On the decay of homogeneous isotropic turbulence
NASA Astrophysics Data System (ADS)
Skrbek, L.; Stalp, Steven R.
2000-08-01
Decaying homogeneous, isotropic turbulence is investigated using a phenomenological model based on the three-dimensional turbulent energy spectra. We generalize the approach first used by Comte-Bellot and Corrsin [J. Fluid Mech. 25, 657 (1966)] and revised by Saffman [J. Fluid Mech. 27, 581 (1967); Phys. Fluids 10, 1349 (1967)]. At small wave numbers we assume the spectral energy is proportional to the wave number to an arbitrary power. The specific case of power 2, which follows from the Saffman invariant, is discussed in detail and is later shown to best describe experimental data. For the spectral energy density in the inertial range we apply both the Kolmogorov -5/3 law, E(k)=Cɛ2/3k-5/3, and the refined Kolmogorov law by taking into account intermittency. We show that intermittency affects the energy decay mainly by shifting the position of the virtual origin rather than altering the power law of the energy decay. Additionally, the spectrum is naturally truncated due to the size of the wind tunnel test section, as eddies larger than the physical size of the system cannot exist. We discuss effects associated with the energy-containing length scale saturating at the size of the test section and predict a change in the power law decay of both energy and vorticity. To incorporate viscous corrections to the model, we truncate the spectrum at an effective Kolmogorov wave number kη=γ(ɛ/v3)1/4, where γ is a dimensionless parameter of order unity. We show that as the turbulence decays, viscous corrections gradually become more important and a simple power law can no longer describe the decay. We discuss the final period of decay within the framework of our model, and show that care must be taken to distinguish between the final period of decay and the change of the character of decay due to the saturation of the energy containing length scale. The model is applied to a number of experiments on decaying turbulence. These include the downstream decay of turbulence in
Helicity statistics in homogeneous and isotropic turbulence and turbulence models
NASA Astrophysics Data System (ADS)
Sahoo, Ganapati; De Pietro, Massimo; Biferale, Luca
2017-02-01
We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.
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
A spiral vortex model of homogeneous isotropic turbulence
NASA Astrophysics Data System (ADS)
Higgins, Keith; Ooi, Andrew; Chong, Min
2002-11-01
The Lundgren-Townsend model of turbulent fine scales has been successful in predicting some of the properties of homogeneous isotropic turbulence. Lundgren obtained these results by averaging over an ensemble of nearly axisymmetric, unsteady, stretched spiral vortices. These vortical structures are represented in the model by a large-time asymptotic solution of the Navier-Stokes equations. Extending on the work of Pullin & Saffman [Phys. Fluids 8, 3072 (1996)], we calculate the energy spectrum and longitudinal velocity structure functions for a specific realisation of the Lundgren-Townsend model. Here the members of our ensemble are time-evolving spiral vortex structures resulting from the merging of stretched Burgers vortex tubes. The merging is computed numerically following the method of Buntine & Pullin [JFM 205, 263 (1989)]. We present results for a range of vortex Reynolds numbers.
Clustering of particles in homogeneous and isotropic turbulence
NASA Astrophysics Data System (ADS)
Hainaux, Franck; Cartellier, Alain; Lasheras, Juan C.
1999-11-01
We have experimentally studied the clustering effect which occurs in a turbulent flow laden with particles of given size distribution. For this purpose we have analyzed using PDPA and image processing techniques the variations of the spatial density distribution of particles in a decaying isotropic turbulent flow. In the case of particles smaller than the Kolmogorov length scale and dilute systems (void fraction 10-5) we have found that the dynamic interaction of the particles with the various turbulent flow structures leads to the accumulation of particles forming clusters of variable fractal dimensions. These clusters were found to result in an enhancement of the particle settling velocity by an amount about 1.2 times the velocity rms. These results are in good qualitative agreement with DNS of particules settling in a homogeneous turbulent flow performed by Wang and Maxey (JFM vol.256, 1993) and also confirmed in recent LES performed by Yang and Lei (JFM vol.371, 1998). The somewhat higher enhancements observed in experiments compared to those predicted by computations seem to result from the convection velocity of dense compact regions.
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.
NASA Astrophysics Data System (ADS)
Eaton, John; Hwang, Wontae; Cabral, Patrick
2002-11-01
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
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
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
Chaos and Predictability of Homogeneous-Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Boffetta, G.; Musacchio, S.
