the vorticity sheets and the current sheets present in the total fields while retaining only a few percent of the degrees of freedom. The incoherent vorticity and current density are shown to be structureless and of mainly dissipative nature. The spectral distributions of kinetic and magnetic energies of the coherent fields only differ in the dissipative range, while the corresponding incoherent fields exhibit near-equipartition of energy. The probability distribution functions of total and coherent fields for both vorticity and current density coincide almost perfectly, while the incoherent fields have strongly reduced variances. Studying the energy flux confirms that the nonlinear dynamics is fully captured by the coherent fields only.
Rapid distortion analysis of high speed homogeneous turbulence subject to periodic shear
Bertsch, Rebecca L. Girimaji, Sharath S.
2015-12-15
The effect of unsteady shear forcing on small perturbation growth in compressible flow is investigated. In particular, flow-thermodynamic field interaction and the resulting effect on the phase-lag between applied shear and Reynolds stress are examined. Simplified linear analysis of the perturbation pressure equation reveals crucial differences between steady and unsteady shear effects. The analytical findings are validated with numerical simulations of inviscid rapid distortion theory (RDT) equations. In contrast to steadily sheared compressible flows, perturbations in the unsteady (periodic) forcing case do not experience an asymptotic growth phase. Further, the resonance growth phenomenon found in incompressible unsteady shear turbulence is absent in the compressible case. Overall, the stabilizing influence of both unsteadiness and compressibility is compounded leading to suppression of all small perturbations. The underlying mechanisms are explained.
Laboratory and Field Observations of Microcystis aeruginosa in nearly homogeneous turbulent flows
NASA Astrophysics Data System (ADS)
Wilkinson, Anne; Hondzo, Miki; Guala, Michele
2015-11-01
Microcystis aeruginosa is a single-celled cyanobacterium, forming large colonies on the surface of freshwater ecosystems during summer, and producing a toxin (microcystin) that in high concentration can be harmful to humans and animals. In addition to water temperature, light and nutrient abundance, fluid motion is also an abiotic environmental factor affecting the growth and metabolism of Microcystis. Systematic investigations in a laboratory bioreactor are paired with field measurements in the lacustrine photic zone from two sites in Lake Minnetonka (MN) to ensure that dissipation levels, water temperature, dissolved oxygen and pH are correctly reproduced under laboratory conditions. Laboratory results for biomass accrual and photosynthetic activity suggest that turbulence levels within the range observed in the field, mediates the metabolism, rather than the cell population growth, of Microcystis aeruginosa. This work was supported by the NSF Graduate Research Fellowship and University of Minnesota start-up funding.
Degradation of homogeneous polymer solutions in high shear turbulent pipe flow
NASA Astrophysics Data System (ADS)
Elbing, B. R.; Winkel, E. S.; Solomon, M. J.; Ceccio, S. L.
2009-12-01
This study quantifies degradation of polyethylene oxide (PEO) and polyacrylamide (PAM) polymer solutions in large diameter (2.72 cm) turbulent pipe flow at Reynolds numbers to 3 × 105 and shear rates greater than 105 1/s. The present results support a universal scaling law for polymer chain scission reported by Vanapalli et al. (2006) that predicts the maximum chain drag force to be proportional to Re 3/2, validating this scaling law at higher Reynolds numbers than prior studies. Use of this scaling gives estimated backbone bond strengths from PEO and PAM of 3.2 and 3.8 nN, respectively. Additionally, with the use of synthetic seawater as a solvent the onset of drag reduction occurred at higher shear rates relative to the pure water solvent solutions, but had little influence on the extent of degradation at higher shear rates. These results are significant for large diameter pipe flow applications that use polymers to reduce drag.
Rapid distortion analysis of high speed homogeneous turbulence subject to periodic shear
Bertsch, Rebecca L.; Girimaji, Sharath S.
2015-12-30
The effect of unsteady shear forcing on small perturbation growth in compressible flow is investigated. In particular, flow-thermodynamic field interaction and the resulting effect on the phase-lag between applied shear and Reynolds stress are examined. Simplified linear analysis of the perturbation pressure equation reveals crucial differences between steady and unsteady shear effects. The analytical findings are validated with numerical simulations of inviscid rapid distortion theory (RDT) equations. In contrast to steadily sheared compressible flows, perturbations in the unsteady (periodic) forcing case do not experience an asymptotic growth phase. Further, the resonance growth phenomenon found in incompressible unsteady shear turbulence is absent in the compressible case. Overall, the stabilizing influence of both unsteadiness and compressibility is compounded leading to suppression of all small perturbations. As a result, the underlying mechanisms are explained.
Rapid distortion analysis of high speed homogeneous turbulence subject to periodic shear
Bertsch, Rebecca L.; Girimaji, Sharath S.
2015-12-30
The effect of unsteady shear forcing on small perturbation growth in compressible flow is investigated. In particular, flow-thermodynamic field interaction and the resulting effect on the phase-lag between applied shear and Reynolds stress are examined. Simplified linear analysis of the perturbation pressure equation reveals crucial differences between steady and unsteady shear effects. The analytical findings are validated with numerical simulations of inviscid rapid distortion theory (RDT) equations. In contrast to steadily sheared compressible flows, perturbations in the unsteady (periodic) forcing case do not experience an asymptotic growth phase. Further, the resonance growth phenomenon found in incompressible unsteady shear turbulence ismore » absent in the compressible case. Overall, the stabilizing influence of both unsteadiness and compressibility is compounded leading to suppression of all small perturbations. As a result, the underlying mechanisms are explained.« less
Rotor noise due to atmospheric turbulence ingestion. I - Fluid mechanics
NASA Technical Reports Server (NTRS)
Simonich, J. C.; Amiet, R. K.; Schlinker, R. H.; Greitzer, E. M.
1986-01-01
In the present analytical procedure for the prediction of helicopter rotor noise generation due to the ingestion of atmospheric turbulence, different models for turbulence fluid mechanics and the ingestion process are combined. The mean flow and turbulence statistics associated with the atmospheric boundary layer are modeled with attention to the effects of atmospheric stability length, windspeed, and altitude. The turbulence field can be modeled as isotropic, locally stationary, and homogeneous. For large mean flow contraction ratios, accurate predictions of turbulence vorticity components at the rotor face requires the incorporation of the differential drift of fluid particles on adjacent streamlines.
NASA Technical Reports Server (NTRS)
Debussche, A.; Dubois, T.; Temam, R.
1993-01-01
Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.
NASA Astrophysics Data System (ADS)
Thornber, B.
2016-04-01
Both experiments and computations are naturally constrained by boundary conditions. In fundamental problems such as homogeneous decaying turbulence (HDT) or shock-induced mixing layers, a size constraint naturally limits the growth of the large scales in the problem, modifying the physics observed. This paper explores through Large Eddy Simulation (LES) the integral properties using computations from 1283 to 10243 for HDT and 1283 to 5123 for the Richtmyer-Meshkov instability (RMI). Kinetic energy decay rates in both cases are shown to be relatively insensitive to the domain size until the spectral peak is at the first wave number. The integral length is significantly more sensitive, showing substantial discrepancies once it is greater than 10% of the domain size. However, the key error is shown to be due to a lack of statistical averaging once the integral length is greater than 5% of the box size, thus appearing earlier than the length scale saturation. This highlights that a single computation at modest grid resolution (≤2563) may not reproduce the correct physics and that at this resolution, numericists need to embrace the practice of using multiple independent realisations to reduce the statistical error, as is the norm for the experimentalist. Finally, an update on the physics of HDT and RMI as predicted through LES computations is presented.
PDF methods for combustion in high-speed turbulent flows
NASA Technical Reports Server (NTRS)
Pope, Stephen B.
1995-01-01
This report describes the research performed during the second year of this three-year project. The ultimate objective of the project is extend the applicability of probability density function (pdf) methods from incompressible to compressible turbulent reactive flows. As described in subsequent sections, progress has been made on: (1) formulation and modelling of pdf equations for compressible turbulence, in both homogeneous and inhomogeneous inert flows; and (2) implementation of the compressible model in various flow configurations, namely decaying isotropic turbulence, homogeneous shear flow and plane mixing layer.
The spatio-temporal spectrum of turbulent flows.
Clark di Leoni, P; Cobelli, P J; Mininni, P D
2015-12-01
Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different restitutive forces. We show how to compute and analyse the spatio-temporal spectrum from data stemming from numerical simulations and from laboratory experiments. Four cases are considered: homogeneous and isotropic turbulence, rotating turbulence, stratified turbulence, and water wave turbulence. For homogeneous and isotropic turbulence, the spectrum allows identification of sweeping by the large-scale flow. For rotating and for stratified turbulence, the spectrum allows identification of the waves, precise quantification of the energy in the waves and in the turbulent eddies, and identification of physical mechanisms such as Doppler shift and wave absorption in critical layers. Finally, in water wave turbulence the spectrum shows a transition from gravity-capillary waves to bound waves as the amplitude of the forcing is increased. PMID:26701711
Effect of Contraction on Turbulence and Temperature Fluctuations Generated by a Warm Grid
NASA Technical Reports Server (NTRS)
Mills, Robert R., Jr.; Corrsin, Stanley
1959-01-01
Hot-wire anemometer measurements were made of several statistical properties of approximately homogeneous and isotropic fields of turbulence and temperature fluctuations generated by a warm grid in a uniform airstream sent through a 4-to-1 contraction. These measurements were made both in the contraction and in the axisymmetric domain farther downstream. In addition to confirming the well-known turbulence anisotropy induced by strain, the data show effects on the skewnesses of both longitudinal velocity fluctuation (which has zero skewness in isotropic turbulence) and its derivative. The concomitant anisotropy in the temperature field accelerates the decay of temperature fluctuations.
NASA Astrophysics Data System (ADS)
Lee, Insu
Confined non-reacting turbulent jets are ideal for recirculating the hot flue gas back into the furnace from an external exhaust duct. Such jets are also used inside the furnace to internally entrain and recirculate the hot flue gas to preheat and dilute the reactants. Both internal and external implementation of confined turbulent jets increase the furnace thermal efficiency. For external implementation, depending on the circumstances, the exhaust gas flow may be co- or counter-flow relative to the jet flow. Inside the furnaces, fuel and air jets are injected separately. To create a condition which can facilitate near homogeneous combustion, these jets have to first mix with the burned gas inside the furnace and simultaneously being heated and diluted prior to combustion. Clearly, the combustion pattern and emissions from reacting confined turbulent jets are affected by jet interactions, mixing and entrainment of hot flue gas. In this work, the flow and mixing characteristics of a non-reacting and reacting confined turbulent jet are investigated experimentally and numerically. This work consists of two parts: (i) A study of flow and mixing characteristics of non-reacting confined turbulent jets with co- or counter-flowing exhaust/flue gas. Here the axial and radial distributions of temperature, velocity and NO concentration (used as a tracer gas) were measured. FLUENT was used to numerically simulate the experimental results. This work provides the basic understanding of the flow and mixing characteristics of confined turbulent jets and develops some design considerations for recirculating flue gas back into the furnace as expressed by the recirculation zone and the stagnation locations. (ii) Numerical calculations of near homogeneous combustion are performed for the existing furnace. The exact geometry of the furnace in the lab is used and the real dimensional boundary conditions are considered. The parameters such as air nozzle diameter (dair), fuel nozzle
Experiments on the interaction between hydrodynamic turbulence and surface waves
NASA Astrophysics Data System (ADS)
Jamin, Timothee; Berhanu, Michael; Falcon, Eric
2014-11-01
Different regimes of interaction between hydrodynamic turbulence and a free surface are investigated in a meter scale basin. A homogeneous and isotropic turbulence is generated by an 8×8 array of jets pointing upwards at the bottom of the tank. The 64 jets are driven individually to reach a random spatiotemporal forcing pattern and produce an intense turbulence. Using fluid velocity measurements, we characterize the turbulence obtained with this setup, then we investigate free-surface deformations induced by hydrodynamic turbulence. In a second stage an electromechanical shaker will generate gravity-capillary waves at the free surface. We aim to study reduction or amplification of surface waves and then measure energy exchange between hydrodynamic turbulence and wave turbulence. This work was supported by the DGA-CNRS Ph.D program and ANR Turbulon 12-BS04-0005.
Power fluctuations, large deviations and turbulence
Bandi, Mahesh M; Chumakov, Sergei; Connaughton, Colm P
2008-01-01
We study local power fluctuations in numerical simulations of stationary, homogenous, isotropic turbulence in two and three dimensions with Gaussian forcing. Due to the near-Gaussianity of the one-point velocity distribution, the probability distribution function (pdf) of the local power is well modeled by the pdf of the product of two joint normally distributed variables. In appropriate units, this distribution is calculated exactly and shown to satisfy a Fluctuation Relation (FR) with a coefficient which depends on {epsilon}.
Structure and scales in turbulence modeling
NASA Astrophysics Data System (ADS)
Reynolds, W. C.; Langer, C. A.; Kassinos, S. C.
2002-07-01
The enstrophy of the large-scale energy-containing turbulence is proposed as the second turbulence scale for use, in conjunction with the turbulence energy, in two-scale one-point engineering turbulence models. Its transport equation is developed in general and modeled for homogeneous turbulence in terms of the two scales and our new one-point structure tensors. The model produces the correct behavior of the scales for both two- and three-dimensional turbulence. Constants in the high Reynolds number model are evaluated only by reference to asymptotic analysis for decaying turbulence in stationary and rotating frames, and this model is then shown to provide an excellent prediction of homogeneous turbulent shear flow when used with the structure tensors for that flow. The low Reynolds number constant in the model is evaluated using the asymptotic decay rate for isotropic turbulence at zero Reynolds number, and numerical simulations of decay for intermediate Reynolds numbers are used to establish one remaining constant, the value of which does not affect high Reynolds number predictions.
NASA Astrophysics Data System (ADS)
Frisch, Uriel
1996-01-01
Written five centuries after the first studies of Leonardo da Vinci and half a century after A.N. Kolmogorov's first attempt to predict the properties of flow, this textbook presents a modern account of turbulence, one of the greatest challenges in physics. "Fully developed turbulence" is ubiquitous in both cosmic and natural environments, in engineering applications and in everyday life. Elementary presentations of dynamical systems ideas, probabilistic methods (including the theory of large deviations) and fractal geometry make this a self-contained textbook. This is the first book on turbulence to use modern ideas from chaos and symmetry breaking. The book will appeal to first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, as well as professional scientists and engineers.
Rotating turbulence under "precession-like" perturbation.
Iyer, Kartik P; Mazzitelli, Irene; Bonaccorso, Fabio; Pouquet, Annick; Biferale, Luca
2015-12-01
The effects of changing the orientation of the rotation axis on homogeneous turbulence is considered. We perform direct numerical simulations on a periodic box of 1024(3) grid points, where the orientation of the rotation axis is changed (a) at a fixed time instant (b) regularly at time intervals commensurate with the rotation time scale. The former is characterized by a dominant inverse energy cascade whereas in the latter, the inverse cascade is stymied due to the recurrent changes in the rotation axis resulting in a strong forward energy transfer and large-scale structures that resemble those of isotropic turbulence. PMID:26637337
A Quadratic Closure for Compressible Turbulence
Futterman, J A
2008-09-16
We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.
Small-scale universality in fluid turbulence
Schumacher, Jörg; Scheel, Janet D.; Krasnov, Dmitry; Donzis, Diego A.; Yakhot, Victor; Sreenivasan, Katepalli R.
2014-01-01
Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re ∼ 102 the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range. PMID:25024175
NASA Technical Reports Server (NTRS)
Schiestel, R.
1987-01-01
The CTR numerical data base generated by direct simulation of homogeneous anisotropic turbulence was used to calculate all of the terms in the spectral balance equations for the turbulent Reynolds stresses. The aim in not only to test the main closure assumptions used in the split-spectrum models, but also to try to devise improved hypotheses deduced from the statistical information. Numerical simulations of turbulent flows provide a large amount of data, a thought provoking wealth of information. The main advantage of this type of comparison is that a great variety of flows can be considered, and this is necessary to test closure hypotheses. Moreover various initial conditions can be introduced in the calculation, even if they are not experimentally feasible. All the terms in the spectral equations can be calculated. The limited Reynolds numbers of the simulations and the statistical noise caused by a small sample, particularly at the large scales, causes some difficulty in the interpretation of the results, but the method of approach proved to be a powerful tool for testing and improving spectral closures.
Direct simulation of compressible turbulence in a shear flow
NASA Technical Reports Server (NTRS)
Sarkar, S.; Erlebacher, G.; Hussaini, M. Y.
1991-01-01
Compressibility effects on the turbulence in homogeneous shear flow are investigated. The growth of the turbulent kinetic energy was found to decrease with increasing Mach number: a phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. Previously, the following results were obtained for isotropic turbulence: (1) the normalized compressible dissipation is of O(M(sub t)(exp 2)); and (2) there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both of these results were substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.
A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing
Schwarzkopf, J. D.; Livescu, D.; Baltzer, J. R.; Gore, R. A.; Ristorcelli, J. R.
2015-09-08
A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. Additionally, the importance of using DNS to calibrate and assess RANS type turbulence models is highlighted.
PDF turbulence modeling and DNS
NASA Technical Reports Server (NTRS)
Hsu, A. T.
1992-01-01
The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.
Turbulent flows near flat plates
NASA Astrophysics Data System (ADS)
Kambe, R.; Imamura, T.; Doi, M.
1980-08-01
The method to study the effect of the plate moving in the homogeneous or isotropic turbulence is presented. The crucial point of this method is to solve the Orr-Sommerfeld like equation, which is satisfied by the kernel of the Wiener-Hermite expansion of the velocity field, under the inhomogeneous boundary condition. In the special case of constant mean flow, our method gives the same result as that of Hunt and Graham and succeeds in explaining the experimental results of Thomas and Hancock. The method is also applied to the case of nonuniform mean flow, where the shear effect comes up.
NASA Technical Reports Server (NTRS)
Liu, Xiao-Feng; Thomas, Flint O.; Nelson, Robert C.
2001-01-01
Turbulence kinetic energy (TKE) is a very important quantity for turbulence modeling and the budget of this quantity in its transport equation can provide insight into the flow physics. Turbulence kinetic energy budget measurements were conducted for a symmetric turbulent wake flow subjected to constant zero, favorable and adverse pressure gradients in year-three of research effort. The purpose of this study is to clarify the flow physics issues underlying the demonstrated influence of pressure gradient on wake development and provide experimental support for turbulence modeling. To ensure the reliability of these notoriously difficult measurements, the experimental procedure was carefully designed on the basis of an uncertainty analysis. Four different approaches, based on an isotropic turbulence assumption, a locally axisymmetric homogeneous turbulence assumption, a semi-isotropy assumption and a forced balance of the TKE equation, were applied for the estimate of the dissipation term. The pressure transport term is obtained from a forced balance of the turbulence kinetic energy equation. This report will present the results of the turbulence kinetic energy budget measurement and discuss their implication on the development of strained turbulent wakes.
Numerical simulation of turbulence in the presence of shear
NASA Technical Reports Server (NTRS)
Shaanan, S.; Ferziger, J. H.; Reynolds, W. C.
1975-01-01
The numerical calculations are presented of the large eddy structure of turbulent flows, by use of the averaged Navier-Stokes equations, where averages are taken over spatial regions small compared to the size of the computational grid. The subgrid components of motion are modeled by a local eddy-viscosity model. A new finite-difference scheme is proposed to represent the nonlinear average advective term which has fourth-order accuracy. This scheme exhibits several advantages over existing schemes with regard to the following: (1) the scheme is compact as it extends only one point away in each direction from the point to which it is applied; (2) it gives better resolution for high wave-number waves in the solution of Poisson equation, and (3) it reduces programming complexity and computation time. Examples worked out in detail are the decay of isotropic turbulence, homogeneous turbulent shear flow, and homogeneous turbulent shear flow with system rotation.
NASA Technical Reports Server (NTRS)
Childs, D. W.; Kim, C. H.
1984-01-01
A theory is presented, based on a simple modification of Hirs' turbulent lubrication equations, to account for different but directionally-homogeneous surface roughness treatments for the rotor and stator of annular seals. The theoretical results agree with von Pragenau's predictions that a damper seal which uses a smooth rotor and a rough stator yields more net damping than a conventional seal which has the same roughness for both the rotor and stator. Experimental results for four stators confirm that properly-designed roughened stators yield higher net damping values and substantially less leakage than seals with smooth surfaces. The best seal from both damping and leakage viewpoints uses a round-hole-pattern stator. Initial results for this stator suggest that, within limits, seals can be designed to yield specified ratios of stiffness to damping.
Maartens, Roy
2011-12-28
The standard model of cosmology is based on the existence of homogeneous surfaces as the background arena for structure formation. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we interpret observations of the cosmic microwave background (CMB) and the galaxy distribution. However, homogeneity cannot be directly observed in the galaxy distribution or CMB, even with perfect observations, since we observe on the past light cone and not on spatial surfaces. We can directly observe and test for isotropy, but to link this to homogeneity we need to assume the Copernican principle (CP). First, we discuss the link between isotropic observations on the past light cone and isotropic space-time geometry: what observations do we need to be isotropic in order to deduce space-time isotropy? Second, we discuss what we can say with the Copernican assumption. The most powerful result is based on the CMB: the vanishing of the dipole, quadrupole and octupole of the CMB is sufficient to impose homogeneity. Real observations lead to near-isotropy on large scales--does this lead to near-homogeneity? There are important partial results, and we discuss why this remains a difficult open question. Thus, we are currently unable to prove homogeneity of the Universe on large scales, even with the CP. However, we can use observations of the cosmic microwave background, galaxies and clusters to test homogeneity itself. PMID:22084298
Coupling Turbulence in Hybrid LES-RANS Techniques
NASA Technical Reports Server (NTRS)
Woodruff, Stephen L.
2011-01-01
A formulation is proposed for hybrid LES-RANS computations that permits accurate computations during resolution changes, so that resolution may be changed at will in order to employ only as much resolution in each subdomain as is required by the physics. The two components of this formulation, establishing the accuracy of a hybrid model at constant resolutions throughout the RANS-to-LES range and maintaining that accuracy when resolution is varied, are demonstrated for decaying, homogeneous, isotropic turbulence.
Measuring turbulent fluid dispersion using laser induced phosphorescence
NASA Astrophysics Data System (ADS)
van der Voort, Dennis; Dam, Nico; van de Water, Willem; Kunnen, Rudie; Clercx, Herman; van Heijst, Gertjan
2015-11-01
Fluid dispersion due to turbulence is an important subject in both natural and engineering processes, from cloud formation to turbulent mixing and liquid spray combustion. The combination of small scales and often high velocities results in few experimental techniques that can follow the course of events. We introduce a novel technique, which measures the dispersion of ``tagged'' fluid particles by means of laser-induced phosphorescence, using a solution containing a europium-based molecular complex with a relatively long phosphorescence half-life. This technique is used to measure transport processes in both the dispersion of droplets in homogeneous isotropic turbulence and the dispersion of fluid of near-nozzle spray breakup processes. By tagging a small amount of droplets/fluid via laser excitation, the tagged droplets can be tracked in a Lagrangian way. The absolute dispersion of the droplets can be measured in a variety of turbulent flows. Using this technique it is shows that droplets around St =τp /τη ~ 1 (Stokes number) disperse faster than true fluid tracers in homogeneous isotropic turbulence, as well as differences between longitudinal and radial dispersion in turbulent sprays. This work is part of the research programme of the Foundation for Fundamental Research on Matter (FOM), which is part of the Dutch Organisation for Scientific Research (NWO).
Second-order closure models for supersonic turbulent flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Sarkar, Sutanu
1991-01-01
Recent work on the development of a second-order closure model for high-speed compressible flows is reviewed. This turbulent closure is based on the solution of modeled transport equations for the Favre-averaged Reynolds stress tensor and the solenoidal part of the turbulent dissipation rate. A new model for the compressible dissipation is used along with traditional gradient transport models for the Reynolds heat flux and mass flux terms. Consistent with simple asymptotic analyses, the deviatoric part of the remaining higher-order correlations in the Reynolds stress transport equations are modeled by a variable density extension of the newest incompressible models. The resulting second-order closure model is tested in a variety of compressible turbulent flows which include the decay of isotropic turbulence, homogeneous shear flow, the supersonic mixing layer, and the supersonic flat-plate turbulent boundary layer. Comparisons between the model predictions and the results of physical and numerical experiments are quite encouraging.
Analysis of two-equation turbulence models for recirculating flows
NASA Technical Reports Server (NTRS)
Thangam, S.
1991-01-01
The two-equation kappa-epsilon model is used to analyze turbulent separated flow past a backward-facing step. It is shown that if the model constraints are modified to be consistent with the accepted energy decay rate for isotropic turbulence, the dominant features of the flow field, namely the size of the separation bubble and the streamwise component of the mean velocity, can be accurately predicted. In addition, except in the vicinity of the step, very good predictions for the turbulent shear stress, the wall pressure, and the wall shear stress are obtained. The model is also shown to provide good predictions for the turbulence intensity in the region downstream of the reattachment point. Estimated long time growth rates for the turbulent kinetic energy and dissipation rate of homogeneous shear flow are utilized to develop an optimal set of constants for the two equation kappa-epsilon model. The physical implications of the model performance are also discussed.
Extreme events in computational turbulence
Yeung, P. K.; Zhai, X. M.; Sreenivasan, Katepalli R.
2015-01-01
We have performed direct numerical simulations of homogeneous and isotropic turbulence in a periodic box with 8,1923 grid points. These are the largest simulations performed, to date, aimed at improving our understanding of turbulence small-scale structure. We present some basic statistical results and focus on “extreme” events (whose magnitudes are several tens of thousands the mean value). The structure of these extreme events is quite different from that of moderately large events (of the order of 10 times the mean value). In particular, intense vorticity occurs primarily in the form of tubes for moderately large events whereas it is much more “chunky” for extreme events (though probably overlaid on the traditional vortex tubes). We track the temporal evolution of extreme events and find that they are generally short-lived. Extreme magnitudes of energy dissipation rate and enstrophy occur simultaneously in space and remain nearly colocated during their evolution. PMID:26424452
NASA Astrophysics Data System (ADS)
Liu, Yangwei; Lu, Lipeng; Fang, Le; Gao, Feng
2011-06-01
The correlation between the velocity helicity and the energy backscatter is proved in a DNS case of 256 3-grid homogeneous isotropic decaying turbulence. The helicity is then proposed to be employed to improve turbulence models and SGS models. Then Spalart-Allmaras turbulence model (SA) is modified with the helicity to take account of the energy backscatter, which is significant in the region of corner separation in compressors. By comparing the numerical results with experiments, it can be concluded that the modification for SA model with helicity can appropriately represent the energy backscatter, and greatly improves the predictive accuracy for simulating the corner separation flow in compressors.
Fluidic harvesters in free stream turbulence undergoing flow-induced vibrations or flutter
NASA Astrophysics Data System (ADS)
Gomez, Joan; Azadeh Ranjbar, Vahid; Goushcha, Oleg; Andreopoulos, Yiannis; Elvin, Niell
2015-11-01
In the present experimental work we investigated the performance of fluidic harvesters consisting of cylindrical body mounted of the tip of a flexible beam in the presence of nearly homogeneous and isotropic turbulence. Circular, semi-circular and square shapes have been tested. It was found that turbulence interferes with resonance conditions between the flow and the structure in the case of vortex induced vibrations and has absolutely no effect in flutter dominated case. As a result, turbulence increases the power output of non-linear harvesters subjected to vortex induces vibration and it has no effect in harvester under flutter conditions. Supported by NSF Grant: CBET #1033117.
Grid superfluid turbulence and intermittency at very low temperature
NASA Astrophysics Data System (ADS)
Krstulovic, Giorgio
2016-06-01
Low-temperature grid-generated turbulence is investigated by using numerical simulations of the Gross-Pitaevskii equation. The statistics of regularized velocity increments are studied. Increments of the incompressible velocity are found to be skewed for turbulent states. Results are later confronted with the (quasi) homogeneous and isotropic Taylor-Green flow, revealing the universality of the statistics. For this flow, the statistics are found to be intermittent and a Kolmogorov constant close to the one of classical fluid is found for the second-order structure function.
Some Results Relevant to Statistical Closures for Compressible Turbulence
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1998-01-01
For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.
NASA Astrophysics Data System (ADS)
Salhi, A.; Cambon, C.
2007-05-01
Angular phase mixing in rapidly rotating or in strongly stratified flows is quantified for single-time single-point energy components, using linear theory. In addition to potential energy, turbulent kinetic energy is more easily analyzed in terms of its toroidal and poloidal components, and then in terms of vertical and horizontal components. Since the axial symmetry around the direction n (which bears both the system angular velocity and the mean density gradient) is consistent with basic dynamical equations, the input of initial anisotropy is investigated in the axisymmetric case. A general way to construct axisymmetric initial data is used, with a classical expansion in terms of scalar spherical harmonics for the 3D spectral density of kinetic energy e, and a modified expansion for the polarization anisotropy Z, which reflects the unbalance in terms of poloidal and toroidal energy components. The expansion involves Legendre polynomials of arbitrary order, P2n0(cosθ), (n=0,1,2,…,N0), in which the term [cosθ=(k•n)/∣k∣] characterizes the anisotropy in k-wavespace; two sets of parameters, β2n(e) and β2n(z), separately generate the directional anisotropy and the polarization anisotropy. In the rotating case, the phase mixing results in damping the polarization anisotropy, so that toroidal and poloidal energy components asymptotically equilibrate after transient oscillations. Complete analytical solutions are found in terms of Bessel functions. The envelope of these oscillations decay with time like (ft)-2 (f being the Coriolis parameter), whereas those for the vertical and horizontal components decay like (ft)-3. The long-time limit of the ratio of horizontal component to vertical one depends only on β2(e), which is eventually related to a classical component in structure-based modeling, independently of the degree of the expansion of the initial data. For the stratified case, both the degree of initial anisotropy and the initial unbalance in terms of
Effects of axisymmetric contractions on turbulence of various scales
NASA Technical Reports Server (NTRS)
Tan-Atichat, J.; Nagib, H. M.; Drubka, R. E.
1980-01-01
Digitally acquired and processed results from an experimental investigation of grid generated turbulence of various scales through and downstream of nine matched cubic contour contractions ranging in area ratio from 2 to 36, and in length to inlet diameter ratio from 0.25 to 1.50 are reported. An additional contraction with a fifth order contour was also utilized for studying the shape effect. Thirteen homogeneous and nearly isotropic test flow conditions with a range of turbulence intensities, length scales and Reynolds numbers were generated and used to examine the sensitivity of the contractions to upstream turbulence. The extent to which the turbulence is altered by the contraction depends on the incoming turbulence scales, the total strain experienced by the fluid, as well as the contraction ratio and the strain rate. Varying the turbulence integral scale influences the transverse turbulence components more than the streamwise component. In general, the larger the turbulence scale, the lesser the reduction in the turbulence intensity of the transverse components. Best agreement with rapid distortion theory was obtained for large scale turbulence, where viscous decay over the contraction length was negligible, or when a first order correction for viscous decay was applied to the results.
The analysis and modeling of dilatational terms in compressible turbulence
NASA Technical Reports Server (NTRS)
Sarkar, S.; Erlebacher, G.; Hussaini, M. Y.; Kreiss, H. O.
1989-01-01
It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.
A Transversely Isotropic Thermoelastic Theory
NASA Technical Reports Server (NTRS)
Arnold, S. M.
1989-01-01
A continuum theory is presented for representing the thermoelastic behavior of composites that can be idealized as transversely isotropic. This theory is consistent with anisotropic viscoplastic theories being developed presently at NASA Lewis Research Center. A multiaxial statement of the theory is presented, as well as plane stress and plane strain reductions. Experimental determination of the required material parameters and their theoretical constraints are discussed. Simple homogeneously stressed elements are examined to illustrate the effect of fiber orientation on the resulting strain distribution. Finally, the multiaxial stress-strain relations are expressed in matrix form to simplify and accelerate implementation of the theory into structural analysis codes.
Accumulation of motile elongated micro-organisms in turbulence
NASA Astrophysics Data System (ADS)
Zhan, Caijuan; Sardina, Gaetano; Lushi, Enkeleida; Brandt, Luca
2014-01-01
We study the effect of turbulence on marine life by performing numerical simulations of motile microorganisms, modelled as prolate spheroids, in isotropic homogeneous turbulence. We show that the clustering and patchiness observed in laminar flows, linear shear and vortex flows, are significantly reduced in a three-dimensional turbulent flow mainly because of the complex topology; elongated micro-orgamisms show some level of clustering in the case of swimmers without any preferential alignment whereas spherical swimmers remain uniformly distributed. Micro-organisms with one preferential swimming direction (e.g. gyrotaxis) still show significant clustering if spherical in shape, whereas prolate swimmers remain more uniformly distributed. Due to their large sensitivity to the local shear, these elongated swimmers react slower to the action of vorticity and gravity and therefore do not have time to accumulate in a turbulent flow. These results show how purely hydrodynamic effects can alter the ecology of microorganisms that can vary their shape and their preferential orientation.
Effects of Gravity on Sheared Turbulence Laden with Bubbles or Droplets
NASA Technical Reports Server (NTRS)
Elghobashi, Said; Lasheras, Juan
1999-01-01
The objective of this numerical/experimental study is to improve the understanding of the effects of gravity on the two-way interaction between dispersed particles (bubbles or liquid droplets) and the carrier turbulent flow. The first phase of the project considers isotropic turbulence. Turbulent homogeneous shear flows laden with droplets/bubbles will be studied in the next phase. The experiments reported here are concerned with the dispersion of liquid droplets by homogeneous turbulence under various gravitational conditions and the effect of these droplets on the evolution of the turbulence of the carrier fluid (air). Direct numerical simulations (DNS) of bubble - laden isotropic decaying turbulence are performed using the two-fluid approach (TF) instead of the Eulerian-Lagrangian approach (EL). The motivation for using the TF formulation is that EL requires considerable computational resources especially for the case of two-way coupling where the instantaneous trajectories of a large number of individual bubbles need to be computed. The TF formulation is developed by spatially averaging the instantaneous equations of the carrier flow and bubble phase over a scale of the order of the Kolmogorov length scale which, in our case, is much larger than the bubble diameter. On that scale, the bubbles are treated as a continuum (without molecular diffusivity) characterized by the bubble phase velocity field and concentration (volume fraction). The bubble concentration, C, is assumed small enough to neglect the bubble-bubble interactions.
Coherence in Turbulence: New Perspective
NASA Astrophysics Data System (ADS)
Levich, Eugene
2009-07-01
It is claimed that turbulence in fluids is inherently coherent phenomenon. The coherence shows up clearly as strongly correlated helicity fluctuations of opposite sign. The helicity fluctuations have cellular structure forming clusters that are actually observed as vorticity bands and coherent structures in laboratory turbulence, direct numerical simulations and most obviously in atmospheric turbulence. The clusters are named BCC - Beltrami Cellular Clusters - because of the observed nearly total alignment of the velocity and vorticity fields in each particular cell, and hence nearly maximal possible helicity in each cell; although when averaged over all the cells the residual mean helicity in general is small and does not play active dynamical role. The Beltrami like fluctuations are short-lived and stabilize only in small and generally contiguous sub-domains that are tending to a (multi)fractal in the asymptotic limit of large Reynolds numbers, Re → ∞. For the model of homogeneous isotropic turbulence the theory predicts the leading fractal dimension of BCC to be: DF = 2.5. This particular BCC is responsible for generating the Kolmogorov -5/3 power law energy spectrum. The most obvious role that BCC play dynamically is that the nonlinear interactions in them are relatively reduced, due to strong spatial alignment between the velocity field v(r, t) and the vorticity field ω(r, t) = curlv(r, t), while the physical quantities typically best characterizing turbulence intermittency, such as entrophy, vorticity stretching and generation, and energy dissipation are maximized in and near them. The theory quantitatively relates the reduction of nonlinear inter-actions to the BCC fractal dimension DF and subsequent turbulence intermittency. It is further asserted that BCC is a fundamental feature of all turbulent flows, e.g., wall bounded turbulent flows, atmospheric and oceanic flows, and their leading fractal dimension remains invariant and universal in these flows
Lagrangian statistics of light particles in turbulence
NASA Astrophysics Data System (ADS)
Mercado, Julián Martínez; Prakash, Vivek N.; Tagawa, Yoshiyuki; Sun, Chao; Lohse, Detlef; (International CollaborationTurbulence Research)
2012-05-01
We study the Lagrangian velocity and acceleration statistics of light particles (micro-bubbles in water) in homogeneous isotropic turbulence. Micro-bubbles with a diameter db = 340 μm and Stokes number from 0.02 to 0.09 are dispersed in a turbulent water tunnel operated at Taylor-Reynolds numbers (Reλ) ranging from 160 to 265. We reconstruct the bubble trajectories by employing three-dimensional particle tracking velocimetry. It is found that the probability density functions (PDFs) of the micro-bubble acceleration show a highly non-Gaussian behavior with flatness values in the range 23 to 30. The acceleration flatness values show an increasing trend with Reλ, consistent with previous experiments [G. Voth, A. La Porta, A. M. Crawford, J. Alexander, and E. Bodenschatz, "Measurement of particle accelerations in fully developed turbulence," J. Fluid Mech. 469, 121 (2002)], 10.1017/S0022112002001842 and numerics [T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, and A. Uno, "Small-scale statistics in highresolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics," J. Fluid Mech. 592, 335 (2007)], 10.1017/S0022112007008531. These acceleration PDFs show a higher intermittency compared to tracers [S. Ayyalasomayajula, Z. Warhaft, and L. R. Collins, "Modeling inertial particle acceleration statistics in isotropic turbulence," Phys. Fluids. 20, 095104 (2008)], 10.1063/1.2976174 and heavy particles [S. Ayyalasomayajula, A. Gylfason, L. R. Collins, E. Bodenschatz, and Z. Warhaft, "Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence," Phys. Rev. Lett. 97, 144507 (2006)], 10.1103/PhysRevLett.97.144507 in wind tunnel experiments. In addition, the micro-bubble acceleration autocorrelation function decorrelates slower with increasing Reλ. We also compare our results with experiments in von Kármán flows and point-particle direct numerical simulations with periodic
Theory and modeling of atmospheric turbulence, part 1
NASA Technical Reports Server (NTRS)
1984-01-01
The cascade transfer which is the only function to describe the mode coupling as the result of the nonlinear hydrodynamic state of turbulence is discussed. A kinetic theory combined with a scaling procedure was developed. The transfer function governs the non-linear mode coupling in strong turbulence. The master equation is consistent with the hydrodynamical system that describes the microdynamic state of turbulence and has the advantages to be homogeneous and have fewer nonlinear terms. The modes are scaled into groups to decipher the governing transport processes and statistical characteristics. An equation of vorticity transport describes the microdynamic state of two dimensional, isotropic and homogeneous, geostrophic turbulence. The equation of evolution of the macrovorticity is derived from group scaling in the form of the Fokker-Planck equation with memory. The microdynamic state of turbulence is transformed into the Liouville equation to derive the kinetic equation of the singlet distribution in turbulence. The collision integral contains a memory, which is analyzed with pair collision and the multiple collision. Two other kinetic equations are developed in parallel for the propagator and the transition probability for the interaction among the groups.
Effect of the driving algorithm on the turbulence generated by a random jet array
NASA Astrophysics Data System (ADS)
Pérez-Alvarado, Alejandro; Mydlarski, Laurent; Gaskin, Susan
2016-02-01
Different driving algorithms for a large random jet array (RJA) were tested and their performance characterized by comparing the statistics of the turbulence generated downstream of the RJA. Of particular interest was the spatial configuration of the jets operating at any given instant (an aspect that has not been documented in previous RJAs studies), as well as the statistics of their respective on/off times. All algorithms generated flows with nonzero skewnesses of the velocity fluctuation normal to the plane of the RJA (identified as an inherent limitation of the system resulting from the unidirectional forcing imposed from only one side of the RJA), and slightly super-Gaussian kurtoses of the velocity fluctuations in all directions. It was observed that algorithms imposing spatial configurations generated the most isotropic flows; however, they suffered from high mean flows and low turbulent kinetic energies. The algorithm identified as RANDOM (also referred to as the "sunbathing algorithm") generated the flow that, on an overall basis, most closely approximated zero-mean-flow homogeneous isotropic turbulence, with variations in horizontal and vertical homogeneities of RMS velocities of no more than ±6 %, deviations from isotropy ( w RMS/ u RMS) in the range of 0.62-0.77, and mean flows on the order of 7 % of the RMS velocities (determined by averaging their absolute values over the three velocity components and three downstream distances). A relatively high turbulent Reynolds number ( Re T = u T ℓ/ ν = 2360, where ℓ is the integral length scale of the flow and u T is a characteristic RMS velocity) was achieved using the RANDOM algorithm and the integral length scale ( ℓ = 11.5 cm) is the largest reported to date. The quality of the turbulence in our large facility demonstrates the ability of RJAs to be scaled-up and to be the laboratory system most capable of generating the largest quasi-homogeneous isotropic turbulent regions with zero mean flow.
A Jet-Stirred Apparatus for Turbulent Combustion Experiments
NASA Astrophysics Data System (ADS)
Davani, Abbasali; Ronney, Paul
2015-11-01
A novel jet-stirred combustion chamber is designed to study turbulent premixed flames. In the new approach, multiple impinging turbulent jets are used to stir the mixture. It is well known that pair of counterflowing turbulent jets produces nearly a constant intensity (u') along the jet axes. In this study, different numbers of impinging jets in various configurations are used to produce isotropic turbulence intensity. FLUENT simulations have been conducted to assess the viability of the proposed chamber. In order to be able to compare different configurations, three different non dimensional indices are introduces. Mean flow index; Homogeneity index, and Isotropicity index. Using these indices one can compare various chambers including conventional Fan-stirred Reactors. Results show that a concentric inlet/outlet chamber (CAIO) with 8 inlets and 8 outlets with inlet velocity of 20 m/s and initial intensity of 15% produces near zero mean flow and 2.5 m/s turbulence intensity which is much more higher than reported values for Fan-stirred chamber. This research was sponsored by National Science Foundation.
Energy spectra in elasto-inertial turbulence
NASA Astrophysics Data System (ADS)
Valente, P. C.; da Silva, C. B.; Pinho, F. T.
2016-07-01
Direct numerical simulations of statistically steady homogeneous isotropic turbulence in viscoelastic fluids described by the FENE-P model are presented. Emphasis is given to large polymer relaxation times compared to the eddy turnover time, which is a regime recently termed elasto-inertial turbulence. In this regime the polymers are ineffective in dissipating kinetic energy but they play a lead role in transferring kinetic energy to the small solvent scales which turns out to be concomitant with the depletion of the usual non-linear energy cascade. However, we show that the non-linear interactions are still highly active, but they lead to no net downscale energy transfer because the forward and reversed energy cascades are nearly balanced. Finally, we show that the tendency for a steeper elasto-inertial power-law spectra is reversed for large polymer relaxation times and the spectra tend towards the usual k-5/3 functional form.
A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing
Schwarzkopf, J. D.; Livescu, D.; Baltzer, J. R.; Gore, R. A.; Ristorcelli, J. R.
2015-09-08
A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales,more » as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. Additionally, the importance of using DNS to calibrate and assess RANS type turbulence models is highlighted.« less
Structure of wind-shear turbulence
NASA Technical Reports Server (NTRS)
Trevino, G.; Laituri, T. R.
1988-01-01
The statistical characteristics of wind-shear turbulence are modelled. Isotropic turbulence serves as the basis of comparison for the anisotropic turbulence which exists in wind shear. The question of how turbulence scales in a wind shear is addressed from the perspective of power spectral density.
Structure of wind-shear turbulence
NASA Technical Reports Server (NTRS)
Trevino, G.; Laituri, T. R.
1989-01-01
The statistical characteristics of wind shear turbulence are modelled. Isotropic turbulence serves as the basis of comparison for the anisotropic turbulence which exists in wind shear. The question of turbulence scales in wind shear is addressed from the perspective of power spectral density.
The alpha dynamo parameter and measurability of helicities in magnetohydrodynamic turbulence
NASA Technical Reports Server (NTRS)
Matthaeus, W. H.; Goldstein, M. L.; Lantz, S. R.
1986-01-01
Alpha, an important parameter in dynamo theory, is shown to be proportional to either the kinetic, current, magnetic, or velocity helicities of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first-order smoothed equations that describe the alpha effect. In two cases, viz., when alpha is proportional to either the magnetic helicity or velocity helicity, alpha can be determined experimentally from two-point measurements of the fluctuating fields in incompressible, homogeneous turbulence with arbitrary rotational symmetry. For the other two possibilities, alpha can be determined if the turbulence is isotropic.
Towed-Grid Studies of Quantum Turbulence
NASA Astrophysics Data System (ADS)
Liu, Shu-Chen; Labbe, Greg; Ihas, Gary G.
2006-11-01
We produce Homogeneous Isotropic Quantum Turbulence (HIQT) in liquid helium at 20 mK to compare with classical experiments and theories. Specifically, in the absence of viscosity, through what path does the turbulence decay? To produce HIQT we must quickly accelerate a grid to about 1 m/s in a channel of superfluid helium, tow it for 1 cm at a nearly constant speed, and then stop it equally quickly. To avoid joule and eddy current heating of the liquid helium, a magnetically shielded superconducting linear motor has been built, guided by simulations, along with the current pulses control program written in LabView with an embedded C compiler. The simulations, design process, and the experimental data demonstrating the functioning motor will be presented. We measure the HIQT energy decay mechanism using a calorimetric technique. Recent theory suggests the decay occurs through a Kelvin-wave cascade on the vortex lines which couples the initially large turbulent eddies to the short wavelength phonon spectrum of the liquid, yielding a characteristic rate of temperature rise. Doped germanium thermometers less than 300 μm diameter immersed in the turbulent helium allow fast calorimetric measurements to be made. The decay of turbulence is detected by the rate of temperature rise in the isolated cell after the grid is pulled.
Characteristics of the laminar-turbulent edge in transitional boundary layers
NASA Astrophysics Data System (ADS)
Lee, Jin; Zaki, Tamer
2015-11-01
Characteristics of the boundary separating the laminar and turbulent regions in a transitional boundary layer are examined using a time series of three-dimensional flow fields extracted from direct numerical simulations (DNS). In order to accurately mimic boundary-layer experiments perturbed by grid turbulence, the current simulation includes the leading edge of the flat plate and the incoming homogeneous isotropic turbulence. The Reynolds number based on the momentum thickness reaches up to 1400, and high-resolution three-dimensional flow fields of the DNS data will be publicly accessible via the Johns Hopkins Turbulence Database (JHTDB). The laminar-turbulence discrimination algorithm isolates the turbulence spots within the transition zone and the bounding surface of the fully-turbulent flow. Attention is placed on the cross-stream surface between the transition zone and fully-turbulent boundary layer. The shape of this interface is dictated by a balance between downstream advection, destabilization of upstream flow and merging of turbulence spots. Conditionally sampled statistics are examined across the interface, and are also compared to the downstream equilibrium turbulent boundary layer.
Diffusion of Sound Waves in a Turbulent Atmosphere
NASA Technical Reports Server (NTRS)
Lyon, Richard H.
1960-01-01
The directional and frequency diffusion of a plane monochromatic 2 sound wave in statistically homogeneous, isotropic, and stationary turbulence is analyzed theoretically. The treatment is based on the diffusion equation for the energy density of sound waves, using the scattering cross section derived by Kraichnan for the type of turbulence assumed here. A form for the frequency-wave number spectrum of the turbulence is adopted which contains the pertinent parameters of the flow and is adapted to ease of calculation. A new approach to the evaluation of the characteristic period of the flow is suggested. This spectrum is then related to the scattering cross section. Finally, a diffusion equation is derived as a small-angle scattering approximation to the rigorous transport equation. The rate of spread of the incident wave in frequency and direction is calculated, as well as the power spectrum and autocorrelation for the wave.
The effects of anisotropic free-stream turbulence on turbulent boundary layer behavior
NASA Technical Reports Server (NTRS)
Liang-Wei, F.; Hoffman, J. A.
1985-01-01
The effects of near-isotropic and highly anisotropic free-stream turbulence on mean flow properties of the turbulence structure of turbulent boundary layers in a near zero pressure gradient flow has been experimentally evaluated. Turbulence levels vary from 0.5% to 8.0% and the momentum thickness Reynolds number varies from 800 to 1100. The results indicate that the effects of free-stream turbulence on the classical boundary layer properties for near-isotropic turbulence which have been published by other investigators are similar to the case of highly anisotropic turbulence fields, while the effects of free-stream turbulence on the properties of the turbulent structure within the boundary layer for the case of near-isotropic turbulence are quite different compared to the highly anisotropic case.
Direct numerical simulation of turbulent reacting flows
Chen, J.H.
1993-12-01
The development of turbulent combustion models that reflect some of the most important characteristics of turbulent reacting flows requires knowledge about the behavior of key quantities in well defined combustion regimes. In turbulent flames, the coupling between the turbulence and the chemistry is so strong in certain regimes that is is very difficult to isolate the role played by one individual phenomenon. Direct numerical simulation (DNS) is an extremely useful tool to study in detail the turbulence-chemistry interactions in certain well defined regimes. Globally, non-premixed flames are controlled by two limiting cases: the fast chemistry limit, where the turbulent fluctuations. In between these two limits, finite-rate chemical effects are important and the turbulence interacts strongly with the chemical processes. This regime is important because industrial burners operate in regimes in which, locally the flame undergoes extinction, or is at least in some nonequilibrium condition. Furthermore, these nonequilibrium conditions strongly influence the production of pollutants. To quantify the finite-rate chemistry effect, direct numerical simulations are performed to study the interaction between an initially laminar non-premixed flame and a three-dimensional field of homogeneous isotropic decaying turbulence. Emphasis is placed on the dynamics of extinction and on transient effects on the fine scale mixing process. Differential molecular diffusion among species is also examined with this approach, both for nonreacting and reacting situations. To address the problem of large-scale mixing and to examine the effects of mean shear, efforts are underway to perform large eddy simulations of round three-dimensional jets.
Structure in turbulent thermal convection
NASA Astrophysics Data System (ADS)
Balachandar, S.
1992-12-01
Small-scale features of vorticity, strain rate, and temperature gradients are considered in a Rayleigh-Bénard convection. The results reported are from a direct numerical simulation of turbulent convection performed in a rectangular box of aspect ratio 2√2 at a Rayleigh number of 6.5×106 and a Prandtl number of 0.72. In agreement with earlier results [Ashurst et al., Phys. Fluids 30, 2343 (1987) and Ruetsch and Maxey, Phys. Fluids A 3, 1587 (1991)], the intermediate strain rate is on an average positive, but the ratio of alpha, beta, and gamma strain rates are measured to be 5.3:1.0:-6.3. This result differs from the earlier result of 3:1:-4 obtained in homogeneous isotropic and shear turbulences. Buoyancy-induced vorticity production makes significant contribution to the overall enstrophy balance, especially close to the boundaries. Vorticity production by buoyancy is exclusively in the horizontal direction and is balanced by preferred production by stretching and tilting in the vertical direction, due to the preferred alignment of extensional alpha strain rate with the vertical direction. Such directional alignment of vorticity, strain rate, and scalar gradient is explained on the basis of preferred spatial orientation of coherent structures in thermal turbulence.
Turbulence modeling and experiments
NASA Technical Reports Server (NTRS)
Shabbir, Aamir
1992-01-01
The best way of verifying turbulence is to do a direct comparison between the various terms and their models. The success of this approach depends upon the availability of the data for the exact correlations (both experimental and DNS). The other approach involves numerically solving the differential equations and then comparing the results with the data. The results of such a computation will depend upon the accuracy of all the modeled terms and constants. Because of this it is sometimes difficult to find the cause of a poor performance by a model. However, such a calculation is still meaningful in other ways as it shows how a complete Reynolds stress model performs. Thirteen homogeneous flows are numerically computed using the second order closure models. We concentrate only on those models which use a linear (or quasi-linear) model for the rapid term. This, therefore, includes the Launder, Reece and Rodi (LRR) model; the isotropization of production (IP) model; and the Speziale, Sarkar, and Gatski (SSG) model. Which of the three models performs better is examined along with what are their weaknesses, if any. The other work reported deal with the experimental balances of the second moment equations for a buoyant plume. Despite the tremendous amount of activity toward the second order closure modeling of turbulence, very little experimental information is available about the budgets of the second moment equations. Part of the problem stems from our inability to measure the pressure correlations. However, if everything else appearing in these equations is known from the experiment, pressure correlations can be obtained as the closing terms. This is the closest we can come to in obtaining these terms from experiment, and despite the measurement errors which might be present in such balances, the resulting information will be extremely useful for the turbulence modelers. The purpose of this part of the work was to provide such balances of the Reynolds stress and heat
Estimating unsteady aerodynamic forces on a cascade in a three-dimensional turbulence field
NASA Technical Reports Server (NTRS)
Norman, T.; Johnson, W.
1985-01-01
An analytical method has been developed to estimate the unsteady aerodynamic forces caused by flow field turbulence on a wind tunnel turning vane cascade system (vane set). This method approximates dynamic lift and drag by linearly perturbing the appropriate steady state force equations, assuming that the dynamic loads are due only to free stream turbulence and that this turbulence is homogeneous, isotropic, and Gaussian. Correlation and unsteady aerodynamic effects are also incorporated into the analytical model. Using these assumptions, equations relating dynamic lift and drag to flow turbulence, mean velocity, and vane set geometry are derived. From these equations, estimates for the power spectra and rms (root mean squared value, delta) loading of both lift and drag can be determined.
NASA Astrophysics Data System (ADS)
Schau, Kyle A.
This thesis presents a complete method of modeling the autospectra of turbulence in closed form via an expansion series using the von Karman model as a basis function. It is capable of modeling turbulence in all three directions of fluid flow: longitudinal, lateral, and vertical, separately, thus eliminating the assumption of homogeneous, isotropic flow. A thorough investigation into the expansion series is presented, with the strengths and weaknesses highlighted. Furthermore, numerical aspects and theoretical derivations are provided. This method is then tested against three highly complex flow fields: wake turbulence inside wind farms, helicopter downwash, and helicopter downwash coupled with turbulence shed from a ship superstructure. These applications demonstrate that this method is remarkably robust, that the developed autospectral models are virtually tailored to the design of white noise driven shaping filters, and that these models in closed form facilitate a greater understanding of complex flow fields in wind engineering.
Modeling the dissipation rate in rotating turbulent flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Raj, Rishi; Gatski, Thomas B.
1990-01-01
A variety of modifications to the modeled dissipation rate transport equation that have been proposed during the past two decades to account for rotational strains are examined. The models are subjected to two crucial test cases: the decay of isotropic turbulence in a rotating frame and homogeneous shear flow in a rotating frame. It is demonstrated that these modifications do not yield substantially improved predictions for these two test cases and in many instances give rise to unphysical behavior. An alternative proposal, based on the use of the tensor dissipation rate, is made for the development of improved models.
Turbulent Sediment Suspension and Induced Ripple Dynamics Absent Mean Shear
NASA Astrophysics Data System (ADS)
Johnson, B. A.; Cowen, E.
2014-12-01
The uprush and backwash phases in the swash zone, the region of the beach that is alternately covered and uncovered by wave run-up, are fundamentally different events. Backwash is dominated by a growing boundary layer where the turbulence is set by the bed shear stress. In this phase traditional boundary layer turbulence models and Shields-type critical stress pickup functions work well. However, the uprush phase, while often viewed in the context of traditional boundary layer turbulence models, has little in common with the backwash phase. During uprush, the entire water column is turbulent, as it rapidly advects well-stirred highly turbulent flow generated offshore from breaking waves or collapsing bores. Turbulence levels in the uprush are several times higher than turbulent boundary layer theory would predict and hence the use of a boundary layer model to predict turbulence levels during uprush grossly under predicts the turbulence and subsequent sediment suspension in the swash zone. To study the importance of this advected turbulence to sediment suspension we conduct experiments in a water tank designed to generate horizontally homogeneous isotropic turbulence absent mean shear using randomly actuated synthetic jet arrays suspended above both a solid glass plate and a narrowly graded sediment bed. Using jet arrays with different jet spacings allows the generation of high Reynolds number turbulence with variable integral length scales, which we hypothesize control the characteristic length scales in the induced ripple field. Particle image velocimetry and acoustic Doppler velocimetry measurements are used to characterize the near-bed flow and this unique turbulent boundary layer. Metrics include the mean flow and turbulence intensities and stresses, temporal and spatial spectra, dissipation of turbulent kinetic energy, and integral length scales of the turbulence. We leverage our unique dataset to compare the flows over impermeable fixed and permeable mobile
Effects of small scale energy injection on large scales in turbulent reaction flows
NASA Astrophysics Data System (ADS)
Xuan, Yuan
2014-11-01
Turbulence causes the generation of eddies of various length scales. In turbulent non-reacting flows, most of the kinetic energy is contained in large scale turbulent structures and dissipated at small scales. This energy cascade process from large scales to small scales provides the foundation of a lot of turbulence models, especially for Large Eddy Simulations. However, in turbulent reacting flows, chemical energy is converted locally to heat and therefore deploys energy at the smallest scales. As such, effects of small scale energy injection due to combustion on large scale turbulent motion may become important. These effects are investigated in the case of auto-ignition under homogeneous isotropic turbulence. Impact of small scale heat release is examined by comparing various turbulent statistics (e.g. energy spectrum, two-point correlation functions, and structure functions) in the reacting case to the non-reacting case. Emphasis is placed on the identification of the most relevant turbulent quantities in reflecting such small-large scale interactions.