2017-08-01
We study the chaoticity and the predictability of a turbulent flow on the basis of high-resolution direct numerical simulations at different Reynolds numbers. We find that the Lyapunov exponent of turbulence, which measures the exponential separation of two initially close solutions of the Navier-Stokes equations, grows with the Reynolds number of the flow, with an anomalous scaling exponent, larger than the one obtained on dimensional grounds. For large perturbations, the error is transferred to larger, slower scales, where it grows algebraically generating an "inverse cascade" of perturbations in the inertial range. In this regime, our simulations confirm the classical predictions based on closure models of turbulence. We show how to link chaoticity and predictability of a turbulent flow in terms of a finite size extension of the Lyapunov exponent.
Observation of quantum decay of homogeneous, isotropic (grid) turbulence
NASA Astrophysics Data System (ADS)
Ihas, Gary; Munday, Lydia; Yang, Jihee; Thompson, Kyle; Guo, Wei; Chapurin, Roman; Fisher, Shaun; McClintock, Peter; Vinen, W. F.
2014-03-01
In classical grid turbulence fluid is forced through a stationary grid. In the quantum case a grid moves through an initially stationary superfluid driven by a linear motor. We have developed a motor using superconducting drive coils and bearings, moving a grid at constant speed (0 and 15 cm/s). Stalp et al[2] report the decay of vortex-line density L in the grid's wake measured by 2nd sound attenuation. L decayed at large times as t - 3 / 2, interpreted as a quasi-classical Richardson cascade of energy-containing eddies size limited by channel width, associated with a Kolmogorov energy spectrum. It is assumed eddies produced on a scale of the grid mesh grow through the classical fluids mechanism.[3] We can now test a semi-quantitative theory with different mesh grids or channel sizes, relating to the possible existence of inverse turbulent cascades. Our 2nd sound system is conventional, but with a novel phase and amplitude feedback loop making stringent constant temperature unnecessary. Both t - 3 / 2 and non-t - 3 / 2 decays have been observed with 2 mesh sizes. US NSF DMR#0602778 and #1007937 and EPSRC EP/H04762X/1.
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.
The role of bulk viscosity on the decay of compressible, homogeneous, isotropic turbulence
NASA Astrophysics Data System (ADS)
Johnsen, Eric; Pan, Shaowu
2016-11-01
The practice of neglecting bulk viscosity in studies of compressible turbulence is widespread. While exact for monatomic gases and unlikely to strongly affect the dynamics of fluids whose bulk-to-shear viscosity ratio is small and/or of weakly compressible turbulence, this assumption is not justifiable for compressible, turbulent flows of gases whose bulk viscosity is orders of magnitude larger than their shear viscosities (e.g., CO2). To understand the mechanisms by which bulk viscosity and the associated phenomena affect compressible turbulence, we conduct DNS of freely decaying compressible, homogeneous, isotropic turbulence for ratios of bulk-to-shear viscosity ranging from 0-1000. Our simulations demonstrate that bulk viscosity increases the decay rate of turbulent kinetic energy; while enstrophy exhibits little sensitivity to bulk viscosity, dilatation is reduced by an order of magnitude within the two eddy turnover time. Via a Helmholtz decomposition of the flow, we determined that bulk viscosity damps the dilatational velocity and reduces dilatational-solenoidal exchanges, as well as pressure-dilatation coupling. In short, bulk viscosity renders compressible turbulence incompressible by reducing energy transfer between translational and internal modes.
Asymptotic form of the longitudinal correlation function for isotropic homogeneous turbulence
NASA Technical Reports Server (NTRS)
Rosen, G.
1981-01-01
An asymptotic form is derived for the longitudinal correlation function for isotropic homogeneous turbulence in an incompressible fluid governed by the Navier-Stokes equation. The result is obtained from an analysis of the algebraic-differential structure of the two-point correlation tensor contained in the complex-valued Fourier transform of the probability measure over the turbulence ensemble, which reveals that the Hopf characteristic functional (the complex-valued Fourier transform of the probability measure) satisfies the Fourier interference inequality. Consequences of the expression obtained, in which the correlation function is a positive definite function of the inverse cube of the spatial coordinate as it approaches infinity, are shown to include the nonexistence of the Loitsianskii invariant, and the solution is shown to be consistent with empirical formulas.