Investigation of turbulence modulation in particle-laden flows using the lattice Boltzmann method.
NASA Astrophysics Data System (ADS)
Peng, Cheng; Geneva, Nicholas; Min, Haoda; Wang, Lian-Ping
2015-11-01
Turbulent modulation by finite-size solid particles has been studied experimentally and numerically in the past several decades. Previous studies have revealed that resolving the interfaces between particle surfaces and fluid is crucial to properly include finite-size effects on local fluid turbulence. Finite-size particles also produce pseudo-turbulence that may not decay locally, leading to a stronger nonlinear dependence of the level of turbulence modulation on the particle volume fraction. In this study we apply the lattice Boltzmann method (LBM) to perform interface-resolved simulations of turbulent particle-laden flow, focusing on local turbulence dynamics at the scale of particle size. We will discuss the accuracy of this mesoscopic approach when compared to other macroscopic methods. We consider both fully developed homogeneous isotropic (HI) turbulent flows and turbulent channel flows laden with finite-size particles. The particle volume fraction is around 10% and the particle-to-fluid density ratio is of the order of one. Conditional statistics as a function of distance from the moving particle surfaces are studied in detail, and are used to help interpret global turbulence modulation by particles. Grid convergence of these conditional statistics will be discussed.
Turbulent Amplification and Structure of the Intracluster Magnetic Field
NASA Astrophysics Data System (ADS)
Beresnyak, Andrey; Miniati, Francesco
2016-02-01
We compare DNS calculations of homogeneous isotropic turbulence with the statistical properties of intracluster turbulence from the Matryoshka Run and find remarkable similarities between their inertial ranges. This allowed us to use the time-dependent statistical properties of intracluster turbulence to evaluate dynamo action in the intracluster medium, based on earlier results from a numerically resolved nonlinear magneto-hydrodynamic turbulent dynamo. We argue that this approach is necessary (a) to properly normalize dynamo action to the available intracluster turbulent energy and (b) to overcome the limitations of low Re affecting current numerical models of the intracluster medium. We find that while the properties of intracluster magnetic field are largely insensitive to the value and origin of the seed field, the resulting values for the Alfvén speed and the outer scale of the magnetic field are consistent with current observational estimates, basically confirming the idea that the magnetic field in today’s galaxy clusters is a record of its past turbulent activity.
NASA Technical Reports Server (NTRS)
Bereketab, Semere; Wang, Hong-Wei; Mish, Patrick; Devenport, William J.
2000-01-01
Two grids have been developed for the Virginia Tech 6 ft x 6 ft Stability wind tunnel for the purpose of generating homogeneous isotropic turbulent flows for the study of unsteady airfoil response. The first, a square bi-planar grid with a 12" mesh size and an open area ratio of 69.4%, was mounted in the wind tunnel contraction. The second grid, a metal weave with a 1.2 in. mesh size and an open area ratio of 68.2% was mounted in the tunnel test section. Detailed statistical and spectral measurements of the turbulence generated by the two grids are presented for wind tunnel free stream speeds of 10, 20, 30 and 40 m/s. These measurements show the flows to be closely homogeneous and isotropic. Both grids produce flows with a turbulence intensity of about 4% at the location planned for the airfoil leading edge. Turbulence produced by the large grid has an integral scale of some 3.2 inches here. Turbulence produced by the small grid is an order of magnitude smaller. For wavenumbers below the upper limit of the inertial subrange, the spectra and correlations measured with both grids at all speeds can be represented using the von Karman interpolation formula with a single velocity and length scale. The spectra maybe accurately represented over the entire wavenumber range by a modification of the von Karman interpolation formula that includes the effects of dissipation. These models are most accurate at the higher speeds (30 and 40 m/s).
Homogeneous and isotropic cosmologies with nonlinear electromagnetic radiation
Vollick, Dan N.
2008-09-15
In this paper I examine cosmological models that contain a stochastic background of nonlinear electromagnetic radiation. I show that for Born-Infeld electrodynamics the equation of state parameter, w=P/{rho}, remains close to 1/3 throughout the evolution of the universe if E{sup 2}=B{sup 2} in the late universe to a high degree of accuracy. Theories with electromagnetic Lagrangians of the form L=-(1/4)F{sup 2}+{alpha}F{sup 4} have recently been studied in magnetic universes, where the electric field vanishes. It was shown that the F{sup 4} term can produce a bounce in the early universe, avoiding an initial singularity. Here I show that the inclusion of an electric field, with E{sup 2}{approx_equal}B{sup 2} in the late universe, eliminates the bounce and the universe begins with an initial singularity. I also examine theories with Lagrangians of the form L=-(1/4)F{sup 2}-{mu}{sup 8}/F{sup 2}, which have been shown to produce a period of late time accelerated expansion in magnetic universes. I show that, if an electric field is introduced, the accelerated phase will only occur if E{sup 2}<3B{sup 2}.
Isotropic sequence order learning.
Porr, Bernd; Wörgötter, Florentin
2003-04-01
In this article, we present an isotropic unsupervised algorithm for temporal sequence learning. No special reward signal is used such that all inputs are completely isotropic. All input signals are bandpass filtered before converging onto a linear output neuron. All synaptic weights change according to the correlation of bandpass-filtered inputs with the derivative of the output. We investigate the algorithm in an open- and a closed-loop condition, the latter being defined by embedding the learning system into a behavioral feedback loop. In the open-loop condition, we find that the linear structure of the algorithm allows analytically calculating the shape of the weight change, which is strictly heterosynaptic and follows the shape of the weight change curves found in spike-time-dependent plasticity. Furthermore, we show that synaptic weights stabilize automatically when no more temporal differences exist between the inputs without additional normalizing measures. In the second part of this study, the algorithm is is placed in an environment that leads to closed sensor-motor loop. To this end, a robot is programmed with a prewired retraction reflex reaction in response to collisions. Through isotropic sequence order (ISO) learning, the robot achieves collision avoidance by learning the correlation between his early range-finder signals and the later occurring collision signal. Synaptic weights stabilize at the end of learning as theoretically predicted. Finally, we discuss the relation of ISO learning with other drive reinforcement models and with the commonly used temporal difference learning algorithm. This study is followed up by a mathematical analysis of the closed-loop situation in the companion article in this issue, "ISO Learning Approximates a Solution to the Inverse-Controller Problem in an Unsupervised Behavioral Paradigm" (pp. 865-884). PMID:12689389
Fundamentals of pair diffusion in kinematic simulations of turbulence
NASA Astrophysics Data System (ADS)
Osborne, D. R.; Vassilicos, J. C.; Sung, K.; Haigh, J. D.
2006-09-01
We demonstrate that kinematic simulation (KS) of three-dimensional homogeneous turbulence produces fluid element pair statistics in agreement with the predictions of L F. Richardson [Proc. R. Soc. London, Ser. A 110, 709 (1926)] even though KS lacks explicit modeling of turbulent sweeping of small eddies by large ones. This scaling is most clearly evident in the turbulent diffusivity’s dependence on rms pair separation and, to a lesser extent, on the pair’s travel time statistics. It is also shown that kinematic simulation generates a probability density function of pair separation which is in good agreement with recent theory [S. Goto and J. C. Vassilicos, New J. Phys. 6, 65 (2004)] and with the scaling of the rms pair separation predicted by L. F. Richardson [Proc. R. Soc. London, Ser. A 110, 709 (1926)]. Finally, the statistical persistence hypothesis (SPH) is formulated mathematically and its validity tested in KS. This formulation introduces the concept of stagnation point velocities and relates these to fluid accelerations. The scaling of accelerations found in kinematic simulation supports the SPH, even though KS does not generate a Kolmogorov scaling for the acceleration variance (except for a specific case and a limited range of outer to inner length-scale ratios). An argument is then presented that suggests that the stagnation points in homogeneous isotropic turbulence are on average long-lived.
Energy Transfer in Rotating Turbulence
NASA Technical Reports Server (NTRS)
Cambon, Claude; Mansour, Nagi N.; Godeferd, Fabien S.; Rai, Man Mohan (Technical Monitor)
1995-01-01
The influence or rotation on the spectral energy transfer of homogeneous turbulence is investigated in this paper. Given the fact that linear dynamics, e.g. the inertial waves regime tackled in an RDT (Rapid Distortion Theory) fashion, cannot Affect st homogeneous isotropic turbulent flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly nonlinear and EDQNM theories), experimental and DNS (Direct Numerical Simulation) results are gathered here and compared in order to give a self-consistent picture of the nonlinear effects of rotation on tile turbulence. The inhibition of the energy cascade, which is linked to a reduction of the dissipation rate, is shown to be related to a damping due to rotation of the energy transfer. A model for this effect is quantified by a model equation for the derivative-skewness factor, which only involves a micro-Rossby number Ro(sup omega) = omega'/(2(OMEGA))-ratio of rms vorticity and background vorticity as the relevant rotation parameter, in accordance with DNS and EDQNM results fit addition, anisotropy is shown also to develop through nonlinear interactions modified by rotation, in an intermediate range of Rossby numbers (Ro(omega) = (omega)' and Ro(omega)w greater than 1), which is characterized by a marco-Rossby number Ro(sup L) less than 1 and Ro(omega) greater than 1 which is characterized by a macro-Rossby number based on an integral lengthscale L and the micro-Rossby number previously defined. This anisotropy is mainly an angular drain of spectral energy which tends to concentrate energy in tile wave-plane normal to the rotation axis, which is exactly both the slow and the two-dimensional manifold. In Addition, a polarization of the energy distribution in this slow 2D manifold enhances horizontal (normal to the rotation axis) velocity components, and underlies the anisotropic structure of the integral lengthscales. Finally is demonstrated the
Presumed PDF Modeling of Early Flame Propagation in Moderate to Intense Turbulence Environments
NASA Technical Reports Server (NTRS)
Carmen, Christina; Feikema, Douglas A.
2003-01-01
The present paper describes the results obtained from a one-dimensional time dependent numerical technique that simulates early flame propagation in a moderate to intense turbulent environment. Attention is focused on the development of a spark-ignited, premixed, lean methane/air mixture with the unsteady spherical flame propagating in homogeneous and isotropic turbulence. A Monte-Carlo particle tracking method, based upon the method of fractional steps, is utilized to simulate the phenomena represented by a probability density function (PDF) transport equation. Gaussian distributions of fluctuating velocity and fuel concentration are prescribed. Attention is focused on three primary parameters that influence the initial flame kernel growth: the detailed ignition system characteristics, the mixture composition, and the nature of the flow field. The computational results of moderate and intense isotropic turbulence suggests that flames within the distributed reaction zone are not as vulnerable, as traditionally believed, to the adverse effects of increased turbulence intensity. It is also shown that the magnitude of the flame front thickness significantly impacts the turbulent consumption flame speed. Flame conditions studied have fuel equivalence ratio s in the range phi = 0.6 to 0.9 at standard temperature and pressure.
Isotrope und homogene Materie - Kosmen; On Dynamics and Thermodynamics of Isotropic Matter-Universes
NASA Astrophysics Data System (ADS)
Treder, H.-J.
Die Dynamik und Thermodynamik großer kosmischer Systeme ist fast unabhängig von den besonderen Theorien über die Gravitation. Nur die Feinstruktur der Kosmologie und Kosmonogie reflektiert die speziellen Hypothesen. Diese Neutralität gegenüber den konkreten Gravodynamiken ist die Konsequenz der fundamentalen Eigenschaften der Gravitation: Der Prinzipien der Äquivalenz von Trägheit und Schwere. The dynamics and thermodynamics of great cosmical systems are nearly independent of the theory of gravitation and only the fine-structure of cosmogony and cosmology reflects the special hypotheses.The neutrality against the concret gravodynamics is a consequence of the fundamental properties of gravitation: the principlies of equivalence of gravity and inertia.
High Reynolds number decay of turbulent Taylor-Couette flow
NASA Astrophysics Data System (ADS)
Verschoof, Ruben A.; Huisman, Sander G.; van der Veen, Roeland C. A.; Sun, Chao; Lohse, Detlef
2015-11-01
We study the decay of high-Reynolds number turbulence in a Taylor-Couette facility for pure inner cylinder rotation. The rotation of the inner cylinder (Rei = 2 ×106) is suddenly decelerated as fast as possible, thus removing the energy input within seconds. Local velocity measurements show that the decay in this wall-bounded inhomogeneous flow is faster than observed for homogeneous isotropic turbulent flows, due to the strong viscous drag applied by the inner and outer cylinder surfaces. We found that the decay over time can be described with the differential equation Re . (t) =cf (Re)Re2 , where the effects of the walls are included through the friction coefficient. A self-similar behavior of the azimuthal velocity is found: its normalized velocity profile as a function of the radius collapses over time during the decay process.
Polymer stretching in the inertial range of turbulence.
Ahmad, Adeel; Vincenzi, Dario
2016-05-01
We study the deformation of flexible polymers whose contour length lies in the inertial range of a homogeneous and isotropic turbulent flow. By using the elastic dumbbell model and a stochastic velocity field with nonsmooth spatial correlations, we obtain the probability density function of the extension as a function of the Weissenberg number and of the scaling exponent of the velocity structure functions. In a spatially rough flow, as in the inertial range of turbulence, the statistics of polymer stretching differs from that observed in laminar flows or in smooth chaotic flows. In particular, the probability distribution of polymer extensions decays as a stretched exponential, and the most probable extension grows as a power law of the Weissenberg number. Furthermore, the ability of the flow to stretch polymers weakens as the flow becomes rougher in space. PMID:27300949
Polymer stretching in the inertial range of turbulence
NASA Astrophysics Data System (ADS)
Ahmad, Adeel; Vincenzi, Dario
2016-05-01
We study the deformation of flexible polymers whose contour length lies in the inertial range of a homogeneous and isotropic turbulent flow. By using the elastic dumbbell model and a stochastic velocity field with nonsmooth spatial correlations, we obtain the probability density function of the extension as a function of the Weissenberg number and of the scaling exponent of the velocity structure functions. In a spatially rough flow, as in the inertial range of turbulence, the statistics of polymer stretching differs from that observed in laminar flows or in smooth chaotic flows. In particular, the probability distribution of polymer extensions decays as a stretched exponential, and the most probable extension grows as a power law of the Weissenberg number. Furthermore, the ability of the flow to stretch polymers weakens as the flow becomes rougher in space.
Large sphere motion in a nonhomogeneous turbulent flow
NASA Astrophysics Data System (ADS)
Machicoane, Nathanaël; Zimmermann, Robert; Fiabane, Lionel; Bourgoin, Mickaël; Pinton, Jean-François; Volk, Romain
2014-01-01
We investigate the dynamics of very large particles freely advected in a turbulent von Kármán flow. Contrary to other experiments for which the particle dynamics is generally studied near the geometrical center of the flow, we track the particles in the whole experiment volume. We observe a strong influence of the mean structure of the flow that generates an unexpected large-scale sampling effect for the larger particles studied. This phenomenon was not observed for neutrally buoyant particles of smaller yet finite sizes, in homogeneous and isotropic turbulence (Fiabane et al 2012 Phys. Rev. E 86 035301). We find that particles whose diameter approaches the flow integral length scale explore the von Kármán flow nonuniformly, with a higher probability to move in the vicinity of two tori situated near the poloidal neutral lines. This preferential sampling is quite robust with respect to changes of varied parameters: Reynolds number, particle density and particle surface roughness.
Depolarization of decaying counterflow turbulence in He II.
Barenghi, C F; Gordeev, A V; Skrbek, L
2006-08-01
We present experimental evidence backed up by numerical simulations that the steady-state vortex tangle created in He II by heat-transfer counterflow is strongly polarized. When the heater that generates the counterflow turbulence is switched off, the vortex tangle decays, the vortex lines randomize their spatial orientation and the tangle's polarization decreases. The process of depolarization slows down the recovery of the transverse second sound signal which measures the vortex line density; at some values of parameters it even leads to a net decrease of the amplitude of the transverse second sound prior to reaching the universal -32 power temporal law decay typical of classical homogeneous isotropic turbulence in a finite-sized channel. PMID:17025541
Depolarization of decaying counterflow turbulence in He II
Barenghi, C. F.; Gordeev, A. V.; Skrbek, L.
2006-08-15
We present experimental evidence backed up by numerical simulations that the steady-state vortex tangle created in He II by heat-transfer counterflow is strongly polarized. When the heater that generates the counterflow turbulence is switched off, the vortex tangle decays, the vortex lines randomize their spatial orientation and the tangle's polarization decreases. The process of depolarization slows down the recovery of the transverse second sound signal which measures the vortex line density; at some values of parameters it even leads to a net decrease of the amplitude of the transverse second sound prior to reaching the universal -3/2 power temporal law decay typical of classical homogeneous isotropic turbulence in a finite-sized channel.
Statistics of polymer extensions in turbulent channel flow.
Bagheri, Faranggis; Mitra, Dhrubaditya; Perlekar, Prasad; Brandt, Luca
2012-11-01
We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elongation for both the Oldroyd-B model (for Weissenberg number Wi<1) and the FENE model. We use the location of the minima of the Cramer's function to define the Weissenberg number precisely such that we observe coil-stretch transition at Wi ≈1. We find agreement with earlier analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon, and Lebedev [Phys. Rev. Lett. 84, 4765 (2000)] for linear polymers (Oldroyd-B model) with Wi <1 and by Chertkov [Phys. Rev. Lett. 84, 4761 (2000)] for nonlinear FENE-P model of polymers. For Wi >1 (FENE model) the polymer are significantly more stretched near the wall than at the center of the channel where the flow is closer to homogenous isotropic turbulence. Furthermore near the wall the polymers show a strong tendency to orient along the streamwise direction of the flow, but near the center line the statistics of orientation of the polymers is consistent with analogous results obtained recently in homogeneous and isotropic flows. PMID:23214883
Statistics of polymer extensions in turbulent channel flow
NASA Astrophysics Data System (ADS)
Bagheri, Faranggis; Mitra, Dhrubaditya; Perlekar, Prasad; Brandt, Luca
2012-11-01
We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elongation for both the Oldroyd-B model (for Weissenberg number Wi<1) and the FENE model. We use the location of the minima of the Cramer's function to define the Weissenberg number precisely such that we observe coil-stretch transition at Wi ≈1. We find agreement with earlier analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon, and Lebedev [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.84.4765 84, 4765 (2000)] for linear polymers (Oldroyd-B model) with Wi <1 and by Chertkov [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.84.4761 84, 4761 (2000)] for nonlinear FENE-P model of polymers. For Wi >1 (FENE model) the polymer are significantly more stretched near the wall than at the center of the channel where the flow is closer to homogenous isotropic turbulence. Furthermore near the wall the polymers show a strong tendency to orient along the streamwise direction of the flow, but near the center line the statistics of orientation of the polymers is consistent with analogous results obtained recently in homogeneous and isotropic flows.
Ke, Tracy; Fan, Jianqing; Wu, Yichao
2014-01-01
This paper explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when regression coefficients corresponding to neighboring geographical regions or a similar cluster of covariates are expected to be approximately the same. Sparsity corresponds to a special case of homogeneity with a large cluster of known atom zero. In this article, we propose a new method called clustering algorithm in regression via data-driven segmentation (CARDS) to explore homogeneity. New mathematics are provided on the gain that can be achieved by exploring homogeneity. Statistical properties of two versions of CARDS are analyzed. In particular, the asymptotic normality of our proposed CARDS estimator is established, which reveals better estimation accuracy for homogeneous parameters than that without homogeneity exploration. When our methods are combined with sparsity exploration, further efficiency can be achieved beyond the exploration of sparsity alone. This provides additional insights into the power of exploring low-dimensional structures in high-dimensional regression: homogeneity and sparsity. Our results also shed lights on the properties of the fussed Lasso. The newly developed method is further illustrated by simulation studies and applications to real data. Supplementary materials for this article are available online. PMID:26085701
Acceleration PDFs of particles in rotating turbulent convection
NASA Astrophysics Data System (ADS)
Clercx, Herman; Perlekar, Prasad; Lavezzo, Valentina; Toschi, Federico
2012-11-01
Particle dispersion in buoyancy-driven rotating turbulent flows has direct relevance for many industrial and environmental applications. We have used a Lattice Boltzmann Method coupled with Lagrangian particle tracking algorithm to investigate the behaviour of passive and inertial particles released in turbulent rotating Rayleigh-Bénard (RB) convection. The flow domain is horizontally periodic and vertically confined. Both the gravity and the rotation vector are oriented in the vertical direction. Here we present the results of the acceleration PDFs of particles in both non-rotating and strongly rotating RB convection. It is found that the bulk acceleration PDF in non-rotating RB turbulence is like in homogeneous isotropic turbulence whereas rotation introduces anisotropy similar to acceleration PDFs obtained from experiments in (isothermal) forced rotating turbulence. These results and those obtained for inertial particles will be discussed. PP and VL were financially supported by the Foundation for Fundamental Research on Matter (FOM), which is part of NWO. This work was sponsored by NWO-NCF (SH-176).
On some physical aspects of isotropic cosmology in Riemann-Cartan spacetime
Minkevich, A.V.; Garkun, A.S.; Kudin, V.I. E-mail: awm@matman.uwm.edu.pl E-mail: kudzin_w@tut.by
2013-03-01
Isotropic cosmology built in the framework of the Poincaré gauge theory of gravity based on sufficiently general expression of gravitational Lagrangian is considered. The derivation of cosmological equations and equations for torsion functions in the case of the most general homogeneous isotropic models is given. Physical aspects of isotropic cosmology connected with possible solution of dark energy problem and problem of cosmological singularity are discussed.
Measuring the cascade rate in anisotropic turbulence through 3rd order structure functions.
NASA Astrophysics Data System (ADS)
Verdini, Andrea; Landi, Simone; Hellinger, Petr
2014-05-01
We employ the Von-Karman-Howart-Yaglom-Politano-Poquet (KHYPP)law, to compute the cascade rate by means of 3rd order structure functions in homogeneous, forced, DNS at high resolution. We consider first the isotropic case (no guide field) and verify that the cascade rate is consistent with the dissipation rate. Then we consider an anisotropic case (with guide field) for which the isotropic KHYPP law does not apply. We compute the parallel and perpendicular cascade rates and find that the latter basically accounts for the total dissipation rate, as expected for anisotropic turbulence. Also, the cascade rate derived from the isotropic law is found to be a good approximation for the total cascade rate. Recent works have shown that the hypothesis of stationary turbulence must be probably relaxed in the solar wind. We present preliminary results on the measure of the cascade rate in the expanding solar wind, obtained with DNS of MHD turbulence in the expanding box model. Such model incorporates the basic physic of expansion thus inducing anisotropies driven by both the magnetic field and expansion, along with an energy decrease due to the conservation of linear invariants (angular momentum and magnetic flux). The correction due to non-stationary conditions is found to be important and to become negligible only at small scales, thus suggesting that solar wind measurements over- estimate the actual cascade rate.
Turbulence in pure superfluid flow
Ashton, R.A.; Opatowsky, L.B.; Tough, J.T.
1981-03-09
A series of experiments is described which provide an unambiguous description of the steady-state properties of turbulence in pure superfluid flow. The turbulence is qualitatively different from that observed in counterflow but comparable to the homogeneous turbulence described by theory.
Pulsating instability and self-acceleration of fast turbulent flames
NASA Astrophysics Data System (ADS)
Poludnenko, Alexei Y.
2015-01-01
A series of three-dimensional numerical simulations is used to study the intrinsic stability of high-speed turbulent flames. Calculations model the interaction of a fully resolved premixed flame with a highly subsonic, statistically steady, homogeneous, isotropic turbulence. The computational domain is unconfined to prevent the onset of thermoacoustic instabilities. We consider a wide range of turbulent intensities and system sizes, corresponding to the Damköhler numbers Da = 0.1 - 6.0. These calculations show that turbulent flames in the regimes considered are intrinsically unstable. In particular, we find three effects. (1) Turbulent flame speed, ST, develops pulsations with the observed peak-to-peak amplitude ST max / ST min > 10 and a characteristic time scale close to a large-scale eddy turnover time. Such variability is caused by the interplay between turbulence, which continuously creates the flame surface, and highly intermittent flame collisions, which consume the flame surface. (2) Unstable burning results in the periodic pressure build-up and the formation of pressure waves or shocks, when ST approaches or exceeds the speed of a Chapman-Jouguet deflagration. (3) Coupling of pressure gradients formed during pulsations with density gradients across the flame leads to the anisotropic amplification of turbulence inside the flame volume and flame acceleration. Such process, which is driven by the baroclinic term in the vorticity transport equation, is a reacting-flow analog of the mechanism underlying the Richtmyer-Meshkov instability. With the increase in turbulent intensity, the limit-cycle instability discussed here transitions to the regime described in our previous work, in which the growth of ST becomes unbounded and produces a detonation.
Tangling clustering instability for small particles in temperature stratified turbulence
NASA Astrophysics Data System (ADS)
Elperin, T.; Kleeorin, N.; Liberman, M.; Rogachevskii, I.
2013-08-01
We study tangling clustering instability of inertial particles in a temperature stratified turbulence with small finite correlation time. It is shown that the tangling mechanism in the temperature stratified turbulence strongly increases the degree of compressibility of particle velocity field. This results in the strong decrease of the threshold for the excitation of the tangling clustering instability even for small particles. The tangling clustering instability in the temperature stratified turbulence is essentially different from the inertial clustering instability that occurs in non-stratified isotropic and homogeneous turbulence. While the inertial clustering instability is caused by the centrifugal effect of the turbulent eddies, the mechanism of the tangling clustering instability is related to the temperature fluctuations generated by the tangling of the mean temperature gradient by the velocity fluctuations. Temperature fluctuations produce pressure fluctuations and cause particle accumulations in regions with increased instantaneous pressure. It is shown that the growth rate of the tangling clustering instability is by sqrtRe (ell _0 / L_T)^2 / (3 Ma)^4 times larger than that of the inertial clustering instability, where Re is the Reynolds number, Ma is the Mach number, ℓ0 is the integral turbulence scale, and LT is the characteristic scale of the mean temperature variations. It is found that depending on the parameters of the turbulence and the mean temperature gradient there is a preferential particle size at which the particle clustering due to the tangling clustering instability is more effective. The particle number density inside the cluster after the saturation of this instability can be by several orders of magnitude larger than the mean particle number density. It is also demonstrated that the evaporation of droplets drastically changes the tangling clustering instability, e.g., it increases the instability threshold in the droplet radius. The
Acceleration Statistics in Rotating and Sheared Turbulence
NASA Astrophysics Data System (ADS)
Jacobitz, Frank; Schneider, Kai; Bos, Wouter; Farge, Marie
2012-11-01
Acceleration statistics are of fundamental interest in turbulence ranging from theoretical questions to modeling of dispersion processes. Direct numerical simulations of sheared and rotating homogeneous turbulence are performed with different ratios of Coriolis parameter to shear rate. The statistics of Lagrangian and Eulerian acceleration are studied with a particular focus on the influence of the rotation ratio and also on the scale dependence of the statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian acceleration show a strong and similar influence on the rotation ratio. The flatness further quantifies its influence and yields values close to three for strong rotation. For moderate and vanishing rotation, the flatness of the Eulerian acceleration is larger than that of the Lagrangian acceleration, contrary to previous results for isotropic turbulence. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian acceleration increases as scale decreases. For strong rotation, the Eulerian acceleration is more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation.
The Effect of Low Energy Turbulence in Estuary Margins on Fine Sediment Settling
NASA Astrophysics Data System (ADS)
Allen, R. M.; MacVean, L. J.; Tse, I.; Mazzaro, L. J.; Stacey, M. T.; Variano, E. A.
2014-12-01
Sediment dynamics in estuaries and near shore regions control the growth or erosion of the bed and fringing wetlands, determine the spread of sediment-associated contaminants, and limit the light availability for primary productivity through turbidity. In estuaries such as San Francisco Bay, this sediment is often cohesive, and can flocculate. Changes to the composition of the sediment and waters, the suspended sediment concentration, and the turbulence can all affect the flocculation of suspended sediment. In turn, flocculation controls the particle diameter, settling velocity, density, and particle inertia. These sediment properties drive the turbulent diffusivity, which balances with the settling velocity to impact the vertical distribution of sediment in the water column. The vertical profile strongly affects how sediment is transported through the estuary by lateral flow. Turbulence may also impact settling velocity in non-cohesive particles. In turbulence, dense particles may get trapped in convergent flow regions, thus particles are more likely to get swept along the downward side of a turbulent eddy than the upward side, resulting in enhanced settling velocities. We isolated the impacts of turbulence level, particle size and type, and suspended sediment concentration on particle settling velocities using uniform grain size particles in homogeneous isotropic turbulence. Controlling the turbulence in a well-defined turbulence tank, we used Two Acoustic Doppler Velocimeters, separated vertically, to measure turbulent velocities (w') and suspended sediment concentrations (C), which yield condition dependent settling velocities (ws), via equation 1. Lab characterization of particle settling velocities help to validate the method for measuring settling velocities in the field, and will serve as a foundation for an extensive field experiment in San Francisco Bay. Characterizing the velocity enhancement relative to the Stokes number, the Rouse number, and the
Bansal, Gaurav; Mascarenhas, Ajith; Chen, Jacqueline H.
2014-10-01
In our paper, two- and three-dimensional direct numerical simulations (DNS) of autoignition phenomena in stratified dimethyl-ether (DME)/air turbulent mixtures are performed. A reduced DME oxidation mechanism, which was obtained using rigorous mathematical reduction and stiffness removal procedure from a detailed DME mechanism with 55 species, is used in the present DNS. The reduced DME mechanism consists of 30 chemical species. This study investigates the fundamental aspects of turbulence-mixing-autoignition interaction occurring in homogeneous charge compression ignition (HCCI) engine environments. A homogeneous isotropic turbulence spectrum is used to initialize the velocity field in the domain. Moreover, the computational configuration corresponds to a constant volume combustion vessel with inert mass source terms added to the governing equations to mimic the pressure rise due to piston motion, as present in practical engines. DME autoignition is found to be a complex three-staged process; each stage corresponds to a distinct chemical kinetic pathway. The distinct role of turbulence and reaction in generating scalar gradients and hence promoting molecular transport processes are investigated. Then, by applying numerical diagnostic techniques, the different heat release modes present in the igniting mixture are identified. In particular, the contribution of homogeneous autoignition, spontaneous ignition front propagation, and premixed deflagration towards the total heat release are quantified.
Bansal, Gaurav; Mascarenhas, Ajith; Chen, Jacqueline H.
2014-10-01
In our paper, two- and three-dimensional direct numerical simulations (DNS) of autoignition phenomena in stratified dimethyl-ether (DME)/air turbulent mixtures are performed. A reduced DME oxidation mechanism, which was obtained using rigorous mathematical reduction and stiffness removal procedure from a detailed DME mechanism with 55 species, is used in the present DNS. The reduced DME mechanism consists of 30 chemical species. This study investigates the fundamental aspects of turbulence-mixing-autoignition interaction occurring in homogeneous charge compression ignition (HCCI) engine environments. A homogeneous isotropic turbulence spectrum is used to initialize the velocity field in the domain. Moreover, the computational configuration corresponds to amore » constant volume combustion vessel with inert mass source terms added to the governing equations to mimic the pressure rise due to piston motion, as present in practical engines. DME autoignition is found to be a complex three-staged process; each stage corresponds to a distinct chemical kinetic pathway. The distinct role of turbulence and reaction in generating scalar gradients and hence promoting molecular transport processes are investigated. Then, by applying numerical diagnostic techniques, the different heat release modes present in the igniting mixture are identified. In particular, the contribution of homogeneous autoignition, spontaneous ignition front propagation, and premixed deflagration towards the total heat release are quantified.« less
Applications of the Lattice Boltzmann Method to Complex and Turbulent Flows
NASA Technical Reports Server (NTRS)
Luo, Li-Shi; Qi, Dewei; Wang, Lian-Ping; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We briefly review the method of the lattice Boltzmann equation (LBE). We show the three-dimensional LBE simulation results for a non-spherical particle in Couette flow and 16 particles in sedimentation in fluid. We compare the LBE simulation of the three-dimensional homogeneous isotropic turbulence flow in a periodic cubic box of the size 1283 with the pseudo-spectral simulation, and find that the two results agree well with each other but the LBE method is more dissipative than the pseudo-spectral method in small scales, as expected.
Isotropic Monte Carlo Grain Growth
2013-04-25
IMCGG performs Monte Carlo simulations of normal grain growth in metals on a hexagonal grid in two dimensions with periodic boundary conditions. This may be performed with either an isotropic or a misorientation - and incliantion-dependent grain boundary energy.
NASA Astrophysics Data System (ADS)
Flad, David; Beck, Andrea; Munz, Claus-Dieter
2016-05-01
Scale-resolving simulations of turbulent flows in complex domains demand accurate and efficient numerical schemes, as well as geometrical flexibility. For underresolved situations, the avoidance of aliasing errors is a strong demand for stability. For continuous and discontinuous Galerkin schemes, an effective way to prevent aliasing errors is to increase the quadrature precision of the projection operator to account for the non-linearity of the operands (polynomial dealiasing, overintegration). But this increases the computational costs extensively. In this work, we present a novel spatially and temporally adaptive dealiasing strategy by projection filtering. We show this to be more efficient for underresolved turbulence than the classical overintegration strategy. For this novel approach, we discuss the implementation strategy and the indicator details, show its accuracy and efficiency for a decaying homogeneous isotropic turbulence and the transitional Taylor-Green vortex and compare it to the original overintegration approach and a state of the art variational multi-scale eddy viscosity formulation.
Test particle study of minor ions in solar wind turbulence
NASA Technical Reports Server (NTRS)
Zurbuchen, Th.; Bochsler, P.; Politano, H.; Pouquet, A.
1995-01-01
We perform a parameter study of the temporal evolution of a test particle distribution function in MHD turbulence. The turbulent fields are calculated using a pseudo-spectral method and periodic boundary conditions on a regular grid of 180(exp 3) points, appropriate for incompressible, homogeneous and isotropic turbulence. Initially, the kinetic and the magnetic energy are equal on the average. Both, deterministic and random initial conditions are used, in the former case with zeros of the magnetic field located at grid points, in the latter case located by interpolation between grid points. The evolution of the minor ion distribution function is studied in detail as these turbulent fields evolve, developing strong current and vorticity sheets. Using the full collisionless equation of motion for the test particles, the efficiency of nonlinear interactions can be studied. The results are compared to theoretical predictions and are then discussed in connection with the observations of the dynamical properties of solar wind minor ions derived from in situ observations.
Evolution of energy-containing turbulent eddies in the solar wind
NASA Technical Reports Server (NTRS)
Matthaeus, William H.; Oughton, Sean; Pontius, Duane H., Jr.; Zhou, YE
1994-01-01
Previous theoretical treatments of fluid-scale turbulence in the solar wind have concentrated on describing the state and dynamical evolution of fluctuations in the inertial range, which are characterized by power law energy spectra. In the present paper a model for the evolution of somewhat larger, more energetic magnetohydrodynamic (MHD) fluctuations is developed by analogy with classical hydrodynamic turbulence in the quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale models for transport of MHD turbulence in a weekly inhomogeneous medium. A set of equations is presented for the evolution of the turbulence, including the transport and nonlinear evolution of magnetic and kinetic energy, cross helicity, and their correlation scales. Two versions of the model are derived, depending on whether the fluctuations are distributed isotropically in three dimensions or restricted to the two-dimensional plane perpendicular to the mean magnetic field. This model includes a number of potentially important physical effects that have been neglected in previous discussions of transport of solar wind turbulence.
Wind tunnel experiments on the interactions between turbulence and small inertial droplets
NASA Astrophysics Data System (ADS)
Bateson, Colin; Aliseda, Alberto
2011-11-01
Understanding the dynamics of particles in turbulent flows is important to many engineering and environmental problems including spray atomization as well as cloud-droplet growth and precipitation. Specifically, we have studied the effect of turbulence on droplet collision-coalescence in an effort to clarify its role in the process of warm rain formation. We are exploring the hypothesis that turbulence-induced-collisions can explain the size gap between the limit of condensational growth and the onset of gravitational collisions and sedimentation. We use wind tunnel experiments to study the evolution of water droplets in homogeneous, isotropic, slowly decaying grid turbulence. We analyze the process of preferential concentration and the enhanced relative velocity of droplets in the 1-100 micron range due to their inertial interactions with the underlying turbulence. We collect droplet size and velocity data from a Phase Doppler Particle Analyzer (PDPA) to understand the influence of turbulence on the droplet collision kernel, and to quantitatively model it in terms of the Radial Distribution Function. We use high-speed visualizations to obtain two-dimensional droplet velocity fields to validate the PDPA point measurements, and to model the relative velocity distribution as a function of droplet pair spacing and Stokes number. Supported by NSF grant ATM-0731248.
Study of the velocity gradient tensor in turbulent flow
NASA Technical Reports Server (NTRS)
Cheng, Wei-Ping; Cantwell, Brian
1996-01-01
The behavior of the velocity gradient tensor, A(ij)=delta u(i)/delta x(j), was studied using three turbulent flows obtained from direct numerical simulation The flows studies were: an inviscid calculation of the interaction between two vortex tubes, a homogeneous isotropic flow, and a temporally evolving planar wake. Self-similar behavior for each flow was obtained when A(ij) was normalized with the mean strain rate. The case of the interaction between two vortex tubes revealed a finite sized coherent structure with topological characteristics predictable by a restricted Euler model. This structure was found to evolve with the peak vorticity as the flow approached singularity. Invariants of A(ij) within this structure followed a straight line relationship of the form: gamma(sup 3)+gammaQ+R=0, where Q and R are the second and third invariants of A(ij), and the eigenvalue gamma is nearly constant over the volume of this structure. Data within this structure have local strain topology of unstable-node/saddle/saddle. The characteristics of the velocity gradient tensor and the anisotropic part of a related acceleration gradient tensor H(ij) were also studied for a homogeneous isotropic flow and a temporally evolving planar wake. It was found that the intermediate principal eigenvalue of the rate-of-strain tensor of H(ij) tended to be negative, with local strain topology of the type stable-node/saddle/saddle. There was also a preferential eigenvalue direction. The magnitude of H(ij) in the wake flow was found to be very small when data were conditioned at high local dissipation regions. This result was not observed in the relatively low Reynolds number simulation of homogeneous isotropic flow. A restricted Euler model of the evolution of A(ij) was found to reproduce many of the topological features identified in the simulations.
Transversely isotropic poroelasticity arising from thin isotropic layers
Berryman, J.G.
1996-11-01
Percolation phenomena play central roles in the field of poroelasticity, where two distinct sets of percolating continua intertwine. A connected solid frame forms the basis of the elastic behavior of a poroelastic medium in the presence of confining forces, while connected pores permit a percolating fluid (if present) to influence the mechanical response of the system from within. The present paper discusses isotropic and anisotropic poroelastic media and establishes general formulas for the behavior of transversely isotropic poroelasticity arising from laminations of isotropic components. The Backus averaging method is shown to provide elementary means of constructing general formulas. The results for confined fluids are then compared with the more general Gassmann formulas that must be satisfied by any anisotropic poroelastic medium and found to be in complete agreement.
Charged Particle Diffusion in Isotropic Random Static Magnetic Fields
NASA Astrophysics Data System (ADS)
Subedi, P.; Sonsrettee, W.; Matthaeus, W. H.; Ruffolo, D. J.; Wan, M.; Montgomery, D.
2013-12-01
Study of the transport and diffusion of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider Diffusion of charged particles in fully three dimensional statistically isotropic magnetic field turbulence with no mean field which is pertinent to many astrophysical situations. We classify different regions of particle energy depending upon the ratio of Larmor radius of the charged particle to the characteristic outer length scale of turbulence. We propose three different theoretical models to calculate the diffusion coefficient each applicable to a distinct range of particle energies. The theoretical results are compared with those from computer simulations, showing very good agreement.
Interaction of a free flame front with a turbulence field
NASA Technical Reports Server (NTRS)
Tucker, Maurice
1956-01-01
Small-perturbation spectral-analysis techniques are used to obtain the root-mean-square flame-generated turbulence velocities and the attenuating pressure fluctuations stemming from interaction of a constant-pressure flame front with a field of isotropic turbulence in the absence of turbulence decay processes.
Stochastic differential equations and turbulent dispersion
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1983-01-01
Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.
NASA Astrophysics Data System (ADS)
Sethi, Munish; Sharma, Arvind; Sharma, Vishal; Sharma, Anupamdeep
2016-08-01
This study discusses the dispersion equation for SH waves in a non-homogeneous monoclinic layer over a semi-infinite isotropic medium. The wave velocity equation has been obtained. In the isotropic case, when the non-homogeneity is absent, the dispersion equation reduces to a standard SH wave equation. The dispersion curves are depicted by means of graphs for different values of non-homogeneity parameters for the layer and semi-infinite medium.
Joint-constraint model for large-eddy simulation of helical turbulence.
Yu, Changping; Xiao, Zuoli; Shi, Yipeng; Chen, Shiyi
2014-04-01
A three-term mixed subgrid-scale (SGS) stress model is proposed for large-eddy simulation (LES) of helical turbulence. The new model includes a Smagorinsky-Lilly term, a velocity gradient term, and a symmetric vorticity gradient term. The model coefficients are determined by minimizing the mean square error between the realistic and modeled Leonard stresses under a joint constraint of kinetic energy and helicity fluxes. The model formulated as such is referred to as joint-constraint dynamic three-term model (JCD3TM). First, the new model is evaluated a priori using the direct numerical simulation (DNS) data of homogeneous isotropic turbulence with helical forcing. It is shown that the SGS dissipation fractions from all three terms in JCD3TM have the properties of length-scale invariance in inertial subrange. JCD3TM can predict the SGS stresses, energy flux, and helicity flux more accurately than the dynamic Smagorinsky model (DSM) and dynamic mixed helical model (DMHM) in both pointwise and statistical senses. Then, the performance of JCD3TM is tested a posteriori in LESs of both forced and freely decaying helical isotropic turbulence. It is found that JCD3TM possesses certain features of superiority over the other two models in predicting the energy spectrum, helicity spectrum, high-order statistics, etc. It is also noteworthy that JCD3TM is capable of simulating the evolutions of both energy and helicity spectra more precisely than other models in decaying helical turbulence. We claim that the present SGS model can capture the main helical features of turbulent motions and may serve as a useful tool for LES of helical turbulent flows. PMID:24827346
Turbulence on a Fractal Fourier Set.
Lanotte, Alessandra S; Benzi, Roberto; Malapaka, Shiva K; Toschi, Federico; Biferale, Luca
2015-12-31
A novel investigation of the nature of intermittency in incompressible, homogeneous, and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension D from the original three dimensional case to a strongly decimated system with D=2.5, where only about 3% of the Fourier modes interact. This is a unique methodology to probe the statistical properties of the turbulent energy cascade, without breaking any of the original symmetries of the equations. While the direct energy cascade persists, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the codimension of the fractal set E(k)∼k(-5/3+3-D) explains the results. At small scales, the intermittency of the vorticity field is observed to be quasisingular as a function of the fractal mode reduction, leading to an almost Gaussian statistics already at D∼2.98. These effects must be connected to a genuine modification in the triad-to-triad nonlinear energy transfer mechanism. PMID:26764993
Dip-moveout error in transversely isotropic media with linear velocity variation in depth
Larner, K.
1992-10-01
Levin (1990) modeled the moveout, within Common-midpoint (CMP) gathers, of reflections from plane-dipping reflectors beneath homogeneous, transversely isotropic media. For some media, when the axis of symmetry for the anisotropy was vertical, he found departures in stacking velocity from predictions based upon the familiar cosine-of-dip correction for isotropic media. Here, I do similar tests, again with transversely isotropic models with vertical axis of symmetry, but now allowing the medium velocity to vary linearly with depth. Results for the same four anisotropic media studied by Levin show behavior of dip-corrected stacking velocity with reflector dip that, for all velocity gradients considered, differs little from that for the counterpart homogeneous media. As with isotropic media, traveltimes in an inhomogeneous, transversely isotropic medium can be modeled adequately with a homogeneous model with vertical velocity equal to the vertical rms velocity of the inhomogeneous medium. In practice, dip-moveout (DMO) is based on the assumption that either the medium is homogeneous or its velocity varies with depth, but in both cases isotropy is assumed. It turns out that for only one of the transversely isotropic media considered here --shale-limestone -- would v(z) DMO fail to give an adequate correction within CMP gathers. For the shale-limestone, fortuitously the constant-velocity DMO gives a better moveout correction than does the v(z) DMO.
Dip-moveout error in transversely isotropic media with linear velocity variation in depth
Larner, K.
1992-01-01
Levin (1990) modeled the moveout, within Common-midpoint (CMP) gathers, of reflections from plane-dipping reflectors beneath homogeneous, transversely isotropic media. For some media, when the axis of symmetry for the anisotropy was vertical, he found departures in stacking velocity from predictions based upon the familiar cosine-of-dip correction for isotropic media. Here, I do similar tests, again with transversely isotropic models with vertical axis of symmetry, but now allowing the medium velocity to vary linearly with depth. Results for the same four anisotropic media studied by Levin show behavior of dip-corrected stacking velocity with reflector dip that, for all velocity gradients considered, differs little from that for the counterpart homogeneous media. As with isotropic media, traveltimes in an inhomogeneous, transversely isotropic medium can be modeled adequately with a homogeneous model with vertical velocity equal to the vertical rms velocity of the inhomogeneous medium. In practice, dip-moveout (DMO) is based on the assumption that either the medium is homogeneous or its velocity varies with depth, but in both cases isotropy is assumed. It turns out that for only one of the transversely isotropic media considered here --shale-limestone -- would v(z) DMO fail to give an adequate correction within CMP gathers. For the shale-limestone, fortuitously the constant-velocity DMO gives a better moveout correction than does the v(z) DMO.
Effects of turbulence on the collision rate of cloud droplets
NASA Astrophysics Data System (ADS)
Ayala, Orlando
This dissertation concerns effects of air turbulence on the collision rate of atmospheric cloud droplets. This research was motivated by the speculation that air turbulence could enhance the collision rate thereby help transform cloud droplets to rain droplets in a short time as observed in nature. The air turbulence within clouds is assumed to be homogeneous and isotropic, and its small-scale motion (1 mm to 10 cm scales) is computationally generated by direct numerical integration of the full Navier-Stokes equations. Typical droplet and turbulence parameters of convective warm clouds are used to determine the Stokes numbers (St) and the nondimensional terminal velocities (Sv) which characterize droplet relative inertia and gravitational settling, respectively. A novel and efficient methodology for conducting direct numerical simulations (DNS) of hydrodynamically-interacting droplets in the context of cloud microphysics has been developed. This numerical approach solves the turbulent flow by the pseudo-spectral method with a large-scale forcing, and utilizes an improved superposition method to embed analytically the local, small-scale (10 mum to 1 mm) disturbance flows induced by the droplets. This hybrid representation of background turbulent air motion and the induced disturbance flows is then used to study the combined effects of hydrodynamic interactions and airflow turbulence on the motion and collisions of cloud droplets. Hybrid DNS results show that turbulence can increase the geometric collision kernel relative to the gravitational geometric kernel by as much as 42% due to enhanced radial relative motion and preferential concentration of droplets. The exact level of enhancements depends on the Taylor-microscale Reynolds number, turbulent dissipation rate, and droplet pair size ratio. One important finding is that turbulence has a relatively dominant effect on the collision process between droplets close in size as the gravitational collision mechanism
Acoustic radiation and surface pressure characteristics of an airfoil due to incident turbulence
NASA Technical Reports Server (NTRS)
Paterson, R. W.
1976-01-01
A theoretical and experimental investigation of the noise and unsteady surface pressure characteristics of an isolated airfoil in a uniform mean velocity, homogeneous, nearly-isotropic turbulence field was conducted. Wind tunnel experiments were performed with a 23 cm chord, two dimensional NACA 0012 airfoil over a free stream Mach number range of 0.1 to 0.5. Far-field noise spectra and directivity were measured in an anechoic chamber that surrounded the tunnel open jet test section. Spanwise and chordwise distribution of unsteady airfoil surface pressure spectra and surface pressure cross-spectra were obtained. Incident turbulence intensities, length scales, spectra, and spanwise cross-spectra, required in the calculation of far-field noise and surface pressure characteristics were also measured.
Regenerative growth due to axial flow induced by vortex-turbulence interaction
NASA Astrophysics Data System (ADS)
Stout, Eric; Hussain, Fazle
2013-11-01
Direct numerical simulations of a vortex column embedded in fine scale homogeneous, isotropic turbulence reveals an inviscid mechanism for induction of axial flow on the column. Vortex threads, produced outside the column during vortex-turbulence interaction, are shown to drive the mechanism of axial flow generation. Oppositely oriented threads radially separate by self-induction, hence causing net axial flow. At computationally accessible Reynolds numbers (Re ≡ vortex circulation/viscosity = 10 000), the axial flow due to a pair of oppositely signed vortex threads outside the column increases both with Re and time. At high Re, the axial flow can increase sufficiently to render the vortex column unstable by the well-known q criterion. The vorticity field reveals that axial flow is another mechanism, perhaps more dominant than the parent-offspring hairpin vortex scenario (Hussain, Pradeep & Stout JFM 2011), of regenerative energy growth - likely to be important for implementing breakup of aircraft trailing vortices.
Relative velocity distribution of inertial particles in turbulence: A numerical study
NASA Astrophysics Data System (ADS)
Perrin, Vincent E.; Jonker, Harm J. J.
2015-10-01
The distribution of relative velocities between particles provides invaluable information on the rates and characteristics of particle collisions. We show that the theoretical model of Gustavsson and Mehlig [K. Gustavsson and B. Mehlig, J. Turbul. 15, 34 (2014), 10.1080/14685248.2013.875188], within its anticipated limits of validity, can predict the joint probability density function of relative velocities and separations of identical inertial particles in isotropic turbulent flows with remarkable accuracy. We also quantify the validity range of the model. The model matches two limits (or two types) of relative motion between particles: one where pair diffusion dominates (i.e., large coherence between particle motion) and one where caustics dominate (i.e., large velocity differences between particles at small separations). By using direct numerical simulation combined with Lagrangian particle tracking, we assess the model prediction in homogeneous and isotropic turbulence. We demonstrate that, when sufficient caustics are present at a given separation and the particle response time is significantly smaller than the integral time scales of the flow, the distribution exhibits the same universal power-law form dictated by the correlation dimension as predicted by the model of Gustavsson and Mehlig. In agreement with the model, no strong dependency on the Taylor-based Reynolds number is observed.
Relative velocity distribution of inertial particles in turbulence: A numerical study.
Perrin, Vincent E; Jonker, Harm J J
2015-10-01
The distribution of relative velocities between particles provides invaluable information on the rates and characteristics of particle collisions. We show that the theoretical model of Gustavsson and Mehlig [K. Gustavsson and B. Mehlig, J. Turbul. 15, 34 (2014)], within its anticipated limits of validity, can predict the joint probability density function of relative velocities and separations of identical inertial particles in isotropic turbulent flows with remarkable accuracy. We also quantify the validity range of the model. The model matches two limits (or two types) of relative motion between particles: one where pair diffusion dominates (i.e., large coherence between particle motion) and one where caustics dominate (i.e., large velocity differences between particles at small separations). By using direct numerical simulation combined with Lagrangian particle tracking, we assess the model prediction in homogeneous and isotropic turbulence. We demonstrate that, when sufficient caustics are present at a given separation and the particle response time is significantly smaller than the integral time scales of the flow, the distribution exhibits the same universal power-law form dictated by the correlation dimension as predicted by the model of Gustavsson and Mehlig. In agreement with the model, no strong dependency on the Taylor-based Reynolds number is observed. PMID:26565347
On the vortex dynamics in fractal Fourier turbulence.
Lanotte, Alessandra S; Malapaka, Shiva Kumar; Biferale, Luca
2016-04-01
Incompressible, homogeneous and isotropic turbulence is studied by solving the Navier-Stokes equations on a reduced set of Fourier modes, belonging to a fractal set of dimension D . By tuning the fractal dimension parameter, we study the dynamical effects of Fourier decimation on the vortex stretching mechanism and on the statistics of the velocity and the velocity gradient tensor. In particular, we show that as we move from D = 3 to D ∼ 2.8 , the statistics gradually turns into a purely Gaussian one. This result suggests that even a mild fractal mode reduction strongly depletes the stretching properties of the non-linear term of the Navier-Stokes equations and suppresses anomalous fluctuations. PMID:27125678
Sedimentation of finite-size particles in quiescent and turbulent environments
NASA Astrophysics Data System (ADS)
Brandt, Luca; Fornari, Walter; Picano, Francesco
2015-11-01
Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows. We present Direct Numerical Simulations of sedimentation in quiescent and turbulent environments using an Immersed Boundary Method to study the behavior of finite-size particles in homogeneous isotropic turbulence. The particle radius is approximately 6 Komlogorov lengthscales, the volume fraction 0.5% and 1% and the density ratio 1.02. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reduction with respect to a single particle in quiescent fluid is about 12% in dilute conditions. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated to the intermittent fast sedimentation of particle pairs in drafting-kissing-tumbling motions. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulas and show that non stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment. This work was supported by the European Research Council Grant No. ERC-2013- CoG-616186, TRITOS.
A novel VLES model accounting for near-wall turbulence: physical rationale and applications
NASA Astrophysics Data System (ADS)
Jakirlic, Suad; Chang, Chi-Yao; Kutej, Lukas; Tropea, Cameron
2014-11-01
A novel VLES (Very Large Eddy Simulation) model whose non-resolved residual turbulence is modelled by using an advanced near-wall eddy-viscosity model accounting for the near-wall Reynolds stress anisotropy influence on the turbulence viscosity by modelling appropriately the velocity scale in the relevant formulation (Hanjalic et al., 2004) is proposed. It represents a variable resolution Hybrid LES/RANS (Reynolds-Averaged Navier-Stokes) computational scheme enabling a seamless transition from RANS to LES depending on the ratio of the turbulent viscosities associated with the unresolved scales corresponding to the LES cut-off and the `unsteady' scales pertinent to the turbulent properties of the VLES residual motion, which varies within the flow domain. The VLES method is validated interactively in the process of the model derivation by computing fully-developed flow in a plane channel (important representative of wall-bounded flows, underlying the log-law for the velocity field, for studying near-wall Reynolds stress anisotropy) and a separating flow over a periodic arrangement of smoothly-contoured 2-D hills. The model performances are also assessed in capturing the natural decay of the homogeneous isotropic turbulence. The model is finally applied to swirling flow in a vortex tube, flow in an IC-engine configuration and flow past a realistic car model.
Least Squares Shadowing Sensitivity Analysis of Chaotic and Turbulent Fluid Flows
NASA Astrophysics Data System (ADS)
Blonigan, Patrick; Wang, Qiqi; Gomez, Steven
2013-11-01
Computational methods for sensitivity analysis are invaluable tools for fluid dynamics research and engineering design. These methods are used in many applications, including aerodynamic shape optimization and adaptive grid refinement. However, traditional sensitivity analysis methods break down when applied to long-time averaged quantities in chaotic fluid flow fields, such as those obtained using high-fidelity turbulence simulations. This break down is due to the ``Butterfly Effect'' the high sensitivity of chaotic dynamical systems to the initial condition. A new sensitivity analysis method developed by the authors, Least Squares Shadowing (LSS), can compute useful and accurate gradients for quantities of interest in chaotic and turbulent fluid flows. LSS computes gradients using the ``shadow trajectory,'' a phase space trajectory (or solution) for which perturbations to the flow field do not grow exponentially in time. This talk will outline Least Squares Shadowing and demonstrate it on several chaotic and turbulent fluid flows, including homogeneous isotropic turbulence, Rayleigh-Bénard convection and turbulent channel flow. We would like to acknowledge AFSOR Award F11B-T06-0007 under Dr. Fariba Fahroo, NASA Award NNH11ZEA001N under Dr. Harold Atkins, as well as financial support from ConocoPhillips, the NDSEG fellowship and the ANSYS Fellowship.
Beta dependence of electron heating in decaying whistler turbulence: Particle-in-cell simulations
Saito, S.; Peter Gary, S.