NASA Astrophysics Data System (ADS)
Bateson, Colin; Aliseda, Alberto
2015-11-01
We present results from wind tunnel experiments on the evolution of small inertial (d ~ 10 - 200 μm) water droplets in homogeneous, isotropic, slowly decaying grid turbulence. High-speed imaging and a Particle Tracking algorithm are used to calculate relative velocity distributions. We analyze the preferential concentration, via the 2D Radial Distribution Function, and enhanced relative velocity of droplets resulting from their inertial interactions with the underlying turbulence. The two-dimensional particle velocities, measured from multi-image tracks along a streamwise plane, are conditionally analyzed with respect to the distance from the nearest particle. We focus on the non-normality of the statistics for the particle-particle separation velocity component to examine the influence of the inertial interaction with the turbulence on the dynamics of the droplets. We observe a negative bias (in the mean and mode) in the separation velocity of particles for short separations, signaling a tendency of particles to collide more frequently than a random agitation by turbulence would predict. The tails of the distribution are interpreted in terms of the collision/coalescence process and the probability of collisions that do not lead to coalescence.
NASA Astrophysics Data System (ADS)
Imtiaz, Ahmad; Lu, Zhi-Ming; Liu, Yu-Lu
2014-01-01
Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin's model, and at the fourth location, close to She—Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.
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.
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)
Marié, J. L.; Tronchin, T.; Grosjean, N.; Méès, L.; Öztürk, O. Can; Fournier, C.; Barbier, B.; Lance, M.
2017-02-01
The evaporation rate of diethyl ether droplets dispersing in a homogeneous, nearly isotropic turbulence is measured by following droplets along their trajectory. Measurements are performed at ambient temperature and pressure by using in-line digital holography. The holograms of droplets are recorded with a single high-speed camera (3 kHz), and droplets trajectories are reconstructed with an "inverse problem approach" (IPA) algorithm previously used in Chareyron et al. (New J Phys 14:043039, 2012) and Marié et al. (Exp Fluid 55(4):1708, 2014. doi: 10.1007/s00348-014-1708-6). The thermal/vapor concentration wakes developing around the droplets are visible behind each hologram. A standard reconstruction process is applied, showing that these wakes are aligned with the relative Lagrangian velocity seen by droplets at each instant. This relative velocity is that obtained from the dynamic equation of droplets motion and the positions and diameter of the droplets measured by holography and the IPA reconstruction. Sequences of time evolution of droplets 3D positions, diameter and 3D relative velocity are presented. In a number of cases, the evaporation rate of droplets changes along the trajectory and deviates from the value estimated with a standard film model of evaporation. This shows that turbulence may significantly influence the phase change process.
Marked drag reduction in non-affine viscoelastic turbulence in homogeneous isotropic and pipe flows
NASA Astrophysics Data System (ADS)
Horiuti, K.; Matsumoto, K.; Adati, M.
2011-12-01
Effect of non-affinity of the molecular motions to the macroscopic deformation in the polymer-diluted flow on turbulent drag reduction (DR) is studied using the DNS data for homogeneous isotropic turbulence and pipe flow. The polymer stress is obtained by solving the non-affine Johnson-Segalman constitutive equation. In both flows, DR is maximal when non-affinity is either minimum or maximum, but the largest reduction is achieved when non-affinity is maximum. As an extreme case, in pipe flow, the mean velocity profile exceeds the Virk's maximum DR limit and almost complete relaminarization of turbulent state is achieved. The normal-stress difference (NSD) is obtained on the basis of new eigenvectors which span the isosurfaces of vortex tube and sheet. It is shown that the first NSD is predominantly positive, while the second NSD is negative along the sheets and tubes. Thus, an extra tension is exerted on the sheet and tube. With an increase of effective viscosity by an addition of elongation viscosity, resistance of the sheet and tube to their stretching is enhanced. The principal mechanism for DR when non-affinity is maximum is that the transformation of the sheet into the tube is restrained because the sheet tends to snap back to the original flat form. When non-affinity is minimum, the tubes are created but its stretching is suppressed by annihilation of lowering of the pressure in the tube-core region. In both cases, cascade of the energy into the small scales is diminished leading to the reduction of drag.