2012-01-15
Two-dimensional particle-in-cell simulations have been carried out to study electron beta dependence of decaying whistler turbulence and electron heating in a homogeneous, collisionless magnetized plasma. Initially, applied whistler fluctuations at relatively long wavelengths cascade their energy into shorter wavelengths. This cascade leads to whistler turbulence with anisotropic wavenumber spectra which are broader in directions perpendicular to the background magnetic field than in the parallel direction. Comparing the development of whistler turbulence at different electron beta values, it is found that both the wavenumber spectrum anisotropy and electron heating anisotropy decrease with increasing electron beta. This indicates that higher electron beta reduces the perpendicular energy cascade of whistler turbulence. Fluctuation energy dissipation by electron Landau damping responsible for the electron parallel heating becomes weaker at higher electron beta, which leads to more isotropic heating. It suggests that electron kinetic processes are important in determining the properties of whistler turbulence. This kinetic property is applied to discuss the generation of suprathermal strahl electron distributions in the solar wind.
Large Eddy Simulation of Stagnation Point Heat Transfer Under Free-Stream Turbulence
NASA Astrophysics Data System (ADS)
Xiong, Zhongmin; Lele, Sanjiva K.
2001-11-01
An implicit dual time stepping scheme with linearized subiterations is developed for efficient solution of the compressible Navier-Stokes equations. The LU decomposition is employed in the subiteration scheme in conjunction with spatially varying pseudo time step; the resultant algorithm is five times faster in comparison with the conventional approximate factorization method. Large eddy simulation based on this method is performed to investigate the effect of free stream turbulence on the stagnation point heat transfer. The pre-computed homogeneous isotropic turbulence is introduced upstream of a compressible leading edge impinging flow. The interaction between free-stream turbulence and the leading edge involves three distinct processes: free turbulence decay, inviscid distortion and viscous interaction. The energetic streamwise vortical structures formed near the surface are found to be temporally persistent, and spatially characterized by a spanwise scale of the order of the local boundary layer thickness. They are identified as the direct cause of the large heat transfer enhancement in the presence of free-stream turbulence.
NASA Astrophysics Data System (ADS)
Druzhinin, O. A.; Elghobashi, S. E.
1999-09-01
In a recent study we showed that the two-fluid (TF) formulation can be used in the direct numerical simulation (DNS) of bubble- (or particle-) laden decaying isotropic turbulence with considerable saving in CPU-time and memory as compared to the trajectory approach employed by many researchers. In the present paper, we develop a Lagrangian-Eulerian mapping (LEM) solver for DNS of bubble-laden turbulent shear flows using TF. The purpose of LEM is to resolve the large gradients of bubble velocity and concentration which result from the absence of the diffusion terms in the equations of bubble-phase motion and the preferential accumulation of bubbles. A standard finite-difference scheme (FDS) fails to resolve these gradients. We examine the performance of the new method in DNS of a bubble-laden Taylor-Green vortex, spatially developing plane mixing layer, and homogeneous shear turbulent flow.
Hierarchical energy spectra in quasi-steady turbulence
NASA Astrophysics Data System (ADS)
Horiuti, Kiyosi; Fujisawa, Takeharu
2007-11-01
The Kolmogorov -5/3 law, E0(k)=CK&2/3circ;k^- 3/5, forms a base state for the energy spectrum in the inertial subrange, which is applied only to a steady state. An expansion for the spectrum about this base state using the perturbation method (Yoshizawa 1998, Woodroff & Rubinstein 2006) yields a nonequilibrium spectrum as E(k)= E0(k)+CNɛ;&-2/3circ;k-7/3+C3(ɛ;&-1circ;-2ɛ^2&-2circ;/3)k-9/3+, where ɛ and ɛ denote the dissipation rate and its time derivative, respectively. This formula indicates that the spectrum contains the hierarchical scaling exponents, and the -7/3 and -9/3 scalings can be induced by the fluctuation of ɛ. Long term-temporal average yields E(k) E0(k), but the -7/3 component can be extracted by conditionally sampling on ɛ . We carried out this extraction using the DNS data for quasi- steady forced homogeneous isotropic turbulence and homogeneous sheared turbulence. It is shown that the -7/3 spectrum is indeed identified in both flows. The relationship between the each decomposed spectra and those induced by the three modes of vorticity configurations in the stretched spiral vortex model (Lundgren 1982, Horiuti & Fujisawa 2007) will be discussed.
a Stochastic Model of the Dispersion of Solid Particles in a Turbulent Gaseous Environment
NASA Astrophysics Data System (ADS)
Lightstone, Marilyn Frances
This thesis is concerned with the development of a model to predict the dispersion of solid particles in a turbulent gaseous environment. The motion of particles in a turbulent flow is relevant to a number of areas of engineering including, for example, combustion where the motion of liquid fuel droplets in a combustion chamber is of interest, and atmospheric lows where one may be interested in calculating the dispersion of pollutants leaving a smokestack. The challenge in this work is to properly account for the effect of the turbulence on the momentum of the particle: the fluctuating turbulent gas-phase velocities impose a random force on the particle hence changing the particle equation of motion from an ordinary differential equation to a random or stochastic differential equation. The approach taken here is to approximate the random force acting on the particle as a Gaussian white noise random process such that the particle equation of motion is treated as a stochastic differential equation with a white noise forcing function. By applying the theories of stochastic mathematics, information on the particle velocities is obtained hence allowing for particle position and concentrations to be determined. The validity of the model was examined by comparing model predictions to analytical or experimental results for particles released into a number of fundamental flows including laminar, uniform flows of homogeneous isotropic and grid-generated turbulence, and round jets. In addition, a number of particle sites were considered ranging from very light 'fluid' particles, which essentially follow the gas-phase turbulence, to heavy particles which have a limited response to the turbulence. Predictions from the model were found to compare favourably with analytical and experimental results for the flows considered. Further, the new model was compared to one which models the effect of the gas-phase turbulence on the particle concentration as a gradient diffusion process
Estimating three-demensional energy transfer in isotropic turbulence
NASA Technical Reports Server (NTRS)
Li, K. S.; Helland, K. N.; Rosenblatt, M.
1980-01-01
To obtain an estimate of the spectral transfer function that indicates the rate of decay of energy, an x-wire probe was set at a fixed position, and two single wire probes were set at a number of locations in the same plane perpendicular to the mean flow in the wind tunnel. The locations of the single wire probes are determined by pseudo-random numbers (Monte Carlo). Second order spectra and cross spectra are estimated. The assumption of isotropy relative to second order spectra is examined. Third order spectra are also estimated corresponding to the positions specified. A Monte Carlo Fourier transformation of the downstream bispectra corresponding to integration across the plane perpendicular to the flow is carried out assuming isotropy. Further integration is carried out over spherical energy shells.
The first-digit frequencies in data of turbulent flows
NASA Astrophysics Data System (ADS)
Biau, Damien
2015-12-01
Considering the first significant digits (noted d) in data sets of dissipation for turbulent flows, the probability to find a given number (d = 1 or 2 or …9) would be 1/9 for a uniform distribution. Instead the probability closely follows Newcomb-Benford's law, namely P(d) = log(1 + 1 / d) . The discrepancies between Newcomb-Benford's law and first-digits frequencies in turbulent data are analysed through Shannon's entropy. The data sets are obtained with direct numerical simulations for two types of fluid flow: an isotropic case initialized with a Taylor-Green vortex and a channel flow. Results are in agreement with Newcomb-Benford's law in nearly homogeneous cases and the discrepancies are related to intermittent events. Thus the scale invariance for the first significant digits, which supports Newcomb-Benford's law, seems to be related to an equilibrium turbulent state, namely with a significant inertial range. A matlab/octave program provided in appendix is such that part of the presented results can easily be replicated.
Early isotropization of the Glasma
NASA Astrophysics Data System (ADS)
Epelbaum, T.
2014-11-01
A first principle treatment of the early stages of a heavy ion collision within the Color Glass Condensate framework seems to indicate an early hydrodynamization of the initially out of equilibrium Quark Gluon Plasma. Contrasting with the leading order CGC result, the improved calculation presented here provides evidence for a fast isotropization of the pressure tensor, as well as an anomalously small shear viscosity over entropy ratio.
Compressible homogeneous shear: Simulation and modeling
NASA Technical Reports Server (NTRS)
Sarkar, S.; Erlebacher, G.; Hussaini, M. Y.
1992-01-01
Compressibility effects were studied on turbulence by direct numerical simulation of homogeneous shear flow. A primary observation is that the growth of the turbulent kinetic energy decreases with increasing turbulent Mach number. The sinks provided by compressible dissipation and the pressure dilatation, along with reduced Reynolds shear stress, are shown to contribute to the reduced growth of kinetic energy. Models are proposed for these dilatational terms and verified by direct comparison with the simulations. The differences between the incompressible and compressible fields are brought out by the examination of spectra, statistical moments, and structure of the rate of strain tensor.
Xu, Ying
2005-05-01
Many particle-laden flows in engineering applications involve turbulent gas flows. Modeling multiphase turbulent flows is an important research topic with applications in fluidized beds and particle conveying. A predictive multiphase turbulence model can help CFD codes to be more useful for engineering applications, such as the scale-up in the design of circulating fluidized combustor and coal gasifications. In engineering applications, the particle volume fraction can vary from dilute (<10{sup -4}) to dense ({approx} 50%). It is reasonable to expect that multiphase turbulence models should at least satisfy some basic modeling and performance criteria and give reasonable predictions for the canonical problems in dilute particle-laden turbulent flows. In this research, a comparative assessment of predictions from Simonin and Ahmadi's turbulence models is performed with direct numerical simulation (DNS) for two canonical problems in particle-laden turbulent flows. Based on the comparative assessment, some criteria and the areas for model improvement are identified: (1) model for interphase TKE transfer, especially the time scale of interphase TKE transfer, and (2) correct prediction of TKE evolution with variation of particle Stokes number. Some deficiencies that are identified in the Simonin and Ahmadi models, limit the applicability. A new multiphase turbulence model, the Equilibration of Energy Model (EEM), is proposed in this work. In EEM, a multiscale interaction time scale is proposed to account for the interaction of a particle with a range of eddy sizes. EEM shows good agreement with the DNS results for particle-laden isotropic turbulence. For particle-laden homogeneous shear flows, model predictions from EEM can be further improved if the dissipation rate in fluid phase is modeled with more accuracy.
Gravitational Landau damping for an isotropic cluster of stars
NASA Technical Reports Server (NTRS)
Habib, Salman; Kandrup, Henry E.; Yip, Ping F.
1986-01-01
The problem of ascertaining the dynamical stability and the existence of Landau damping in static, isotropic 'collisionless' star clusters is addressed. The second-order formalism of Kandrup and Sygnet (1985) is applied to a homogeneous and isotropic plasma, demonstrating formally that the unperturbed configuration will always be stable and that the modes must be purely oscillatory. The form of these modes is explicitly examined, culminating in an analytic expression for the time evolution of the density induced by an initial perturbation. It is shown how these considerations can be adapted trivially to localized, nonradial disturbances of a self-gravitating system of stars. The possible existence of gravitational Landau damping for more generic perturbations is discussed.
Anisotropic turbulence in the solar wind
NASA Technical Reports Server (NTRS)
Matthaeus, W. H.; Bieber, J. W.; Zank, G. P.
1995-01-01
Solar wind turbulence has been viewed traditionally as composed of parallel propagating ('slab' fluctuations) or otherwise as isotropic turbulence. A variety of recent investigations, reviewed here, indicate that the spectrum may contain a significant admixture of two dimensional fluctuations, having variations mainly perpendicular to the local magnetic field. These indications come from simulations, from the theory of nearly incompressible MHD, from cosmic ray transport studies and from transport theory for solar wind turbulence, as well as from interpretations of direct observations. Thus, solar wind turbulence may be more like bundles of spaghetti than like parallel phase fronts.
Stirring turbulence with turbulence
NASA Astrophysics Data System (ADS)
Cekli, Hakki Ergun; Joosten, René; van de Water, Willem
2015-12-01
We stir wind-tunnel turbulence with an active grid that consists of rods with attached vanes. The time-varying angle of these rods is controlled by random numbers. We study the response of turbulence on the statistical properties of these random numbers. The random numbers are generated by the Gledzer-Ohkitani-Yamada shell model, which is a simple dynamical model of turbulence that produces a velocity field displaying inertial-range scaling behavior. The range of scales can be adjusted by selection of shells. We find that the largest energy input and the smallest anisotropy are reached when the time scale of the random numbers matches that of the largest eddies of the wind-tunnel turbulence. A large mismatch of these times creates a highly intermittent random flow with interesting but quite anomalous statistics.
Induced piezoelectricity in isotropic biomaterial.
Zimmerman, R L
1976-12-01
Isotropic material can be made to exhibit piezoelectric effects by the application of a constant electric field. For insulators, the piezoelectric strain constant is proportional to the applied electric field and for semiconductors, an additional out-of-phase component of piezoelectricity is proportional to the electric current density in the sample. The two induced coefficients are proportional to the strain-dependent dielectric constant (depsilon/dS + epsilon) and resistivity (drho/dS - rho), respectively. The latter is more important at frequencies such that rhoepsilonomega less than 1, often the case in biopolymers. Signals from induced piezoelectricity in nature may be larger than those from true piezoelectricity. PMID:990389
Isotropic microscale mechanical properties of coral skeletons
Pasquini, Luca; Molinari, Alan; Fantazzini, Paola; Dauphen, Yannicke; Cuif, Jean-Pierre; Levy, Oren; Dubinsky, Zvy; Caroselli, Erik; Prada, Fiorella; Goffredo, Stefano; Di Giosia, Matteo; Reggi, Michela; Falini, Giuseppe
2015-01-01
Scleractinian corals are a major source of biogenic calcium carbonate, yet the relationship between their skeletal microstructure and mechanical properties has been scarcely studied. In this work, the skeletons of two coral species: solitary Balanophyllia europaea and colonial Stylophora pistillata, were investigated by nanoindentation. The hardness HIT and Young's modulus EIT were determined from the analysis of several load–depth data on two perpendicular sections of the skeletons: longitudinal (parallel to the main growth axis) and transverse. Within the experimental and statistical uncertainty, the average values of the mechanical parameters are independent on the section's orientation. The hydration state of the skeletons did not affect the mechanical properties. The measured values, EIT in the 76–77 GPa range, and HIT in the 4.9–5.1 GPa range, are close to the ones expected for polycrystalline pure aragonite. Notably, a small difference in HIT is observed between the species. Different from corals, single-crystal aragonite and the nacreous layer of the seashell Atrina rigida exhibit clearly orientation-dependent mechanical properties. The homogeneous and isotropic mechanical behaviour of the coral skeletons at the microscale is correlated with the microstructure, observed by electron microscopy and atomic force microscopy, and with the X-ray diffraction patterns of the longitudinal and transverse sections. PMID:25977958
A Lagrangian dynamic subgrid-scale model turbulence
NASA Technical Reports Server (NTRS)
Meneveau, C.; Lund, T. S.; Cabot, W.
1994-01-01
A new formulation of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic Lagrangian time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.
Interaction of turbulence with flexible beams in fluidic energy harvesting
NASA Astrophysics Data System (ADS)
Danesh Yazdi, Amir Hossein
Advances in the development and fabrication of microelectronics have enhanced the energy efficiency of these devices to such an extent that they can now operate at very low power levels, typically on the order of a few microwatts or less. Batteries are primarily thought of as the most convenient source of power for electronic devices, but in instances where a device needs to be deployed in a difficult-to-access location such as under water, the added weight and especially maintenance of such a power source becomes costly. A solution that avoids this problem and is particularly attractive in a "deploy & forget" setting involves designing a device that continuously harvests energy from the surrounding environment. Piezoelectric energy harvesters, which employ the direct piezoelectric effect to convert mechanical strain into electrical energy, have garnered a great deal of attention in the literature. This work presents an overview of the experimental and analytical results related to fluidic energy extraction from vortex and turbulent flow using piezoelectric cantilever beams. In particular, the development of the FTGF (Fourier Transform-Green's Function) solution approach to the coupled, continuous electromechanical equations governing piezoelectric cantilever beams and the associated TFB (Train of Frozen Boxcars) method, which models the flow of vortices and turbulent eddies over the beams, is discussed. In addition, the behavior of fluidic energy harvesters in decaying isotropic, homogeneous grid turbulence generated by passive, semi-passive and active grids is examined and a novel grid-turbulence forcing model is introduced. An expression for the expected power output of the piezoelectric beam is obtained by utilizing this forcing function model in the single degree-of-freedom electromechanical equations. Furthermore, approximate, closed-form solutions to the theoretical expected power are derived from deterministic turbulence forcing models and are compared with
Supersonic turbulence in 3D isothermal flow collision
NASA Astrophysics Data System (ADS)
Folini, Doris; Walder, Rolf; Favre, Jean M.
2014-02-01
Large scale supersonic bulk flows are present in a wide range of astrophysical objects, from O-star winds to molecular clouds, galactic sheets, accretion, or γ-ray bursts. Associated flow collisions shape observable properties and internal physics alike. Our goal is to shed light on the interplay between large scale aspects of such collision zones and the characteristics of the compressible turbulence they harbor. Our model setup is as simple as can be: 3D hydrodynamical simulations of two head-on colliding, isothermal, and homogeneous flows with identical upstream (subscript u) flow parameters and Mach numbers 2 < Mu < 43. The turbulence in the collision zone is driven by the upstream flows, whose kinetic energy is partly dissipated and spatially modulated by the shocks confining the zone. Numerical results are in line with expectations from self-similarity arguments. The spatial scale of modulation grows with the collision zone. The fraction of energy dissipated at the confining shocks decreases with increasing Mu. The mean density is ρm ≈ 20ρu, independent of Mu. The root mean square Mach number is Mrms ≈ 0.25Mu. Deviations toward weaker turbulence are found as the collision zone thickens and for small Mu. The density probability function is not log-normal. The turbulence is inhomogeneous, weaker in the center of the zone than close to the confining shocks. It is also anisotropic: transverse to the upstream flows Mrms is always subsonic. We argue that uniform, head-on colliding flows generally disfavor turbulence that is at the same time isothermal, supersonic, and isotropic. The anisotropy carries over to other quantities like the density variance - Mach number relation. Line-of-sight effects thus exist. Structure functions differ depending on whether they are computed along a line-of-sight perpendicular or parallel to the upstream flow. Turbulence characteristics generally deviate markedly from those found for uniformly driven, supersonic, isothermal
Isotropic Negative Thermal Expansion Metamaterials.
Wu, Lingling; Li, Bo; Zhou, Ji
2016-07-13
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale. PMID:27333052
Simultaneous amplification and attenuation in isotropic chiral materials
NASA Astrophysics Data System (ADS)
Mackay, Tom G.; Lakhtakia, Akhlesh
2016-05-01
The electromagnetic field phasors in an isotropic chiral material (ICM) are superpositions of two Beltrami fields of different handedness. Application of the Bruggeman homogenization formalism to two-component composite materials delivers ICMs wherein Beltrami fields of one handedness attenuate whereas Beltrami fields of the other handedness amplify. One component material is a dissipative ICM, the other an active dielectric material. The range of the volume fraction of the active component material for which simultaneous amplification and attenuation is exhibited decreases—but does not vanish—as the ICM component becomes more dissipative and as its chirality parameter reduces in magnitude.
A stochastic model of particle dispersion in turbulent reacting gaseous environments
NASA Astrophysics Data System (ADS)
Sun, Guangyuan; Lignell, David; Hewson, John
2012-11-01
We are performing fundamental studies of dispersive transport and time-temperature histories of Lagrangian particles in turbulent reacting flows. The particle-flow statistics including the full particle temperature PDF are of interest. A challenge in modeling particle motions is the accurate prediction of fine-scale aerosol-fluid interactions. A computationally affordable stochastic modeling approach, one-dimensional turbulence (ODT), is a proven method that captures the full range of length and time scales, and provides detailed statistics of fine-scale turbulent-particle mixing and transport. Limited results of particle transport in ODT have been reported in non-reacting flow. Here, we extend ODT to particle transport in reacting flow. The results of particle transport in three flow configurations are presented: channel flow, homogeneous isotropic turbulence, and jet flames. We investigate the functional dependence of the statistics of particle-flow interactions including (1) parametric study with varying temperatures, Reynolds numbers, and particle Stokes numbers; (2) particle temperature histories and PDFs; (3) time scale and the sensitivity of initial and boundary conditions. Flow statistics are compared to both experimental measurements and DNS data.
Numerical study of turbulence subjected to a straining-relaxation-destraining cycle.
NASA Astrophysics Data System (ADS)
Hierro, Juan; Meneveau, Charles
2004-11-01
The response of turbulence subjected to planar straining and de-straining is studied using Direct Numerical Simulation (DNS). The impact of the applied distortions on the energy transfer across different length scales is quantified. Recently, experimental results (Chen, Meneveau & Katz, 2004) have found a global backscatter during non-equilibrium conditions when turbulence is being destrained; this leads to a lack of symmetry between the straining and the destraining regimes. In this work, DNS of initially homogeneous, isotropic, incompressible turbulent velocity fields under the action of a mean planar strain are performed. After some time, the straining is halted and later reversed to provide a full cycle of strain, relaxation, and destraining. The present data is at a Reynolds number lower than that of the experiments, but a full 3-D database is available for analysis. Also, variations in strain history are explored. The data are processed to yield the time evolution of Reynolds stresses, anisotropy tensors, turbulence kinetic energy production, and mean subgrid dissipation rate at various scales. The dependence on global backscatter upon straining history, length scale, and filter type is studied in detail. The aim is to complement the experimental results and to obtain a-priori data which can be useful in the development of SubGrid Scale (SGS) models for Large Eddy Simulations (LES).
Decaying turbulence in the presence of a shearless uniform kinetic energy gradient
NASA Astrophysics Data System (ADS)
Thormann, Adrien; Meneveau, Charles
2013-11-01
The study of decaying isotropic turbulent flow is an important point of reference for turbulence theories and numerical simulations. For the past several decades, most experimental results have focussed on possible power-law decays and found exponents between -1 and -1.4, approximately. Another class of experiments have been shear less mixing layers in which there are two regions with different kinetic energy levels that slowly diffuse into each other downstream. In this study we consider flow without shear-production of turbulence with a cross-stream uniform spatial gradient of kinetic energy k(z) = C z. Such gradient is generated with the use of an active grid and screens mounted upstream of the wind-tunnel's test section iteratively designed to produce a linear gradient of kinetic energy without mean shear. In such a flow, deviations from constant lateral flux of kinetic energy are due only to spatial variations in turbulent diffusivity of k (turbophoresis). Data are acquired using X-wire thermal anemometry at different spanwise and downstream locations. Tests of homogeneity, as well as spectral characteristics of the flow, decay and diffusion rates of the kinetic energy will be presented. This research is supported by NSF-CBET-1033942.
Non-Linear Aerodynamic Coupling of Piezoelectric Harvesters in Grid Turbulence
NASA Astrophysics Data System (ADS)
Danesh-Yazdi, Amir; Goushcha, Oleg; Elvin, Niell; Andreopoulos, Yiannis
2015-11-01
Experimental and analytical results relating to the extraction of fluidic energy from decaying homogeneous and isotropic turbulence using two side-by-side cantilever beams with attached piezoelectric patches are reported. Turbulence carries mechanical energy distributed over a range of temporal and spatial scales and the resulting interaction of these scales with the immersed piezoelectric beams creates a strain field in the beam which generates electric charge. Experiments are carried out in a large scale wind tunnel in which a turbulence-generating grid is used to excite the piezoelectric cantilever beams for different gap widths between the beams at various distances from the grids and for different flow velocities. We observe that the aerodynamic coupling decays exponentially with increasing gap width between the beams. More importantly, however, it is observed that the aerodynamic coupling due to the presence of a second beam greatly improves the energy harvesting process, so much so that when the aerodynamic coupling between the beams is strong, the average power generated per beam increases by up to 20 times, potentially allowing for significant power extraction from a random, non-resonant phenomenon such as turbulence. Sponsored by NSF Grant: CBET #1033117.
A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence
NASA Astrophysics Data System (ADS)
Grebenev, Vladimir N.; Oberlack, Martin
2009-02-01
We primarily deal with homogeneous isotropic turbulence and use a closure model for the von Kármán-Howarth equation to study several geometric properties of turbulent fluid dynamics. We focus our attention on the application of Riemannian geometry methods in turbulence. Some advantage of this approach consists in exploring the specific form of a closure model for the von Kármán-Howarth equation that enables to equip a model manifold (a cylindrical domain in the correlation space) by a family of inner metrics (length scales of turbulent motion) which depends on time. We show that for large Reynolds numbers (in the limit of large Reynolds numbers) the radius of this manifold can be evaluated in terms of the second-order structure function and the correlation distance. This model manifold presents a shrinking cylindrical domain as time evolves. This result is derived by using a selfsimilar solution of the closure model for the von Kármán-Howarth equation under consideration. We demonstrate that in the new variables the selfsimilar solution obtained coincides with the element of Beltrami surface (or pseudo-sphere): a canonical surface of the constant sectional curvature equals - 1.
A study of the interactions between turbulence and small inertial droplets
NASA Astrophysics Data System (ADS)
Bateson, Colin; Molina, Alberto; Rosa, Bogdan; Wang, Lian-Ping; Aliseda, Alberto
2010-11-01
Understanding the dynamics of particles in turbulent flows is important to many engineering and environmental problems including spray atomization and cloud droplet growth and precipitation. Specifically, we have studied the effect of turbulence on droplet collision-coalescence in an effort to clarify its role in the process of warm rain formation. The hypothesis that turbulence-induced-collisions can explain the size gap between the limit of condensational growth and the onset of gravitational collisions and sedimentation is supported by our measurements and analysis. Wind tunnel experiments were used to study the evolution of water droplets in homogeneous, isotropic, slowly decaying grid turbulence. Droplets between 1 and 120 μm were injected into the wind tunnel and their diameter, position and velocity were measured at different distances downstream by Phase Doppler Particle Analysis (PDPA). Statistics of the radial distribution function (RDF), relative velocity distribution and settling velocity have been produced and analyzed. They will be compared to the same statistics computed from 3D hybrid direct numerical simulations (DNS) at similar Re. High-speed visualizations of the droplet dynamics will be explored in an effort to understand and quantify coalescence efficiency.
NASA Astrophysics Data System (ADS)
Schlickeiser, R.
2011-05-01
A new transport theory of cosmic rays in magnetized space plasmas with axisymmetric incompressible magnetic turbulence is developed extending the quasilinear approximation to the particle orbit. Arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field are allowed. For quasi-stationary and spatially homogeneous magnetic turbulence, we derive the small Larmor radius approximation gyrophase-averaged cosmic ray Fokker-Planck coefficients. The generalized Fokker-Planck coefficients correctly reduce to their known quasilinear values in the corresponding limit. New forms of the quasilinear Fokker-Planck coefficients in axisymmetric turbulence are derived which no longer involve infinite sums of products of Bessel functions, which facilitate their numerical computation for specified turbulence field correlation tensors. The Fokker-Planck coefficients for arbitrary phase orbits of the cosmic ray particles provide strict upper limits for the perpendicular and pitch-angle Fokker-Planck coefficients, which in turn yield strict upper and lower limits for the perpendicular and parallel spatial diffusion coefficients, respectively, describing the spatial diffusion of the isotropic part of the cosmic ray phase space density. For the associated mean free paths, we find for this general case that the product of the minimum parallel mean free path with the sum of the maximum perpendicular mean free paths equals R 2 L , where RL denotes the cosmic ray gyroradius.
ANISOTROPY LENGTHENS THE DECAY TIME OF TURBULENCE IN MOLECULAR CLOUDS
Hansen, Charles E.; McKee, Christopher F.; Klein, Richard I.
2011-09-01
The decay of isothermal turbulence with velocity anisotropy is investigated using computational simulations and synthetic observations. We decompose the turbulence into isotropic and anisotropic components with total velocity dispersions {sigma}{sub iso} and {sigma}{sub ani}, respectively. We find that the decay rate of the turbulence depends on the crossing time of the isotropic component only. A cloud of size L with significant anisotropy in its turbulence has a dissipation time, t{sub diss} = L/(2{sigma}{sub iso}). This translates into turbulent energy decay rates on the cloud scale that can be much lower for anisotropic turbulence than for isotropic turbulence. To help future observations determine whether observed molecular clouds have the level of anisotropy required to maintain the observed level of turbulence over their lifetimes, we performed a principal component analysis on our simulated clouds. Even with projection effects washing out the anisotropic signal, there is a measurable difference in the axis-constrained principal component analysis performed in directions parallel and perpendicular to the direction of maximum velocity dispersion. When this relative difference, {psi}, is 0.1, there is enough anisotropy for the dissipation time to triple the expected isotropic value. We provide a fit for converting {psi} into an estimate for the dissipation time, t{sub diss}.
Helicopter rotor noise due to ingestion of atmospheric turbulence
NASA Astrophysics Data System (ADS)
Simonich, J. C.; Amiet, R. K.; Schlinker, R. H.; Greitzer, E. M.