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
Time resolved measurements of rigid fiber dispersion in near homogeneous isotropic turbulence
NASA Astrophysics Data System (ADS)
Sabban, Lilach; Cohen, Asaf; van Hout, Rene; Empfl Environmental Multi-Phase Flow Laboratory Team
2013-11-01
Time resolved, planar particle image velocimetry (PIV, 3kHz) and two-orthogonal view, digital holographic cinematography (2kHz) was used to measure 3D fiber trajectories/orientation dynamics in near homogeneous isotropic air turbulence (HIT) with dilute suspended fibers. The PIV covered a field of view of 6 × 12 mm2 and the holography a volume of interest of 173 mm3, positioned at the center of the chamber. HIT (Reλ = 144) was generated in the center of a 403 cm3 cube by eight woofers mounted on each of its corners. Three different nylon fibers having a length of 0.5 mm and diameter of 10, 14 and 19 μm were released from the top of the chamber. Fibers had Stokes numbers of order one and are expected to accumulate in regions of low vorticity and settle along a path of local minimal drag. Fiber 3D trajectories/orientations have been obtained from the holography measurements and orientational/translational dispersion coefficients will be presented. In addition the flow field in the vicinity of tracked fibers has been resolved by the PIV, and results on fluid and fiber accelerations and position correlation with in-plane strain rate and out-of-plane vorticity will be presented.
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.
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.
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.
Direct numerical simulations of homogeneous isotropic turbulence in a dense gas
NASA Astrophysics Data System (ADS)
Giauque, A.; Corre, C.; Menghetti, M.
2017-03-01
A study of turbulence in BZT dense gas flows is performed using DNS. It is shown that for a large but realistic intensity, the turbulence in dense gas flows behaves in a highly compressible manner when the average thermodynamic state lies within the inversion region in which the gas fundamental derivative is negative. A close similarity is observed in the evolution of the kinetic energy when the initial turbulent Mach number and the Taylor Reynolds number are matched regardless of the Equation of State (EoS) considered. A large turbulent Mach number is yet more easily attained in dense gas flows lying in the inversion region because of the low speed of sound associated with it. In this case the turbulence shows a highly compressible evolution with periodic exchanges between the internal and kinetic energies. In order to assess the capabilities of currently available Large Eddy Simulation (LES) subgrid-scale models, a-posteriori tests are performed using the dynamic Smagorinsky model. Coherently with the hypothesis it relies on, the model perfectly captures the evolution of the kinetic energy when the turbulent Mach number is low enough. When using the perfect gas EoS at a higher turbulent Mach number the agreement is reasonable. Yet, when the average thermodynamic state lies within the inversion region and when using the thermal and caloric Martin&Hou EoS, the model is not able to capture the correct evolution of the kinetic energy. The results presented in this study call for a specific research effort directed towards the assessment and possibly the development of advanced subgrid-scale models for LES of turbulent dense gas flows.
NASA Astrophysics Data System (ADS)
Tang, S. L.; Antonia, R. A.; Djenidi, L.; Danaila, L.; Zhou, Y.
2016-09-01
The transport equation for the mean scalar dissipation rate ɛ ¯ θ is derived by applying the limit at small separations to the generalized form of Yaglom's equation in two types of flows, those dominated mainly by a decay of energy in the streamwise direction and those which are forced, through a continuous injection of energy at large scales. In grid turbulence, the imbalance between the production of ɛ ¯ θ due to stretching of the temperature field and the destruction of ɛ ¯ θ by the thermal diffusivity is governed by the streamwise advection of ɛ ¯ θ by the mean velocity. This imbalance is intrinsically different from that in stationary forced periodic box turbulence (or SFPBT), which is virtually negligible. In essence, the different types of imbalance represent different constraints imposed by the large-scale motion on the relation between the so-called mixed velocity-temperature derivative skewness ST and the scalar enstrophy destruction coefficient Gθ in different flows, thus resulting in non-universal approaches of ST towards a constant value as Reλ increases. The data for ST collected in grid turbulence and in SFPBT indicate that the magnitude of ST is bounded, this limit being close to 0.5.
The influence of search strategies and homogeneous isotropic turbulence on planktonic contact rates
NASA Astrophysics Data System (ADS)
Rhodes, C. J.; Reynolds, A. M.
2007-12-01
Many species have been shown to adopt a Lévy-flight pattern of movement which are consistent with the most efficient way to locate sparsely distributed targets. Here, we consider a predator that conducts its search for prey in a turbulent environment. Such a situation is relevant to zooplankton-phytoplankton ecosystems. Kinematic simulation is used to represent the turbulent velocity field in the surface layers of the open ocean and contact with the prey is maximised for a predator swimming a Lévy flight with an exponent μsime1.2. The contact rate exceeds that recorded during straight-line swimming and passive advection. The observation that the contact rate is maximised for μsime1.2 appears to be not strongly dependent on predator swimming speed. The results are discussed in the context of recent work on planktonic search in laboratory conditions where Lévy-flight exponents of μsime2 were noted.