1986-05-01
A theoretical study was conducted to develop an analytical prediction method for helicopter main rotor noise due to the ingestion of atmospheric turbulence. This study incorporates an atmospheric turbulence model, a rotor mean flow contraction model and a rapid distortion turbulence model which together determine the statistics of the non-isotropic turbulence at the rotor plane. Inputs to the combined mean inflow and turbulence models are controlled by atmospheric wind characteristics and helicopter operating conditions. A generalized acoustic source model was used to predict the far field noise generated by the non-isotropic flow incident on the rotor. Absolute levels for acoustic spectra and directivity patterns were calculated for full scale helicopters, without the use of empirical or adjustable constants. Comparisons between isotropic and non-isotropic turbulence at the rotor face demonstrated pronounced differences in acoustic spectra. Turning and contraction of the flow for hover and low speed vertical ascent cases result in a 3 dB increase in the acoustic spectrum energy and a 10 dB increase in tone levels. Compared to trailing edge noise, turbulence ingestion noise is the dominant noise mechanism below approximately 30 rotor harmonics, while above 100 harmonics, trailing edge noise levels exceed turbulence ingestion noise by 25 dB.
Helicopter rotor noise due to ingestion of atmospheric turbulence
NASA Technical Reports Server (NTRS)
Simonich, J. C.; Amiet, R. K.; Schlinker, R. H.; Greitzer, E. M.
1986-01-01
A theoretical study was conducted to develop an analytical prediction method for helicopter main rotor noise due to the ingestion of atmospheric turbulence. This study incorporates an atmospheric turbulence model, a rotor mean flow contraction model and a rapid distortion turbulence model which together determine the statistics of the non-isotropic turbulence at the rotor plane. Inputs to the combined mean inflow and turbulence models are controlled by atmospheric wind characteristics and helicopter operating conditions. A generalized acoustic source model was used to predict the far field noise generated by the non-isotropic flow incident on the rotor. Absolute levels for acoustic spectra and directivity patterns were calculated for full scale helicopters, without the use of empirical or adjustable constants. Comparisons between isotropic and non-isotropic turbulence at the rotor face demonstrated pronounced differences in acoustic spectra. Turning and contraction of the flow for hover and low speed vertical ascent cases result in a 3 dB increase in the acoustic spectrum energy and a 10 dB increase in tone levels. Compared to trailing edge noise, turbulence ingestion noise is the dominant noise mechanism below approximately 30 rotor harmonics, while above 100 harmonics, trailing edge noise levels exceed turbulence ingestion noise by 25 dB.
Macroscopic simulation of isotropic permanent magnets
NASA Astrophysics Data System (ADS)
Bruckner, Florian; Abert, Claas; Vogler, Christoph; Heinrichs, Frank; Satz, Armin; Ausserlechner, Udo; Binder, Gernot; Koeck, Helmut; Suess, Dieter
2016-03-01
Accurate simulations of isotropic permanent magnets require to take the magnetization process into account and consider the anisotropic, nonlinear, and hysteretic material behaviour near the saturation configuration. An efficient method for the solution of the magnetostatic Maxwell equations including the description of isotropic permanent magnets is presented. The algorithm can easily be implemented on top of existing finite element methods and does not require a full characterization of the hysteresis of the magnetic material. Strayfield measurements of an isotropic permanent magnet and simulation results are in good agreement and highlight the importance of a proper description of the isotropic material.
New Exact Relations for Helicities in Hall Magnetohydrodynamic Turbulence
NASA Astrophysics Data System (ADS)
Banerjee, Supratik; Galtier, Sebastien
2016-04-01
Hall magnetohydrodynamics is a mono-fluid plasma model appropriate for probing Final{some of the} physical processes (other than pure kinetic effects) at length scales smaller than the scales of standard MHD. In sub-ionic space plasma turbulence (e.g. the solar wind) this fluid model has been proved to be useful. Three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses three inviscid invariants which are the total energy, the magnetic helicity and the generalized helicity. In this presentation, we would like to discuss new exact relations for helicities (magnetic helicities and generalized helicities) which are derived for homogeneous stationary (not necessarily isotropic) Hall MHD turbulence (and also for its inertialess electron MHD limit) in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e. the scalar product of two different increments and are written simply as ηM = di < δ ( {b} × {j}) \\cdot δ {b} >, with ηM the average magnetic helicity flux rate, {b} the magnetic field, {j} the current and ± ηG = < δ ( {v} × {Ω} ) \\cdot δ {Ω} > , with ηM the average generalized helicity flux rate, {v} the fluid velocity and {Ω} = {b} + dI {ω} being the generalized helicity where ω is simply the fluid vorticity ( = nabla × {v}). It provides, therefore, a direct measurement of the dissipation rates for the corresponding helicities even in case of an anisotropic plasma turbulence. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations while the magnetic helicity cascade is linked to the right polarized fluctuations. The newly derived relations also show that like energy, a non-zero helicity flux can only be associated to a departure of Beltrami flow state. {Reference} S. Banerjee & S. Galtier, {Chiral Exact Relations for Helicities in Hall Magnetohydrodynamic Turbulence} (submitted).
Kinematics of velocity and vorticity correlations in turbulent flow
NASA Technical Reports Server (NTRS)
Bernard, P. S.
1983-01-01
The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.
Transport and Lagrangian Statistics in Rotating Stratified Turbulence
NASA Astrophysics Data System (ADS)
Rosenberg, D. L.
2015-12-01
Transport plays a crucial role in geophysical flows, both in theatmosphere and in the ocean. Transport in such flows is ultimatelycontrolled by small-scale turbulence, although the large scales arein geostrophic balance between pressure gradient, gravity and Coriolisforces. As a result of the seemingly random nature of the flow, singleparticles are dispersed by the flow and on time scales significantlylonger than the eddy turn-over time, they undergo a diffusive motionwhose diffusion coefficient is the integral of the velocity correlationfunction. On intermediate time scales, in homogeneous, isotropic turbuilence(HIT) the separation between particle pairs has been argued to grow withtime according to the Richardson law: <(Δ x)2(t)> ~ t3, with aproportionality constant that depends on the initial particleseparation. The description of the phenomena associated withthe dispersion of single particles, or of particle pairs, ultimatelyrests on relatively simple statistical properties of the flowvelocity transporting the particles, in particular on its temporalcorrelation function. In this work, we investigate particle dispersionin the anisotropic case of rotating stratified turbulence examining whetherthe dependence on initial particle separation differs from HIT,particularly in the presence of an inverse cascade.
Entropic multirelaxation lattice Boltzmann models for turbulent flows.
Bösch, Fabian; Chikatamarla, Shyam S; Karlin, Ilya V
2015-10-01
We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014)] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows. PMID:26565366
Dynamical similarities of the direct and inverse turbulent cascades
NASA Astrophysics Data System (ADS)
Vela-Martin, Alberto; Jimenez, Javier
2015-11-01
A fully reversible homogeneous isotropic turbulent system is constructed using inviscid LES to model energy fluxes in the inertial range. It recovers energy and other turbulent quantities when reversed after being allowed to decay. During the first phase, a direct cascade transfers energy from large to small scales while, during the second, an inverse cascade does the opposite. Short-time Lyapunov (STL) analysis is used to study and compare the dynamics of both cascades. This allows us to identify a smallest length scale for the chaotic flow behavior, below which the system behaves as a unit dynamically enslaved to larger motions by the contracting effect of the model. Above it, the inertial forces become relevant and the system is fully chaotic. When the inertial scales are isolated, the leading STL exponent is similar for both cascades, suggesting that the dynamics of the inertial range is conservative and time-symmetric, and that the direct and inverse energy cascades share similar energy transfer mechanisms. The cascade would thus be a bi-directional reversible process with similar up and down mechanisms, although, because the L2 norm used in the STL analysis respects the geometry of phase space, the entropy-driven cascade directionally is not precluded. Funded by the ERC Multiflow program.
Entropic multirelaxation lattice Boltzmann models for turbulent flows
NASA Astrophysics Data System (ADS)
Bösch, Fabian; Chikatamarla, Shyam S.; Karlin, Ilya V.
2015-10-01
We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014), 10.1103/PhysRevE.90.031302] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.
Turbulent pair dispersion in the presence of gravity
NASA Astrophysics Data System (ADS)
Chang, Kelken; Malec, Benedict J.; Shaw, Raymond A.
2015-03-01
Turbulent pair dispersion of heavy particles is strongly altered when particles of two different Stokes numbers (bidisperse) are considered, and this is further compounded when a uniform gravitational acceleration is present. Lagrangian trajectories of fluid tracers, and bidisperse heavy particles with and without gravity were calculated from a direct numerical simulation of homogeneous, isotropic turbulence. Particle pair dispersion shows a short-time, ballistic (Batchelor) regime and a transition to super-ballistic dispersion that is suggestive of the emergence of Richardson scaling. A simple equation of motion for inertial, sedimenting particles captures the essential features of the pair dispersion at very short time and length scales. Kolmogorov scaling arguments are able to qualitatively describe the competition between gravity-induced and fluid-induced relative motion in modifying the amount of time the heavy particles spend in the ballistic regime. The transition from ballistic to super-ballistic dispersion for fluid tracers and monodisperse inertial particles exhibits a pronounced sub-ballistic behavior that can be attributed to the mixed velocity-acceleration structure function. The sub-ballistic behavior is strongly suppressed for bidisperse particles, both in the presence or absence of gravity, primarily because of a reduction in the correlation between velocity and acceleration increments.
Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids
Schumacher, Jörg; Götzfried, Paul; Scheel, Janet D.
2015-01-01
Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr=0.7 and in liquid mercury at Pr=0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications. PMID:26195793
Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids.
Schumacher, Jörg; Götzfried, Paul; Scheel, Janet D
2015-08-01
Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr=0.7 and in liquid mercury at Pr=0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications. PMID:26195793
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Lindholm, Ulric S.; Chan, Kwai S.
1986-01-01
The objective of the program is to evaluate and develop existing constitutive models for use in finite-element structural analysis of turbine engine hot section components. The class of constitutive equation studied is considered unified in that all inelastic deformation including plasticity, creep, and stress relaxation are treated in a single term rather than a classical separation of plasticity (time independent) and creep (time dependent) behavior. The unified theories employed also do not utilize the classical yield surface or plastic potential concept. The models are constructed from an appropriate flow law, a scalar kinetic relation between strain rate, temperature and stress, and evolutionary equations for internal variables describing strain or work hardening, both isotropic and directional (kinematic). This and other studies have shown that the unified approach is particularly suited for determining the cyclic behavior of superalloy type blade and vane materials and is entirely compatible with three-dimensional inelastic finite-element formulations. The behavior was examined of a second nickel-base alloy, MAR-M247, and compared it with the Bodner-Partom model, further examined procedures for determining the material-specific constants in the models, and exercised the MARC code for a turbine blade under simulated flight spectrum loading. Results are summarized.
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Chan, K. S.; Lindholm, U. S.; Bodner, S. R.
1988-01-01
The third and fourth years of a 4-year research program, part of the NASA HOST Program, are described. The program goals were: (1) to develop and validate unified constitutive models for isotropic materials, and (2) to demonstrate their usefulness for structural analysis of hot section components of gas turbine engines. The unified models selected for development and evaluation were those of Bodner-Partom and of Walker. The unified approach for elastic-viscoplastic constitutive equations is a viable method for representing and predicting material response characteristics in the range where strain rate and temperature dependent inelastic deformations are experienced. This conclusion is reached by extensive comparison of model calculations against the experimental results of a test program of two high temperature Ni-base alloys, B1900+Hf and Mar-M247, over a wide temperature range for a variety of deformation and thermal histories including uniaxial, multiaxial, and thermomechanical loading paths. The applicability of the Bodner-Partom and the Walker models for structural applications has been demonstrated by implementing these models into the MARC finite element code and by performing a number of analyses including thermomechanical histories on components of hot sections of gas turbine engines and benchmark notch tensile specimens. The results of the 4-year program have been published in four annual reports. The results of the base program are summarized in this report. The tasks covered include: (1) development of material test procedures, (2) thermal history effects, and (3) verification of the constitutive model for an alternative material.
Characterizing inertial and convective optical turbulence by detrended fluctuation analysis
NASA Astrophysics Data System (ADS)
Funes, Gustavo; Figueroa, Eduardo; Gulich, Damián.; Zunino, Luciano; Pérez, Darío. G.
2013-10-01
Atmospheric turbulence is usually simulated at the laboratory by generating convective free flows with hot surfaces, or heaters. It is tacitly assumed that propagation experiments in this environment are comparable to those usually found outdoors. Nevertheless, it is unclear under which conditions the analogy between convective and isotropic turbulence is valid; that is, obeying Kolmogorov isotropic models. For instance, near-ground-level turbulence often is driven by shear ratchets deviating from established inertial models. In this case, a value for the structure constant can be obtained but it would be unable to distinguish between both classes of turbulence. We have performed a conceptually simple experiment of laser beam propagation through two types of artificial turbulence: isotropic turbulence generated by a turbulator [Proc. SPIE 8535, 853508 (2012)], and convective turbulence by controlling the temperature of electric heaters. In both cases, a thin laser beam propagates across the turbulent path, and its wandering is registered by a position sensor detector. The strength of the optical turbulence, in terms of the structure constant, is obtained from the wandering variance. It is expressed as a function of the temperature difference between cold and hot sources in each setup. We compare the time series behaviour for each turbulence with increasing turbulence strength by estimating the Hurst exponent, H, through detrended fluctuation analysis (DFA). Refractive index fluctuations are inherently fractal; this characteristic is reflected in their spectra power-law dependence—in the inertial range. This fractal behaviour is inherited by time series of optical quantities, such as the wandering, by the occurrence of long-range correlations. By analyzing the wandering time series with this technique, we are able to correlate the turbulence strength to the value of the Hurt exponent. Ultimately, we characterize both types of turbulence.
Broken symmetry in ideal magnetohydrodynamic turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1993-01-01
A numerical study of the long-time evolution of a number of cases of inviscid, isotropic, incompressible, three-dimensional fluid, and magneto-fluid turbulence has been completed. The results confirm that ideal magnetohydrodynamic turbulence is non-ergodic if there is no external magnetic field present. This is due essentially to a canonical symmetry being broken in an arbitrary dynamical representation. The broken symmetry manifests itself as a coherent structure, i.e., a non-zero time-averaged part of the turbulent magnetic field. The coherent structure is observed, in one case, to contain about eighteen percent of the total energy.
Quantum gravity stability of isotropy in homogeneous cosmology
NASA Astrophysics Data System (ADS)
Broda, Bogusław
2011-10-01
It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric can be damped by quantum fluctuations coming from perturbative quantum gravity in one-loop approximation. Also, a formal argument, not limited to one-loop approximation, is put forward in favor of stability of isotropy in the exactly isotropic case.
Outflow Driven Turbulence in Star Forming Clouds
NASA Astrophysics Data System (ADS)
Frank, Adam
Setting young stellar object jets and outflows in their broadest context requires an understanding of outflows as “feedback” in the development of molecular cloud turbulence and the determination of star formation efficiencies. In this contribution I review our group’s recent studies exploring relationships between protostellar outflows and turbulence in molecular clouds. We first present studies of turbulence and fossil cavities driven by YSO outflows using numerical simulations which track the evolution of single transient jets driven into a turbulent medium. Our simulations show both the effect of turbulence on outflow structures and, conversely, the effect of outflows on the ambient turbulence. These studies demonstrate that individual transient outflows have the capacity to re-energize decaying turbulence. Next we present simulations of multiple interacting jets. We show that turbulence can readily be sustained by these interactions and show that it is possible to broadly characterize an effective driving scale of the outflows. Comparing the velocity spectrum obtained in our studies to that of an isotropically forced control we show that in outflow driven turbulence a power law of the form E(k) ∝ k - β is indeed achieved. However we find a steeper spectrum β ˜ 3 is obtained in outflow driven turbulence models than in isotropically forced simulations β ˜ 2. 0. Taken together both studies provide broad support for the conclusion that fossil cavities driven by decaying jets can provide a source of turbulence and feedback which mediate star formation processes in molecular clouds. Whether this does obtain in real clouds remains a point which must be demonstrated
Tunable dynamics of microtubule-based active isotropic gels
Henkin, Gil; DeCamp, Stephen J.; Chen, Daniel T. N.; Sanchez, Tim; Dogic, Zvonimir
2014-01-01
We investigate the dynamics of an active gel of bundled microtubules (MTs) that is driven by clusters of kinesin molecular motors. Upon the addition of ATP, the coordinated action of thousands of molecular motors drives the gel to a highly dynamical turbulent-like state that persists for hours and is only limited by the stability of constituent proteins and the availability of the chemical fuel. We characterize how enhanced transport and emergent macroscopic flows of active gels depend on relevant molecular parameters, including ATP, kinesin motor and depletant concentrations, MT volume fraction, as well as the stoichiometry of the constituent motor clusters. Our results show that the dynamical and structural properties of MT-based active gels are highly tunable. They also indicate existence of an optimal concentration of molecular motors that maximize far-from-equilibrium activity of active isotropic MT gels. PMID:25332391
Two-dimensional convective turbulence
Gruzinov, A.V.; Kukharkin, N.; Sudan, R.N.
1996-02-01
We show that 2D {bold E{times}B} ionospheric turbulence of the electron density in the equatorial electrojet is isomorphic to the viscous convection of an ordinary fluid in a porous medium due to temperature gradients. Numerical simulations reveal the strong anisotropy in the turbulence, which consists of rising hot bubbles and falling cool bubbles. These bubbles break up into fingers leading to the formation of stable shear flows. After reaching a quasisteady state, the omnidirectional energy spectrum approaches a {ital k}{sup {minus}2} behavior, rather than {ital k}{sup {minus}5/3} as expected from isotropic turbulence. Physical mechanisms that lead to anisotropy are analyzed. {copyright} {ital 1996 The American Physical Society.}
Active control for turbulent premixed flame simulations
Bell, John B.; Day, Marcus S.; Grcar, Joseph F.; Lijewski, Michael J.
2004-03-26
Many turbulent premixed flames of practical interest are statistically stationary. They occur in combustors that have anchoring mechanisms to prevent blow-off and flashback. The stabilization devices often introduce a level of geometric complexity that is prohibitive for detailed computational studies of turbulent flame dynamics. As a result, typical detailed simulations are performed in simplified model configurations such as decaying isotropic turbulence or inflowing turbulence. In these configurations, the turbulence seen by the flame either decays or, in the latter case, increases as the flame accelerates toward the turbulent inflow. This limits the duration of the eddy evolutions experienced by the flame at a given level of turbulent intensity, so that statistically valid observations cannot be made. In this paper, we apply a feedback control to computationally stabilize an otherwise unstable turbulent premixed flame in two dimensions. For the simulations, we specify turbulent in flow conditions and dynamically adjust the integrated fueling rate to control the mean location of the flame in the domain. We outline the numerical procedure, and illustrate the behavior of the control algorithm. We use the simulations to study the propagation and the local chemical variability of turbulent flame chemistry.
Effects of free-stream turbulence on turbulent boundary layers with mild adverse pressure gradients
NASA Technical Reports Server (NTRS)
Hoffmann, J. A.; Kassir, S. M.
1988-01-01
The influence of near isotropic free-stream turbulence on the shape factors and skin friction coefficients of turbulent boundary layers is presented for the cases of zero and mild adverse pressure gradients. With free-stream turbulence, improved fluid mixing occurs in boundary layers with adverse pressure gradients relative to the zero pressure gradient condition, with the same free-stream turbulence intensity and length scale. Stronger boundary layers with lower shape factors occur as a result of a lower ratio of the integral scale of turbulence to the boundary layer thickness, and to vortex stretching of the turbulent eddies in the free-stream, both of which act to improve the transmission of momentum from the free-stream to the boundary layers.
NASA Technical Reports Server (NTRS)
Hoffmann, Jon A.
1988-01-01
The influence of near isotropic free-stream turbulence on the shape factors and skin friction coefficients of turbulent bounday layers is presented for the cases of zero and mild adverse pressure gradients. With free-stream turbulence, improved fluid mixing occurs in boundary layers with adverse pressure gradients relative to the zero pressure gradient condition, with the same free-stream turbulence intensity and length scale. Stronger boundary layers with lower shape factors occur as a result of a lower ratio of the integral scale of turbulence to the boundary layer thickness, and to vortex stretching of the turbulent eddies in the free stream, both of which act to improve the transmission of momentum from the free stream to the boundary layers.
NASA Technical Reports Server (NTRS)
Hoffmann, J. A.; Kassir, S. M.; Larwood, S. M.
1989-01-01
The influence of near isotropic free-stream turbulence on the shape factors and skin friction coefficients of turbulent boundary layers is presented for the cases of zero and mild adverse pressure gradients. With free-stream turbulence, improved fluid mixing occurs in boundary layers with adverse pressure gradients relative to the zero pressure gradient condition, with the same free-stream turbulence intensity and length scale. Stronger boundary layers with lower shape factors occur as a result of a lower ratio of the integral scale of turbulence to the boundary layer thickness, and to vortex stretching of the turbulent eddies in the free-stream, both of which act to improve the transmission of momentum from the free-stream to the boundary layers.
Hierarchical structures in a turbulent pipe flow
NASA Astrophysics Data System (ADS)
Zou, Zhengping; Zhu, Yuanjie; Zhou, Mingde; She, Zhen-Su
2003-12-01
A hierarchical structure (HS) analysis ( β-test and γ-test) is applied to a fully developed turbulent pipe flow. Velocity signals are measured at two cross sections in the pipe and at a series of radial locations from the pipe wall. Particular attention is paid to the variation of turbulent statistics at wall units 10< y+<3000. It is shown that at all locations the velocity fluctuations satisfy the She-Leveque hierarchical symmetry (Phys. Rev. Lett. 72 (1994) 336). The measured HS parameters, β and γ, are interpreted in terms of the variation of fluid structures. Intense anisotropic fluid structures generated near the wall appear to be more singular than the most intermittent structures in isotropic turbulence and appear to be more outstanding compared to the background fluctuations; this yields a more intermittent velocity signal with smaller γ and β. As turbulence migrates into the logarithmic region, small-scale motions are generated by an energy cascade and large-scale organized structures emerge which are also less singular than the most intermittent structures of isotropic turbulence. At the center, turbulence is nearly isotropic, and β and γ are close to the 1994 She-Leveque predictions. A transition is observed from the logarithmic region to the center in which γ drops and the large-scale organized structures break down. We speculate that it is due to the growing eddy viscosity effects of widely spread turbulent fluctuations in a similar way as in the breakdown of the Taylor vortices in a turbulent Couette-Taylor flow at high Reynolds numbers.
Absorption of waves by large-scale winds in stratified turbulence.
Clark di Leoni, P; Mininni, P D
2015-03-01
The atmosphere is a nonlinear stratified fluid in which internal gravity waves are present. These waves interact with the flow, resulting in wave turbulence that displays important differences with the turbulence observed in isotropic and homogeneous flows. We study numerically the role of these waves and their interaction with the large-scale flow, consisting of vertically sheared horizontal winds. We calculate their space- and time-resolved energy spectrum (a four-dimensional spectrum) and show that most of the energy is concentrated along a dispersion relation that is Doppler shifted by the horizontal winds. We also observe that when uniform winds are let to develop in each horizontal layer of the flow, waves whose phase velocity is equal to the horizontal wind speed have negligible energy. This indicates a nonlocal transfer of their energy to the mean flow. Both phenomena, the Doppler shift and the absorption of waves traveling with the wind speed, are not accounted for in current theories of stratified wave turbulence. PMID:25871210
Lattice Boltzmann simulation of turbulence-induced flocculation of cohesive sediment
NASA Astrophysics Data System (ADS)
Zhang, Jin-Feng; Zhang, Qing-He; Maa, Jerome P.-Y.; Qiao, Guang-Quan
2013-10-01
Both the floc formation and floc breakup of cohesive sediment are affected by turbulent shear which is recognized as one of the most important parameters, and thus, on the settling and transport of cohesive sediment. In this study, the development of floc characteristics at early stage and steady-state of flocculation were investigated via a three-dimensional lattice Boltzmann numerical model for turbulence-induced flocculation. Simulations for collision and aggregation of various size particles, floc growth, and breakup in isotropic and homogenous turbulent flows with different shear stresses were conducted. Model results for the temporal evolution of floc size distribution show that the normalized floc size distributions is time-independent during early stage of flocculation, and at steady-state, shear rate has no effect on the shape of normalized floc size distribution. Furthermore, the size, settling velocity, and effective density of flocs at the non-equilibrium flocculation stage do not change significantly for shear stresses in the range 0-0.4 N m-2. The relationships between floc size and settling velocity established during floc growth stages and that during steady-states are different.
Multi-time multi-scale correlation functions in hydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Biferale, Luca; Calzavarini, Enrico; Toschi, Federico
2011-08-01
High Reynolds numbers Navier-Stokes equations are believed to break self-similarity concerning both spatial and temporal properties: correlation functions of different orders exhibit distinct decorrelation times and anomalous spatial scaling properties. Here, we present a systematic attempt to measure multi-time and multi-scale correlations functions, by using high Reynolds numbers numerical simulations of fully homogeneous and isotropic turbulent flow. The main idea is to set-up an ensemble of probing stations riding the flow, i.e., measuring correlations in a reference frame centered on the trajectory of distinct fluid particles (the quasi-Lagrangian reference frame introduced by Belinicher and L'vov [Sov. Phys. JETP 66, 303 (1987)]). In this way, we reduce the large-scale sweeping and measure the non-trivial temporal dynamics governing the turbulent energy transfer from large to small scales. We present evidences of the existence of the dynamic multiscaling properties of turbulence - first proposed by L'vov et al. [Phys. Rev. E 55, 7030 (1997)] - in which multi-time correlation functions are characterized by an infinite set of characteristic times.
Investigation of Hill's optical turbulence model by means of direct numerical simulation.
Muschinski, Andreas; de Bruyn Kops, Stephen M
2015-12-01
For almost four decades, Hill's "Model 4" [J. Fluid Mech. 88, 541 (1978) has played a central role in research and technology of optical turbulence. Based on Batchelor's generalized Obukhov-Corrsin theory of scalar turbulence, Hill's model predicts the dimensionless function h(κl(0), Pr) that appears in Tatarskii's well-known equation for the 3D refractive-index spectrum in the case of homogeneous and isotropic turbulence, Φn(κ)=0.033C2(n)κ(-11/3) h(κl(0), Pr). Here we investigate Hill's model by comparing numerical solutions of Hill's differential equation with scalar spectra estimated from direct numerical simulation (DNS) output data. Our DNS solves the Navier-Stokes equation for the 3D velocity field and the transport equation for the scalar field on a numerical grid containing 4096(3) grid points. Two independent DNS runs are analyzed: one with the Prandtl number Pr=0.7 and a second run with Pr=1.0 . We find very good agreement between h(κl(0), Pr) estimated from the DNS output data and h(κl(0), Pr) predicted by the Hill model. We find that the height of the Hill bump is 1.79 Pr(1/3), implying that there is no bump if Pr<0.17 . Both the DNS and the Hill model predict that the viscous-diffusive "tail" of h(κl(0), Pr) is exponential, not Gaussian. PMID:26831396
NASA Technical Reports Server (NTRS)
Goldstein, M. E.; Rosenbaum, B. M.
1972-01-01
A model, based on Lighthill's theory, for predicting aerodynamic noise from a turbulent shear flow is developed. This model is a generalization of the one developed by Ribner. Unlike Ribner's model, it does not require that the turbulent correlations factor into space and time-dependent parts. It replaces his assumption of isotropic. turbulence by the more realistic one of axisymmetric turbulence. The implications of the model for jet noise are discussed.
Experimental assessment of helicopter rotor turbulence ingestion noise in hover
NASA Technical Reports Server (NTRS)
Simonich, J. C.; Schlinker, R. H.; Amiet, R. K.
1989-01-01
An experiment was conducted to assess the accuracy of a theory for non-isotropic turbulence ingestion. In order to generate non-isotropic turbulence in a controlled environment, a scale model rotor in a closed chamber was used so that the turbulence generated by the rotor was reingested by the recirculating flow. Simultaneous measurements of turbulence inflow properties and far field acoustics were acquired. Measurements confirmed that the inflow turbulence was highly non-isotropic. The measured aerodynamic properties were used as inputs for the noise prediction procedure. The general agreement between the non-isotropic noise prediction procedure and the experiment was good, although the procedure generally overpredicts the quasi-tonal low to mid range frequencies and underpredicts the higher broadband signals. The predicted sound power level as a function of polar angle was in close agreement with measurements, except near the rotor plane, which is not modeled by the present analysis. It is determined that the most sensitive parameter influencing the predicted noise was the turbulence intensity.
An object-oriented model for the prediction of turbulence effects on plankton
NASA Astrophysics Data System (ADS)
Mariani, Patrizio; Botte, Vincenzo; Ribera d'Alcalà, Maurizio
2005-05-01
In this work, we propose an object-oriented individual based model for the analysis of the effects of turbulence on the interactions and the behaviour of planktonic organisms at microscopic scales. We model homogeneous isotropic turbulence by adopting a kinematic simulation of the flow, where the velocity field is prescribed as a combination of a large number of unsteady random Fourier modes. As for the biotic component we use special contact classes to build a "memory" of an individual particle, allowing the storage of frequency, duration and identity of each interaction experienced by the individuals throughout the whole time span of the simulation. This, in turn, allows classifying the different interactions. We tested our model on the classical problem of the encounter rate between a consumer and a food particle. The model reproduces well the results of analytical bulk models or of previous numerical simulations, which demonstrated the enhancement of contact numbers due to the turbulent flow especially for slow moving or ambushing consumers. The results also highlight that a critical parameter in the encounter is the duration of the contacts. This suggests that the evident decrease in clearance rate of grazers in experimental setups in the high turbulence range may be significantly affected by the decrease of the encounter duration and its impact on detection, capturing and handling the prey. As a matter of fact, the encounter duration sets a typical scale dependent on the swimming speed, the typical scale of turbulence, and the encounter radius, beyond which the enhancement of useful encounter rates becomes negligible.
Zhou, Ye; Schilling, Oleg; Ghosh, Sanjoy
2002-08-01
The spectral eddy and backscatter viscosity and the spectral eddy and backscatter resistivity for incompressible, three-dimensional, isotropic, nonhelical magnetohydrodynamic (MHD) turbulence are constructed using the eddy-damped quasinormal Markovian statistical closure model developed by Pouquet, Frisch, and Léorat [J. Fluid Mech. 77, 321 (1976)] in terms of primitive variables. The approach used is an extension of the methodology developed by Leslie and Quarini [J. Fluid Mech. 91, 65 (1979)] for fluid turbulence to MHD turbulence. The eddy and backscatter viscosities and the eddy and backscatter resistivities are calculated numerically for assumed kinetic and magnetic energy spectra, E(v)(k) and E(B)(k), with a production subrange and a k(-5/3) inertial subrange for the two cases r(A)=1 and r(A)=1 / 2, where r(A)=E(v)(k)/E(B)(k) is the Alfvén ratio. It is shown that the effects of the unresolved subgrid scales on the resolved-scale velocity and magnetic field consist of an eddy damping and backscatter. The eddy viscosity and resistivity, and the backscatter viscosity and resistivity (the correlation function of the stochastic velocity and magnetic backscatter force) are shown to have a dependence on k/k(c), where k(c) is the cutoff wave number, which is very similar to the dependence calculated in the pure (i.e., nonmagnetic) Navier-Stokes turbulence case. The eddy viscosity and resistivity, and the backscatter viscosity and resistivity numerically calculated here can be used to develop improved subgrid-scale parametrizations for spectral large-eddy simulations of homogenous MHD turbulence. PMID:12241287
Monte-Carlo computation of turbulent premixed methane/air ignition
NASA Astrophysics Data System (ADS)
Carmen, Christina Lieselotte
The present work describes the results obtained by a time dependent numerical technique that simulates the early flame development of a spark-ignited premixed, lean, gaseous methane/air mixture with the unsteady spherical flame propagating in homogeneous and isotropic turbulence. The algorithm described is based upon a sub-model developed by an international automobile research and manufacturing corporation in order to analyze turbulence conditions within internal combustion engines. Several developments and modifications to the original algorithm have been implemented including a revised chemical reaction scheme and the evaluation and calculation of various turbulent flame properties. Solution of the complete set of Navier-Stokes governing equations for a turbulent reactive flow is avoided by reducing the equations to a single transport equation. The transport equation is derived from the Navier-Stokes equations for a joint probability density function, thus requiring no closure assumptions for the Reynolds stresses. A Monte-Carlo method is also utilized to simulate phenomena represented by the probability density function transport equation by use of the method of fractional steps. Gaussian distributions of fluctuating velocity and fuel concentration are prescribed. Attention is focused on the evaluation of the three primary parameters that influence the initial flame kernel growth-the ignition system characteristics, the mixture composition, and the nature of the flow field. Efforts are concentrated on the effects of moderate to intense turbulence on flames within the distributed reaction zone. Results are presented for lean conditions with the fuel equivalence ratio varying from 0.6 to 0.9. The present computational results, including flame regime analysis and the calculation of various flame speeds, provide excellent agreement with results obtained by other experimental and numerical researchers.
Subdiffusive dynamics of a liquid crystal in the isotropic phase
NASA Astrophysics Data System (ADS)
De Gaetani, Luca; Prampolini, Giacomo; Tani, Alessandro
2008-05-01
The isotropic phase dynamics of a system of 4-n-hexyl-4'-cyano-biphenyl (6CB) molecules has been studied by molecular dynamics computer simulations. We have explored the range of 275-330K keeping the system isotropic, although supercooled under its nematic transition temperature. The weak rototranslational coupling allowed us to separately evaluate translational (TDOF) and orientational degrees of freedom (ODOF). Evidences of subdiffusive dynamics, more apparent at the lowest temperatures, are found in translational and orientational dynamics. Mean square displacement as well as self-intermediate center of mass and rotational scattering functions show a plateau, also visible in the orientational correlation function. According to the mode coupling theory (MCT), this plateau is the signature of the β-relaxation regime. Three-time intermediate scattering functions reveal that the plateau is related to a homogeneous dynamics, more extended in time for the orientational degrees of freedom (up to 1ns). The time-temperature superposition principle and the factorization property predicted by the idealized version of MCT hold, again for both kinds of dynamics. The temperature dependence of diffusion coefficient and orientational relaxation time is well described by a power law. Critical temperatures Tc are 244±6 and 258±6K, respectively, the latter is some 10K below the corresponding experimental values. The different values of Tc we obtained indicate that ODOF freezes earlier than TDOF. This appears due to the strongly anisotropic environment that surrounds a 6CB molecule, even in the isotropic phase. The lifetime of these "cages," estimated by time dependent conditional probability functions, is strongly temperature dependent, ranging from some hundreds of picoseconds at 320K to a few nanoseconds at 275K.
Dynamic elastic moduli during isotropic densification of initially granular media
NASA Astrophysics Data System (ADS)
Vasseur, Jérémie; Wadsworth, Fabian B.; Lavallée, Yan; Dingwell, Donald B.
2016-03-01
The elastic properties of homogeneous, isotropic materials are well constrained. However, in heterogeneous and evolving materials, these essential properties are less well-explored. During sintering of volcanic ash particles by viscous processes as well as during compaction and cementation of sediments, microstructure and porosity undergo changes that affect bulk dynamic elastic properties. Here using a model system of glass particles as an analogue for initially granular rock-forming materials, we have determined porosity and P-wave velocity during densification. Using these results, we test models for the kinetics of densification and the resultant evolution of the elastic properties to derive a quantitative description of the coupling between the kinetics of isotropic densification and the evolving dynamic elastic moduli. We demonstrate the power of the resultant model on a wide range of data for non-coherent sediments as well as sedimentary and volcanic rocks. We propose that such constraints be viewed as an essential ingredient of time-dependent models for the deformation of evolving materials in volcanoes and sedimentary basins.
Resonant ultrasound spectroscopy and homogeneity in polycrystals.
Kaplan, Gunes; Darling, T W; McCall, K R
2009-01-01
Resonant ultrasound spectroscopy (RUS) is capable of determining the bulk elastic properties of a solid from its characteristic vibration frequencies, given the dimensions, density and shape of the sample. The model used for extracting values of the elastic constants assumes perfect homogeneity, which can be approximated by average-isotropic polycrystals. This approximation is excellent in the small grain regime assumed for most averaging procedures, but for real samples with indeterminate grain size distributions, it is not clear where the approximation breaks down. RUS measurements were made on pure copper samples where the grain size distribution was changed by progressive heat treatments in order to find a quantitative limit for the loss of homogeneity. It is found that when a measure of the largest grains is 15% of the sample's smallest dimension, the deviation in RUS fits indicates elastic inhomogeneity. PMID:18804831
Miniati, Francesco
2014-02-10
We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at redshift z = 0. The development of turbulence is ensured as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. We achieve a large dynamic range of spatial scales through a novel Eulerian refinement strategy where the cluster volume is refined with progressively finer uniform nested grids during gravitational collapse. This provides an unprecedented resolution of 7.3 h {sup –1} kpc across the virial volume. The probability density functions of various velocity-derived quantities exhibit the features characteristic of fully developed compressible turbulence observed in dedicated periodic-box simulations. Shocks generate only 60% of the total vorticity within the R {sub vir}/3 region and 40% beyond that. We compute second- and third-order longitudinal and transverse structure functions for both solenoidal and compressional components in the cluster core, virial region, and beyond. The structure functions exhibit a well-defined inertial range of turbulent cascade. The injection scale is comparable to the virial radius but increases toward the outskirts. Within R {sub vir}/3, the spectral slope of the solenoidal component is close to Kolmogorov's, but for the compressional component is substantially steeper and close to Burgers's; the flow is mostly solenoidal and statistically rigorously, which is consistent with fully developed homogeneous and isotropic turbulence. Small-scale anisotropy appears due to numerical artifact. Toward the virial region, the flow becomes increasingly compressional, the structure functions become flatter, and modest genuine anisotropy appear particularly close to the injection scale. In comparison, mesh adaptivity based on Lagrangian refinement and the same finest resolution leads to a lack of turbulent power on a small scales, an excess thereof on large scales, and
NASA Astrophysics Data System (ADS)
Miniati, Francesco
2014-02-01
We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at redshift z = 0. The development of turbulence is ensured as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. We achieve a large dynamic range of spatial scales through a novel Eulerian refinement strategy where the cluster volume is refined with progressively finer uniform nested grids during gravitational collapse. This provides an unprecedented resolution of 7.3 h -1 kpc across the virial volume. The probability density functions of various velocity-derived quantities exhibit the features characteristic of fully developed compressible turbulence observed in dedicated periodic-box simulations. Shocks generate only 60% of the total vorticity within the R vir/3 region and 40% beyond that. We compute second- and third-order longitudinal and transverse structure functions for both solenoidal and compressional components in the cluster core, virial region, and beyond. The structure functions exhibit a well-defined inertial range of turbulent cascade. The injection scale is comparable to the virial radius but increases toward the outskirts. Within R vir/3, the spectral slope of the solenoidal component is close to Kolmogorov's, but for the compressional component is substantially steeper and close to Burgers's; the flow is mostly solenoidal and statistically rigorously, which is consistent with fully developed homogeneous and isotropic turbulence. Small-scale anisotropy appears due to numerical artifact. Toward the virial region, the flow becomes increasingly compressional, the structure functions become flatter, and modest genuine anisotropy appear particularly close to the injection scale. In comparison, mesh adaptivity based on Lagrangian refinement and the same finest resolution leads to a lack of turbulent power on a small scales, an excess thereof on large scales, and unreliable density
Particle dispersion models and drag coefficients for particles in turbulent flows
NASA Technical Reports Server (NTRS)
Crowe, C. T.; Chung, J. N.; Troutt, T. R.
1988-01-01
Some of the concepts underlying particle dispersion due to turbulence are reviewed. The traditional approaches to particle dispersion in homogeneous, stationary turbulent fields are addressed, and recent work on particle dispersion in large scale turbulent structures is reviewed. The state of knowledge of particle drag coefficients in turbulent gas-particle flows is also reviewed.
Shock-turbulence interaction and the generation of noise
NASA Technical Reports Server (NTRS)
Ribner, H S
1954-01-01
Interaction of convected field of turbulence with shock wave is analyzed to yield modified turbulence, entropy spottiness, and noise generated downstream of the shock. Analysis is generalization of single-spectrum-wave treatment of NACA-TN-2864. Formulas for spectra and correlations are obtained. Numerical calculations yield curves of rms velocity components, temperature, pressure, and noise in db against Mach number for m = 1 to infinity; both isotropic and strongly axisymmetric (lateral/longitudinal = 36/1) initial turbulence are treated. In either case, turbulence of 0.1 percent longitudinal component generates about 120 dbs of noise.
Consistent Initial Conditions for the DNS of Compressible Turbulence
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.; Blaisdell, G. A.
1996-01-01
Relationships between diverse thermodynamic quantities appropriate to weakly compressible turbulence are derived. It is shown that for turbulence of a finite turbulent Mach number there is a finite element of compressibility. A methodology for generating initial conditions for the fluctuating pressure, density and dilatational velocity is given which is consistent with finite Mach number effects. Use of these initial conditions gives rise to a smooth development of the flow, in contrast to cases in which these fields are specified arbitrarily or set to zero. Comparisons of the effect of different types of initial conditions are made using direct numerical simulation of decaying isotropic turbulence.
Premixed Turbulent Flame Propagation in Microgravity
NASA Technical Reports Server (NTRS)
Menon, Suresh
1999-01-01
A combined numerical-experimental study has been carried out to investigate the structure and propagation characteristics of turbulent premixed flames with and without the influence of buoyancy. Experimentally, the premixed flame characteristics are studied in the wrinkled regime using a Couette flow facility and an isotropic flow facility in order to resolve the scale of flame wrinkling. Both facilities were chosen for their ability to achieve sustained turbulence at low Reynolds number. This implies that conventional diagnostics can be employed to resolve the smallest scales of wrinkling. The Couette facility was also built keeping in mind the constraints imposed by the drop tower requirements. Results showed that the flow in this Couette flow facility achieves full-developed turbulence at low Re and all turbulence statistics are in good agreement with past measurements on large-scale facilities. Premixed flame propagation studies were then carried out both using the isotropic box and the Couette facility. Flame imaging showed that fine scales of wrinkling occurs during flame propagation. Both cases in Ig showed significant buoyancy effect. To demonstrate that micro-g can remove this buoyancy effect, a small drop tower was built and drop experiments were conducted using the isotropic box. Results using the Couette facility confirmed the ability to carry out these unique reacting flow experiments at least in 1g. Drop experiments at NASA GRC were planned but were not completed due to termination of this project.
On the Lundgren-Townsend model of turbulent fine scales
NASA Astrophysics Data System (ADS)
Pullin, D. I.; Saffman, P. G.
1993-01-01
The strained-spiral vortex model of turbulent fines scales given by Lundgren [Phys. Fluids 25, 2193 (1982)] is used to calculate vorticity and velocity-derivative moments for homogeneous isotropic turbulence. A specific form of the relaxing spiral vortex is proposed modeled by a rolling-up vortex layer embedded in a background containing opposite signed vorticity and with zero total circulation at infinity. The numerical values of two dimensionless groups are fixed in order to give a Kolmogorov constant and skewness which are within the range of experiment. This gives the result that the ratio of the ensemble average hyperskewness S2p+1≡ (∂u/∂x)2p+1/[(∂u/∂x)2](2p+1)/2 to the hyperflatness F2p≡(∂u/∂x)2p/[(∂u/∂x)2] p, p=2,3,..., is constant independent of Taylor-Reynolds number Rλ, as is the ratio of the 2pth moment of one component of the vorticity Ω2p≡ω2px/(ω2x)p to F2p. A cutoff in a relevant time integration is then used to eliminate vortex-sheet-induced divergences in the integrals corresponding to ω2px, p=2,3,..., and an assumption is made that the lateral scale of the spiral vortex in the model is the geometric mean of the Taylor and the Kolmogorov microscales. This gives Ω2p=Ω̂2pRλp/2-3/4, F2p=F̂2pRλp/2-3/4 and S2p+1=Ŝ2p+1Rλp/2-3/4, p=2,3,..., with explicit calculation of the numbers Ω̂2p, F̂2p, and Ŝ2p+1. The results of the model are compared with experimental compilation of Van Atta and Antonia [Phys. Fluids 23, 252 (1980)] for F4 and with the isotropic turbulence calculations of Kerr [J. Fluid Mech. 153, 31 (1985)] and of Vincent and Meneguzzi [J. Fluid Mech. 225, 1 (1991)].
Studying Turbulence Using Numerical Simulation Databases, 2. Proceedings of the 1988 Summer Program
NASA Technical Reports Server (NTRS)
1988-01-01
The focus of the program was on the use of direct numerical simulations of turbulent flow for study of turbulence physics and modeling. A special interest was placed on turbulent mixing layers. The required data for these investigations were generated from four newly developed codes for simulation of time and spatially developing incompressible and compressible mixing layers. Also of interest were the structure of wall bounded turbulent and transitional flows, evaluation of diagnostic techniques for detection of organized motions, energy transfer in isotropic turbulence, optical propagation through turbulent media, and detailed analysis of the interaction of vortical structures.
Isotropic Growth of Graphene toward Smoothing Stitching.
Zeng, Mengqi; Tan, Lifang; Wang, Lingxiang; Mendes, Rafael G; Qin, Zhihui; Huang, Yaxin; Zhang, Tao; Fang, Liwen; Zhang, Yanfeng; Yue, Shuanglin; Rümmeli, Mark H; Peng, Lianmao; Liu, Zhongfan; Chen, Shengli; Fu, Lei
2016-07-26
The quality of graphene grown via chemical vapor deposition still has very great disparity with its theoretical property due to the inevitable formation of grain boundaries. The design of single-crystal substrate with an anisotropic twofold symmetry for the unidirectional alignment of graphene seeds would be a promising way for eliminating the grain boundaries at the wafer scale. However, such a delicate process will be easily terminated by the obstruction of defects or impurities. Here we investigated the isotropic growth behavior of graphene single crystals via melting the growth substrate to obtain an amorphous isotropic surface, which will not offer any specific grain orientation induction or preponderant growth rate toward a certain direction in the graphene growth process. The as-obtained graphene grains are isotropically round with mixed edges that exhibit high activity. The orientation of adjacent grains can be easily self-adjusted to smoothly match each other over a liquid catalyst with facile atom delocalization due to the low rotation steric hindrance of the isotropic grains, thus achieving the smoothing stitching of the adjacent graphene. Therefore, the adverse effects of grain boundaries will be eliminated and the excellent transport performance of graphene will be more guaranteed. What is more, such an isotropic growth mode can be extended to other types of layered nanomaterials such as hexagonal boron nitride and transition metal chalcogenides for obtaining large-size intrinsic film with low defect. PMID:27403842
Mechanical homogenization increases bacterial homogeneity in sputum.
Stokell, Joshua R; Khan, Ammad; Steck, Todd R
2014-07-01
Sputum obtained from patients with cystic fibrosis (CF) is highly viscous and often heterogeneous in bacterial distribution. Adding dithiothreitol (DTT) is the standard method for liquefaction prior to processing sputum for molecular detection assays. To determine if DTT treatment homogenizes the bacterial distribution within sputum, we measured the difference in mean total bacterial abundance and abundance of Burkholderia multivorans between aliquots of DTT-treated sputum samples with and without a mechanical homogenization (MH) step using a high-speed dispersing element. Additionally, we measured the effect of MH on bacterial abundance. We found a significant difference between the mean bacterial abundances in aliquots that were subjected to only DTT treatment and those of the aliquots which included an MH step (all bacteria, P = 0.04; B. multivorans, P = 0.05). There was no significant effect of MH on bacterial abundance in sputum. Although our results are from a single CF patient, they indicate that mechanical homogenization increases the homogeneity of bacteria in sputum. PMID:24759710
Fischer, F.D. . E-mail: mechanik@unileoben.ac.at; Boehm, H.J.
2005-01-10
The jumps of the strain and stress tensors on the surface of elastic homogeneous or inhomogeneous ellipsoidal inclusions embedded in an elastic matrix are obtained from results reported in the literature. They are used to derive closed-form expressions for the thermodynamic force in such matrix-inclusion systems that are subjected to a generally defined homogeneous transformation eigenstrain. A detailed study is presented for an isotropic spheroidal inclusion in an isotropic matrix in which the most important parameters are the inclusion's aspect ratio {alpha} and an eigenstrain triaxiality parameter d-bar. The fluctuations of the thermodynamic force are investigated for a set of specific transformation eigenstrain tensors and are presented for inclusion shapes ranging from disk-like to fiber-like spheroids.
Horton, W.; Hu, G.
1998-07-01
The origin of plasma turbulence from currents and spatial gradients in plasmas is described and shown to lead to the dominant transport mechanism in many plasma regimes. A wide variety of turbulent transport mechanism exists in plasmas. In this survey the authors summarize some of the universally observed plasma transport rates.
Static spherically symmetric wormholes with isotropic pressure
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
2016-06-01
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there are no spherically symmetric traversable wormholes sustained by sources with a linear equation of state p = ωρ for the isotropic pressure, independently of the form of the redshift function ϕ (r). We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
Kazansky, Peter G; Shimotsuma, Yasuhiko; Sakakura, Masaaki; Beresna, Martynas; Gecevičius, Mindaugas; Svirko, Yuri; Akturk, Selcuk; Qiu, Jianrong; Miura, Kiyotaka; Hirao, Kazuyuki
2011-10-10
We present the first experimental evidence of anisotropic photosensitivity of an isotropic homogeneous medium under uniform illumination. Our experiments reveal fundamentally new type of light induced anisotropy originated from the hidden asymmetry of pulsed light beam with a finite tilt of intensity front. We anticipate that the observed phenomenon, which enables employing mutual orientation of a light polarization plane and pulse front tilt to control interaction of matter with ultrashort light pulses, will open new opportunities in material processing. PMID:21997076
NASA Astrophysics Data System (ADS)
Urakami, Naohito; Imai, Masayuki; Sano, Yoh; Takasu, Masako
1999-08-01
The isotropic-nematic transition of the tobacco mosaic virus (TMV) particles by polysaccharide is related to a high inhibitory activity against TMV infection. We study the process of the isotropic-nematic transition of the TMV particles as a function of the polysaccharide concentration by Monte Carlo simulations in three-dimensional continuous space. In these simulations, we simplify the TMV particles and the polysaccharide molecules as the hard spherocylinders and semirigid chains, respectively, and we assume the simple interactions for the TMV particles and the polysaccharide chains. In our simulation, with increasing concentration of the polysaccharide the homogeneously dispersed TMV particles begin to segregate without orientational ordering, that is isotropic phase separation, and then transform to the nematic state of the TMV particles. The isotropic-nematic transition is caused by simple interactions such as the excluded volume effect, and the complicated biological interaction is not necessary.
Velocity Resolved---Scalar Modeled Simulations of High Schmidt Number Turbulent Transport
NASA Astrophysics Data System (ADS)
Verma, Siddhartha
The objective of this thesis is to develop a framework to conduct velocity resolved - scalar modeled (VR-SM) simulations, which will enable accurate simulations at higher Reynolds and Schmidt (Sc) numbers than are currently feasible. The framework established will serve as a first step to enable future simulation studies for practical applications. To achieve this goal, in-depth analyses of the physical, numerical, and modeling aspects related to Sc " 1 are presented, specifically when modeling in the viscous-convective subrange. Transport characteristics are scrutinized by examining scalar-velocity Fourier mode interactions in Direct Numerical Simulation (DNS) datasets and suggest that scalar modes in the viscous-convective subrange do not directly affect large-scale transport for high Sc . Further observations confirm that discretization errors inherent in numerical schemes can be sufficiently large to wipe out any meaningful contribution from subfilter models. This provides strong incentive to develop more effective numerical schemes to support high Sc simulations. To lower numerical dissipation while maintaining physically and mathematically appropriate scalar bounds during the convection step, a novel method of enforcing bounds is formulated, specifically for use with cubic Hermite polynomials. Boundedness of the scalar being transported is effected by applying derivative limiting techniques, and physically plausible single sub-cell extrema are allowed to exist to help minimize numerical dissipation. The proposed bounding algorithm results in significant performance gain in DNS of turbulent mixing layers and of homogeneous isotropic turbulence. Next, the combined physical/mathematical behavior of the subfilter scalar-flux vector is analyzed in homogeneous isotropic turbulence, by examining vector orientation in the strain-rate eigenframe. The results indicate no discernible dependence on the modeled scalar field, and lead to the identification of the tensor
Negative Poisson's ratio materials via isotropic interactions.
Rechtsman, Mikael C; Stillinger, Frank H; Torquato, Salvatore
2008-08-22
We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, a negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic. PMID:18764632
Negative Poisson's Ratio Materials via Isotropic Interactions
NASA Astrophysics Data System (ADS)
Rechtsman, Mikael C.; Stillinger, Frank H.; Torquato, Salvatore
2008-08-01
We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, have a negative Poisson’s ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson’s ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, a negative Poisson’s ratio can be exhibited even when the material is constrained to be elastically isotropic.
Validation of a Pseudo-Sound Theory for the Pressure-Dilatation in DNS of Compressible Turbulence
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.; Blaisdell, G. A.
1997-01-01
The results of an asymptotic theory for statistical closures for compressible turbulence are explored and validated with the direct numerical simulation of the isotropic decay and the homogeneous shear. An excellent collapse of the data is seen. The slow portion is found to scale, as predicted by the theory, with the quantity M(sub t)(sup 2) and epsilon(sub s). The rapid portion has an unambiguous scaling with alpha(sup 2)M(sub t)(sup s)epsilon(sub s)[P(sub k)/epsilon - l](Sk/epsilon)(sup 2). Implicit in the scaling is a dependence, as has been noted by others, on the gradient Mach number. A new feature of the effects of compressibility, that of the Kolmogorov scaling coefficient, alpha, is discussed. It is suggested that alpha may contain flow specific physics associated with large scales that might provide further insight into the structural effects of compressibility.
Numerical model of sonic boom in 3D kinematic turbulence
NASA Astrophysics Data System (ADS)
Coulouvrat, François; Luquet, David; Marchiano, Régis
2015-10-01
stratified wind superimposed to a 3D random turbulent realization. Propagation is performed either in the case of a shadow zone or of an atmospheric waveguide. To model the turbulent ABL, the mean flow and the fluctuations are handled separately. The wind fluctuations are generated using the Random Fluctuations Generation method assuming a von Kármán spectrum and a homogeneous and isotropic turbulence. The mean stratified wind is modeled based on the Monin-Obhukov Similarity Theory (MOST). To illustrate the method, the typical case of a sunny day with a strong wind has been chosen. Statistics are obtained on several parameters. It shows the importance of turbulence, which leads to an increase of the mean maximum peak pressure in the shadow zone and to its decrease in the waveguide. Moreover, the formation of random caustics that can lead to an increase of the noise perceived locally is outlined.
Estimating formation properties from early-time recovery in wells subject to turbulent head losses
Shapiro, A.M.; Oki, D.S.; Greene, E.A.
1998-01-01
A mathematical model is developed to interpret the early-time recovering water level following the termination of pumping in wells subject to turbulent head losses. The model assumes that turbulent head losses dissipate immediately when pumping ends. In wells subject to both borehole storage and turbulent head losses, the early-time recovery exhibits a slope equal to 1/2 on log-log plots of the recovery versus time. This half-slope response should not be confused with the half-slope response associated with a linear flow regime during aquifer tests. The presence of a borehole skin due to formation damage or stimulation around the pumped well alters the early-time recovery in wells subject to turbulent head losses and gives the appearance of borehole storage, where the recovery exhibits a unit slope on log-log plots of recovery versus time. Type curves can be used to estimate the formation storafivity from the early-time recovery data. In wells that are suspected of having formation damage or stimulation, the type curves can be used to estimate the 'effective' radius of the pumped well, if an estimate of the formation storativity is available from observation wells or other information. Type curves for a homogeneous and isotropic dual-porosity aquifer are developed and applied to estimate formation properties and the effect of formation stimulation from a single-well test conducted in the Madison limestone near Rapid City, South Dakota.A mathematical model is developed to interpret the early-time recovering water level following the termination of pumping in wells subject to turbulent head losses. The model assumes that turbulent head losses dissipate immediately when pumping ends. In wells subject to both borehole storage and turbulent head losses, the early-time recovery exhibits a slope equal to 1/2 on log-log plots of the recovery versus time. This half-slope response should not be confused with the half-slope response associated with a linear flow regime during
Biomimetic Isotropic Nanostructures for Structural Coloration
Forster, Jason D.; Noh, Heeso; Liew, Seng Fatt; Saranathan, Vinodkumar; Schreck, Carl F.; Yang, Lin; Park, Jin-Gyu; Prum, Richard O.; Mochrie, Simon G.J.; O'Hern, Corey S.; Cao, Hui; Dufresne, Eric R.
2010-08-09
The self-assembly of films that mimic color-producing nanostructures in bird feathers is described. These structures are isotropic and have a characteristic length-scale comparable to the wavelength of visible light. Structural colors are produced when wavelength-independent scattering is suppressed by limiting the optical path length through geometry or absorption.
Hierarchical structures in a turbulent pipe flow
NASA Astrophysics Data System (ADS)
She, Zhen-Su; Zou, Zhengping; Zhu, Yuanjie; Zhou, Mingde
2003-11-01
Statistical structures of a series of longitudinal velocity fluctuation signals at different distances (10
Transversely isotropic elasticity imaging of cancellous bone.
Shore, Spencer W; Barbone, Paul E; Oberai, Assad A; Morgan, Elise F
2011-06-01
To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ɛ₁₂ is necessary to reconstruct C₁₂₁₂), and the application of regularization is shown to improve accuracy. Finally
NASA Astrophysics Data System (ADS)
Kotiang, Stephen; Choi, Jaeho
2015-11-01
The degrading effects of atmospheric turbulence on an imaging system can be characterized by the atmospheric modulation transfer function (MTF). In this paper, we derived analytically a new expression for the wave structure function (WSF) of a Gaussian-beam based on the weak fluctuation theory. We assumed the beam-wave is propagating through a horizontal path experiencing isotropic and homogeneous non-Kolmogorov atmospheric turbulence where the power spectrum has a generalized spectral power-law exponent which varies between 3 and 4 instead of the fixed classical Kolmogorov power-law exponent of 11/3. Using the WSF, we derived mathematical expressions for the spatial coherence radius and the long-exposure turbulence MTF of the Gaussian-beam wave. These new expressions were used to analyze the influence of power-law variations and beam sizes on the WSF and quality of imaging systems. The simulation results show that different exponent values produce varying effects on both WSF and imaging systems.
Quenching and Anisotropy of Hydromagnetic Turbulent Transport
NASA Astrophysics Data System (ADS)
Karak, Bidya Binay; Rheinhardt, Matthias; Brandenburg, Axel; Käpylä, Petri J.; Käpylä, Maarit J.
2014-11-01
Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the α effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the α effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the {\\boldsymbolΩ} × \\boldsymbol {{J}} effect nearly the same quenching exponent is obtained as for α. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.
Quenching and anisotropy of hydromagnetic turbulent transport
Karak, Bidya Binay; Brandenburg, Axel; Rheinhardt, Matthias; Käpylä, Petri J.; Käpylä, Maarit J.
2014-11-01
Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the α effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the α effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the Ω×J effect nearly the same quenching exponent is obtained as for α. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.
NASA Astrophysics Data System (ADS)
Sinai, G.; Dirksen, C.
2006-12-01
This paper describes laboratory experimental evidence for lateral flow in the top layer of unsaturated sloping soil due to rainfall. Water was applied uniformly on horizontal and V-shaped surfaces of fine sand, at rates about 100 times smaller than the saturated hydraulic conductivity. Flow regimes near the surface and in the soil bulk were studied by using dyes. Streamlines and streak lines and wetting fronts were visually studied and photographed through a vertical glass wall. Near wetting fronts the flow direction was always perpendicular to the fronts owing to dominant matrix potential gradients. Thus, during early wetting of dry sloping sand, the flow direction is directed upslope. Far above a wetting front the flow was vertical due to the dominance of gravity. Downslope flow was observed during decreasing rainfall and dry periods. The lateral movement was largest near the soil surface and decayed with soil depth. Unstable downslope lateral flow close to the soil surface was attributed to non-Darcian flow due to variable temporal and spatial raindrop distributions. The experiments verify the theory that predicts unsaturated downslope lateral flow in sloping soil due to rainfall dynamics only, without apparent soil texture difference or anisotropy. This phenomenon could have significant implications for hillside hydrology, desert agriculture, irrigation management, etc., as well as for the basic mechanisms of surface runoff and erosion.
ERIC Educational Resources Information Center
Hanratty, Thomas J.
1980-01-01
This paper gives an account of research on the structure of turbulence close to a solid boundary. Included is a method to study the flow close to the wall of a pipe without interferring with it. (Author/JN)
NASA Astrophysics Data System (ADS)
Nazarenko, Sergey
2015-07-01
Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence - Kolmogorov-Zakharov (KZ) spectra.
NASA Astrophysics Data System (ADS)
Hickel, Stefan; Egerer, Christian P.; Larsson, Johan
2014-10-01
We derive and analyze a model for implicit Large Eddy Simulation (LES) of compressible flows that is applicable to a broad range of Mach numbers and particularly efficient for LES of shock-turbulence interaction. Following a holistic modeling philosophy, physically sound turbulence modeling and numerical modeling of unresolved subgrid scales (SGS) are fully merged, in a manner quite different from that of traditional implicit LES approaches. The implicit subgrid model is designed in such a way that asymptotic consistency with incompressible turbulence theory is maintained in the low Mach number limit. Compressibility effects are properly accounted for by a novel numerical flux function, which can capture strong shock waves in supersonic flows and also ensures an accurate representation of smooth waves and turbulence without excessive numerical dissipation. Simulations of shock-tube problems, Noh's three-dimensional implosion problem, large-scale forced and decaying three-dimensional homogeneous isotropic turbulence, supersonic turbulent boundary layer flows, and a Mach = 2.88 compression-expansion ramp flow demonstrate the good performance of the SGS model; across this range of flows, predictions are in excellent agreement with theory, direct numerical simulations, and experimental reference data. Results for implicit LES of canonical shock-turbulence interaction are compared with results of explicit LES using the dynamic Smagorinsky model. The analysis shows that details of the numerical method used for shock capturing clearly outweigh the effect of different turbulence modeling strategies in explicit and implicit LES. The implicit LES model recovers the ideal 2nd-order grid convergence of shock-capturing errors that has been predicted using Rapid Distortion Theory. The dynamic Smagorinsky model in conjunction with a hybrid method that combines sixth-order central differences with a seventh-order weighted essentially non-oscillatory scheme yields turbulence
Temperature variance dissipation equation and its relevance for optical turbulence modeling.
Muschinski, Andreas
2015-11-01
The 3D spectrum Φ(κ) of the turbulent air temperature fluctuations is a key quantity for the physics of optical propagation through the turbulent atmosphere. The standard model, which was derived in the 1950s by Tatarskii from the Obukhov-Corrsin theory of homogeneous and isotropic turbulence, is Φ(κ)=0.033CT2κ(-11/3)h(κl(0)), where κ=|κ| is the wavenumber, CT2 is the temperature structure parameter, l(0) is the inner temperature scale, and h(κl(0) is a universal function that approaches 1 for wavenumbers in the inertial range and drops to zero for κl(0)≫1. Certain performance characteristics of optical systems, such as the scintillation index for small receiving apertures, depend sensitively on the functional form of h(y) at y≈1. During the last 70 years, the optical-turbulence community has developed and applied various heuristic h(y) models. There is a constraint that any valid h(y) model has to fulfill: ∫0∞h(y)y(1/3)dy=(27/10)Γ(1/3)=7.233. This constraint is a dimensionless form of the spectral temperature variance dissipation equation, which follows directly from first-principle fluid mechanics. We show that Tatarskii's cutoff (1961) and Gaussian (1971) models fulfill this constraint, while three more recent models, including the widely used Andrews model [J. Mod. Opt.39, 1849 (1992)JMOPEW0950-034010.1080/09500349214551931], do not. The dissipation constraint can be used to "recalibrate" the coefficients in these models. PMID:26560934
Nonstationary homogeneous nucleation
NASA Technical Reports Server (NTRS)
Harstad, K. G.
1974-01-01
The theory of homogeneous condensation is reviewed and equations describing this process are presented. Numerical computer solutions to transient problems in nucleation (relaxation to steady state) are presented and compared to a prior computation.
Saturation effects associated with sound propagation in a turbulent medium
NASA Technical Reports Server (NTRS)
Wenzel, A. R.
1975-01-01
A theoretical analysis of the acoustic wave field radiated by a time-harmonic point source in a homogeneous, isotropic turbulent medium is presented. The smoothing method is used to study the incoherent, or randomly fluctuating, component of the wave field. The analysis considers the effect on the wave of the velocity fluctuations, as well as the index-of-refraction fluctuations, of the medium. An approximate expression for the second moment of the incoherent wave is obtained for the case in which the wavelenght is much less than the minimum correlation length of the medium. This expression shows that the fluctuations of the wave increase initially in proportion to the propagation distance, but that at larger distances they tend to a limiting, or saturation, value. These results agree with observations of waves propagating in real media. It is also found that the mean square of the total (i.e., coherent plus incoherent) acoustic pressure is unaffected by the randomness of the medium.
Spatial and velocity statistics of inertial particles in turbulent flows
NASA Astrophysics Data System (ADS)
Bec, J.; Biferale, L.; Cencini, M.; Lanotte, A. S.; Toschi, F.
2011-12-01
Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Reλ ~ 200 and Reλ ~ 400, corresponding to resolutions of 5123 and 20483 grid points, respectively. Particles Stokes number values range from St ≈ 0.2 to 70. Stationary small-scale particle distribution is shown to display a singular -multifractal- measure, characterized by a set of generalized fractal dimensions with a strong sensitivity on the Stokes number and a possible, small Reynolds number dependency. Velocity increments between two inertial particles depend on the relative weight between smooth events - where particle velocity is approximately the same of the fluid velocity-, and caustic contributions - when two close particles have very different velocities. The latter events lead to a non-differentiable small-scale behaviour for the relative velocity. The relative weight of these two contributions changes at varying the importance of inertia. We show that moments of the velocity difference display a quasi bi-fractal-behavior and that the scaling properties of velocity increments for not too small Stokes number are in good agreement with a recent theoretical prediction made by K. Gustavsson and B. Mehlig arXiv: 1012.1789v1 [physics.flu-dyn], connecting the saturation of velocity scaling exponents with the fractal dimension of particle clustering.
NASA Astrophysics Data System (ADS)
Fathali, M.; Deshiri, M. Khoshnami
2016-04-01
The shearless mixing layer is generated from the interaction of two homogeneous isotropic turbulence (HIT) fields with different integral scales ℓ1 and ℓ2 and different turbulent kinetic energies E1 and E2. In this study, the sensitivity of temporal evolutions of two-dimensional, incompressible shearless mixing layers to the parametric variations of ℓ1/ℓ2 and E1/E2 is investigated. The sensitivity methodology is based on the nonintrusive approach; using direct numerical simulation and generalized polynomial chaos expansion. The analysis is carried out at Reℓ 1=90 for the high-energy HIT region and different integral length scale ratios 1 /4 ≤ℓ1/ℓ2≤4 and turbulent kinetic energy ratios 1 ≤E1/E2≤30 . It is found that the most influential parameter on the variability of the mixing layer evolution is the turbulent kinetic energy while variations of the integral length scale show a negligible influence on the flow field variability. A significant level of anisotropy and intermittency is observed in both large and small scales. In particular, it is found that large scales have higher levels of intermittency and sensitivity to the variations of ℓ1/ℓ2 and E1/E2 compared to the small scales. Reconstructed response surfaces of the flow field intermittency and the turbulent penetration depth show monotonic dependence on ℓ1/ℓ2 and E1/E2 . The mixing layer growth rate and the mixing efficiency both show sensitive dependence on the initial condition parameters. However, the probability density function of these quantities shows relatively small solution variations in response to the variations of the initial condition parameters.
Nonasymptotic homogenization of periodic electromagnetic structures: Uncertainty principles
NASA Astrophysics Data System (ADS)
Tsukerman, Igor; Markel, Vadim A.
2016-01-01
We show that artificial magnetism of periodic dielectric or metal/dielectric structures has limitations and is subject to at least two "uncertainty principles." First, the stronger the magnetic response (the deviation of the effective permeability tensor from identity), the less accurate ("certain") the predictions of any homogeneous model. Second, if the magnetic response is strong, then homogenization cannot accurately reproduce the transmission and reflection parameters and, simultaneously, power dissipation in the material. These principles are general and not confined to any particular method of homogenization. Our theoretical analysis is supplemented with a numerical example: a hexahedral lattice of cylindrical air holes in a dielectric host. Even though this case is highly isotropic, which might be thought of as conducive to homogenization, the uncertainty principles remain valid.
Turbulent transport with intermittency: Expectation of a scalar concentration
NASA Astrophysics Data System (ADS)
Rast, Mark Peter; Pinton, Jean-François; Mininni, Pablo D.
2016-04-01
Scalar transport by turbulent flows is best described in terms of Lagrangian parcel motions. Here we measure the Eulerian distance travel along Lagrangian trajectories in a simple point vortex flow to determine the probabilistic impulse response function for scalar transport in the absence of molecular diffusion. As expected, the mean squared Eulerian displacement scales ballistically at very short times and diffusively for very long times, with the displacement distribution at any given time approximating that of a random walk. However, significant deviations in the displacement distributions from Rayleigh are found. The probability of long distance transport is reduced over inertial range time scales due to spatial and temporal intermittency. This can be modeled as a series of trapping events with durations uniformly distributed below the Eulerian integral time scale. The probability of long distance transport is, on the other hand, enhanced beyond that of the random walk for both times shorter than the Lagrangian integral time and times longer than the Eulerian integral time. The very short-time enhancement reflects the underlying Lagrangian velocity distribution, while that at very long times results from the spatial and temporal variation of the flow at the largest scales. The probabilistic impulse response function, and with it the expectation value of the scalar concentration at any point in space and time, can be modeled using only the evolution of the lowest spatial wave number modes (the mean and the lowest harmonic) and an eddy based constrained random walk that captures the essential velocity phase relations associated with advection by vortex motions. Preliminary examination of Lagrangian tracers in three-dimensional homogeneous isotropic turbulence suggests that transport in that setting can be similarly modeled.
Rapid Distortion Theory in astrophysical turbulence
NASA Astrophysics Data System (ADS)
Safonov, Sergey; Petrosyan, Arakel
2016-04-01
In this report, we study statistical properties of astrophysical turbulent plasma flows using Rapid Distortion Theory (RDT). The core assumption is that the turbulence responds to the external distortion so fast, that inertial and viscous forces result in a negligible change in velocity distribution. Thus it is assumed that the response to the external effect takes place in the time interval much smaller than turbulence decay time. This allows to linearize equations and to derive equations for second moments of turbulence. We apply RDT to incompressible turbulent MHD flows distorted with external magnetic field and linear velocity shear in cases of rotating and non-rotating plasma. It is shown that even with a strong nonlinearity many properties of turbulence can be qualitatively studied using a linear theory. A closed system of linear equations for velocity and magnetic field fluctuations is derived. Development of initially isotropic turbulence and transition to anisotropy are studied. Equations for fluid, current and cross helicity are derived. Differences in cases of rotating and non-rotating flows are discussed. Changes introduced by considering Hall effect are discussed.
Anisotropy in turbulent flows and in turbulent transport
NASA Astrophysics Data System (ADS)
Biferale, Luca; Procaccia, Itamar
2005-07-01
The problem of anisotropy and its effects on the statistical theory of high Reynolds number (Re) turbulence (and turbulent transport) is intimately related and intermingled with the problem of the universality of the (anomalous) scaling exponents of structure functions. Both problems had seen tremendous progress in the last 5 years. In this review we present a detailed description of the new tools that allow effective data analysis and systematic theoretical studies such as to separate isotropic from anisotropic aspects of turbulent statistical fluctuations. Employing the invariance of the equations of fluid mechanics to all rotations, we show how to decompose the (tensorial) statistical objects in terms of the irreducible representation of the SO(d) symmetry group (with d being the dimension, d=2 or 3). This device allows a discussion of the scaling properties of the statistical objects in well-defined sectors of the symmetry group, each of which is determined by the “angular momenta” sector numbers (j,m). For the case of turbulent advection of passive scalar or vector fields, this decomposition allows rigorous statements to be made: (i) the scaling exponents are universal, (ii) the isotropic scaling exponents are always leading, (iii) the anisotropic scaling exponents form a discrete spectrum which is strictly increasing as a function of j. This emerging picture offers a complete understanding of the decay of anisotropy upon going to smaller and smaller scales. Next, we explain how to apply the SO(3) decomposition to the statistical Navier-Stokes theory. We show how to extract information about the scaling behavior in the isotropic sector. Doing so furnishes a systematic way to assess the universality of the scaling exponents in this sector, clarifying the anisotropic origin of the many measurements that claimed the opposite. A systematic analysis of direct numerical simulations (DNS) of the Navier-Stokes equations and of experiments provides a strong support
Advanced Numerical Modeling of Turbulent Atmospheric Flows
NASA Astrophysics Data System (ADS)
Kühnlein, Christian; Dörnbrack, Andreas; Gerz, Thomas
The present chapter introduces the method of computational simulation to predict and study turbulent atmospheric flows. This includes a description of the fundamental approach to computational simulation and the practical implementation using the technique of large-eddy simulation. In addition, selected contributions from IPA scientists to computational model development and various examples for applications are given. These examples include homogeneous turbulence, convective boundary layers, heated forest canopy, buoyant thermals, and large-scale flows with baroclinic wave instability.
Relative diffusion of a pair of inertial particles in the inertial sub-range of turbulence
NASA Astrophysics Data System (ADS)
Enohata, Kei; Morishita, Koji; Ishihara, Takashi
2015-11-01
Turbulent diffusion of a pair of inertial particles in 3-dimensional homogeneous and isotropic turbulence was studied using direct numerical simulation (DNS) with 20483 grid points; the Taylor micro-scale Reynolds number in the DNS is approximately 425. For each set of the inertial particles with different values of the Stokes number (St = 0 , 0 . 1 , 0 . 2 , 0 . 5 , 1 , 2 , 5 , 10), 2563 particles are tracked using cubic spline interpolation for the velocity data in the DNS. Here St = 0 corresponds to fluid particles. The DNS showed that for each value of St , the mean square of the distance δx between the two inertial particles grows with time t as < δx2 > ~ Cɛt3 in the inertial subrange, which is in agreement with Richardson (1926) and Obukhov (1941). Here ɛ is the mean energy dissipation rate per unit mass, and C is a constant of O(1) depending on the value of St and the initial distance between the inertial particles. The DNS shows also that large clusters of strong vortices enhance relative diffusion of inertial particles of St > 1 .
Hall effects and sub-grid-scale modeling in magnetohydrodynamic turbulence simulations
NASA Astrophysics Data System (ADS)
Miura, Hideaki; Araki, Keisuke; Hamba, Fujihiro
2016-07-01
Effects of the Hall term on short-wave components of magnetohydrodynamic turbulence and sub-grid-scale modeling of the effects are studied. Direct numerical simulations of homogeneous magnetohydrodynamic turbulence with and without the Hall term are carried out. The Hall term excites short-wave components in the magnetic field, demanding a high numerical resolution to resolve the scales smaller than the ion skin depth. A k 7 / 3-like scaling-law in the magnetic energy spectrum associated with the excitation of the short-wave components is clearly shown by the use of both an isotropic spectrum and a one-dimensional spectrum. It is also shown that the introduction of the Hall term can cause a structural transition in the vorticity field from tubes to sheets. In order to overcome a strong demand on high-resolution in space and time and to enable quicker computations, large eddy simulations with a Smagorinsky-type sub-grid-scale model are carried out. It is shown that our large eddy simulations successfully reproduce not only the energy spectrum but also tubular vortex structures, reducing the computational cost considerably.
A study of local anisotropy in globally isotropic incompressible MHD
NASA Astrophysics Data System (ADS)
Milano, L. J.; Dmitruk, P.; Matthaeus, W. H.; Montgomery, D.
2000-10-01
It is a well known fact that in presence of a DC applied field, MHD turbulence develops spectral anisotropy from an isotropic initial condition [1]. Typically, the reduced spectrum is steeper in the direction of the magnetic field than it is in any transverse direction. Theoretical insight into the origin of this effect has been derived from simulations in which there is a uniform DC magnetic field, but suggestions of a similar anisotropy is seen in various laboratory devices and also in the solar wind [2,3]. One might expect that a DC field is not essential, and it is the local mean field that is responsible. Here we investigate the occurence of local anisotropy in 3 dimensional MHD, i.e. we search for a local version of the spectral anisotropy effect. We perform 3D MHD pseudo-spectral incompressible relaxation simulations, and compute structure functions accumulated according to whether the separation is parallel to, or transverse to, the local magnetic field. Preliminary results show that correlations decay slower in the locally averaged magnetic field direction. [1] J. Shebalin, W. Matthaeus and D. Montgomery, J. Plasma Phys. 29, 525 (1983) [2] W.H. Matthaeus, M.L. Goldsteon and D.A. Roberts, J. Geophys. Res. 95, 20 673 (1990) [3] J. Armstrong, W. Coles, M. Kojima and B. Rickett, Ap. J. 358, 685 (1990)
Exploiting similarity in turbulent shear flows for turbulence modeling
NASA Technical Reports Server (NTRS)
Robinson, David F.; Harris, Julius E.; Hassan, H. A.
1992-01-01
It is well known that current k-epsilon models cannot predict the flow over a flat plate and its wake. In an effort to address this issue and other issues associated with turbulence closure, a new approach for turbulence modeling is proposed which exploits similarities in the flow field. Thus, if we consider the flow over a flat plate and its wake, then in addition to taking advantage of the log-law region, we can exploit the fact that the flow becomes self-similar in the far wake. This latter behavior makes it possible to cast the governing equations as a set of total differential equations. Solutions of this set and comparison with measured shear stress and velocity profiles yields the desired set of model constants. Such a set is, in general, different from other sets of model constants. The rational for such an approach is that if we can correctly model the flow over a flat plate and its far wake, then we can have a better chance of predicting the behavior in between. It is to be noted that the approach does not appeal, in any way, to the decay of homogeneous turbulence. This is because the asymptotic behavior of the flow under consideration is not representative of the decay of homogeneous turbulence.
Applications of direct numerical simulation of turbulence in second order closures
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Lumley, John L.
1995-01-01
This paper discusses two methods of developing models for the rapid pressure-strain correlation term in the Reynolds stress transport equation using direct numerical simulation (DNS) data. One is a perturbation about isotropic turbulence, the other is a perturbation about two-component turbulence -- an extremely anisotropic turbulence. A model based on the latter method is proposed and is found to be very promising when compared with DNS data and other models.
Statistical Properties of the T-Exponential of Isotropically Distributed Random Matrices
NASA Astrophysics Data System (ADS)
Il'yn, A. S.; Sirota, V. A.; Zybin, K. P.
2016-05-01
A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random N× N matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and higher correlation functions of the T-exponent are derived from the statistical properties of the process. The approach may be of use in a wide range of physical problems. For example, in theory of turbulence the account of non-gaussian statistics is very important since the non-Gaussian behavior is responsible for the time asymmetry of the energy flow.
Anisotropy in MHD turbulence due to a mean magnetic field
NASA Technical Reports Server (NTRS)
Shebalin, J. V.; Matthaeus, W. H.; Montgomery, D.
1982-01-01
The development of anisotropy in an initially isotropic spectrum is studied numerically for two-dimensional magnetohydrodynamic turbulence. The anisotropy develops due to the combined effects of an externally imposed dc magnetic field and viscous and resistive dissipation at high wave numbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wave numbers.
On curve and surface stretching in turbulent flow
NASA Technical Reports Server (NTRS)
Etemadi, Nassrollah
1989-01-01
Cocke (1969) proved that in incompressible, isotropic turbulence the average material line (material surface) elements increase in comparison with their initial values. Good estimates of how much they increase in terms of the eigenvalues of the Green deformation tensor were rigorously obtained.
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
Theoretical and numerical works in atmospheric turbulence have used the Navier-Stokes fluid equations exclusively for describing large-scale motions. Controversy over the existence of an average temperature gradient for the very large eddies in the atmosphere suggested that a new theoretical basis for describing large-scale turbulence was necessary. A new soliton formalism as a fluid analogue that generalizes the Schrodinger equation and the Zakharov equations has been developed. This formalism, processing all the nonlinearities including those from modulation provided by the density fluctuations and from convection due to the emission of finite sound waves by velocity fluctuations, treats large-scale turbulence as coalescing and colliding solitons. The new soliton system describes large-scale instabilities more explicitly than the Navier-Stokes system because it has a nonlinearity of the gradient type, while the Navier-Stokes has a nonlinearity of the non-gradient type. The forced Schrodinger equation for strong fluctuations describes the micro-hydrodynamical state of soliton turbulence and is valid for large-scale turbulence in fluids and plasmas where internal waves can interact with velocity fluctuations.
Zonal flow generation and its feedback on turbulence production in drift wave turbulence
NASA Astrophysics Data System (ADS)
Pushkarev, Andrey V.; Bos, Wouter J. T.; Nazarenko, Sergey V.
2013-04-01
Plasma turbulence described by the Hasegawa-Wakatani equations is simulated numerically for different models and values of the adiabaticity parameter C. It is found that for low values of C turbulence remains isotropic, zonal flows are not generated and there is no suppression of the meridional drift waves and particle transport. For high values of C, turbulence evolves towards highly anisotropic states with a dominant contribution of the zonal sector to the kinetic energy. This anisotropic flow leads to a decrease of turbulence production in the meridional sector and limits the particle transport across the mean isopycnal surfaces. This behavior allows to consider the Hasegawa-Wakatani equations a minimal PDE model, which contains the drift-wave/zonal-flow feedback loop mechanism.
Zonal flow generation and its feedback on turbulence production in drift wave turbulence
Pushkarev, Andrey V.; Bos, Wouter J. T.; Nazarenko, Sergey V.
2013-04-15
Plasma turbulence described by the Hasegawa-Wakatani equations is simulated numerically for different models and values of the adiabaticity parameter C. It is found that for low values of C turbulence remains isotropic, zonal flows are not generated and there is no suppression of the meridional drift waves and particle transport. For high values of C, turbulence evolves towards highly anisotropic states with a dominant contribution of the zonal sector to the kinetic energy. This anisotropic flow leads to a decrease of turbulence production in the meridional sector and limits the particle transport across the mean isopycnal surfaces. This behavior allows to consider the Hasegawa-Wakatani equations a minimal PDE model, which contains the drift-wave/zonal-flow feedback loop mechanism.
ODTLES : a model for 3D turbulent flow based on one-dimensional turbulence modeling concepts.
McDermott, Randy; Kerstein, Alan R.; Schmidt, Rodney Cannon
2005-01-01
This report describes an approach for extending the one-dimensional turbulence (ODT) model of Kerstein [6] to treat turbulent flow in three-dimensional (3D) domains. This model, here called ODTLES, can also be viewed as a new LES model. In ODTLES, 3D aspects of the flow are captured by embedding three, mutually orthogonal, one-dimensional ODT domain arrays within a coarser 3D mesh. The ODTLES model is obtained by developing a consistent approach for dynamically coupling the different ODT line sets to each other and to the large scale processes that are resolved on the 3D mesh. The model is implemented computationally and its performance is tested and evaluated by performing simulations of decaying isotropic turbulence, a standard turbulent flow benchmarking problem.
Attenuation of Gas Turbulence by a Nearly Stationary Dispersion of Fine Particles
NASA Technical Reports Server (NTRS)
Paris, A. D.; Eaton, J. K.; Hwang, W.
1999-01-01
particles fall through the measurement volume. Measurements will be acquired using a high resolution image velocimetry (PIV) system being developed specifically for work in particle-laden flows. The measurements will include the decay of the turbulence kinetic energy under various particle loadings. The spatial spectra of the turbulence will also be measured. In a second set of experiments, the interaction of a single eddy with a collection of nearly stationary particles will be examined. The eddy will be a vortex ring emitted by a jet pulse through an orifice. The distortion of the vortex under the influence of the particles will be examined to gain a better understanding of how fine particles can cause such large reductions in turbulence levels. This experiment could not be conducted in terrestrial gravity because the high particle velocities would overwhelm the relatively low speed motion of the vortex ring. This experimental program is just getting underway. The initial challenge is to build a closed facility containing reasonably homogeneous and isotropic turbulence with zero mean velocity. Our approach is to use a set of synthetic jets mounted on the periphery of a transparent plexiglass box to create the turbulence. A synthetic jet is a plenum chamber with an orifice open to the volume of interest. The volume of the chamber fluctuates periodically so alternately a jet is ejected from the volume or flow is drawn back in as a sink. The asymmetry of this situation results in a net transport of momentum and kinetic energy into the volume of interest. The present apparatus includes eight synthetic jets each powered independently by a six inch loudspeaker. The synthetic jets discharge through ejector tubes to increase the scale of the turbulence. Construction of the apparatus is now complete and preliminary flow visualization studies have been conducted. The PIV system is also under development. A compact dual-pulse YAG laser has been acquired as the light source and