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)
van Hinsberg, M. A. T.; Clercx, H. J. H.; Toschi, F.
2017-02-01
The Stokes drag force and the gravity force are usually sufficient to describe the behavior of sub-Kolmogorov-size (or pointlike) heavy particles in turbulence, in particular when the particle-to-fluid density ratio ρp/ρf≳103 (with ρp and ρf the particle and fluid density, respectively). This is, in general, not the case for smaller particle-to-fluid density ratios, in particular not for ρp/ρf≲102 . In that case the pressure gradient force, added mass effects, and the Basset history force also play important roles. In this study we focus on the understanding of the role of these additional forces, all of hydrodynamic origin, in the settling of particles in turbulence. In order to qualitatively elucidate the complex dynamics of such particles in homogeneous isotropic turbulence, we first focus on the case of settling of such particles in the flow field of a single vortex. After having explored this simplified case we extend our analysis to homogeneous isotropic turbulence. In general, we found that the pressure gradient force leads to a decrease in the settling velocity. This can be qualitatively understood by the fact that this force prevents the particles from sweeping out of vortices, a mechanism known as preferential sweeping which causes enhanced settling. Additionally, we found that the Basset history force can both increase and decrease the enhanced settling, depending on the particle Stokes number. Finally, the role of the nonlinear Stokes drag has been explored, confirming that it affects settling of inertial particles in turbulence, but only in a limited way for the parameter settings used in this investigation.
NASA Astrophysics Data System (ADS)
Hosokawa, Iwao
2007-01-01
A decaying homogeneous isotropic turbulence is treated on the combined bases of the Kolmogorov hypothesis and the cross-independence hypothesis (for a closure of the Monin-Lundgren (ML) hierarchy of many-point velocity distributions) in turbulence. Similarity solutions for one- and two-point velocity distributions are obtained in the viscous, inertial and large-scale ranges of separation distance, from which we can give a reasonable picture of longitudinal and transverse velocity autocorrelation functions for any Reynolds number, even though they are distant from exact solutions of the infinite ML hierarchy. Possibility of non-similarity solutions with other reasonable and more realistic features is unveiled within the same theoretical framework. The cross-independence hypothesis is proved to be inconsistent with the Kolmogorov [1941b. Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16-18.] theory in the inertial range. This is the main factor by which our special strategy (described in Introduction) is taken for solving this problem.
Scaling of Lyapunov Exponents in Homogeneous, Isotropic DNS
NASA Astrophysics Data System (ADS)
Fitzsimmons, Nicholas; Malaya, Nicholas; Moser, Robert
2013-11-01
Lyapunov exponents measure the rate of separation of initially infinitesimally close trajectories in a chaotic system. Using the exponents, we are able to probe the chaotic nature of homogeneous isotropic turbulence and study the instabilities of the chaotic field. The exponents are measured by calculating the instantaneous growth rate of a linear disturbance, evolved with the linearized Navier-Stokes equation, at each time step. In this talk, we examine these exponents in the context of homogeneous isotropic turbulence with two goals: 1) to investigate the scaling of the exponents with respect to the parameters of forced homogeneous isotropic turbulence, and 2) to characterize the instabilities that lead to chaos in turbulence. Specifically, we explore the scaling of the Lyapunov exponents with respect to the Reynolds number and with respect to the ratio of the integral length scale and the computational domain size.
NASA Astrophysics Data System (ADS)
Chareyron, D.; Marié, J. L.; Fournier, C.; Gire, J.; Grosjean, N.; Denis, L.; Lance, M.; Méès, L.
2012-04-01
An in-line digital holography technique is tested, the objective being to measure Lagrangian three-dimensional (3D) trajectories and the size evolution of droplets evaporating in high-Reλ strong turbulence. The experiment is performed in homogeneous, nearly isotropic turbulence (50 × 50 × 50 mm3) created by the meeting of six synthetic jets. The holograms of droplets are recorded with a single high-speed camera at frame rates of 1-3 kHz. While hologram time series are generally processed using a classical approach based on the Fresnel transform, we follow an ‘inverse problem’ approach leading to improved size and 3D position accuracy and both in-field and out-of-field detection. The reconstruction method is validated with 60 μm diameter water droplets released from a piezoelectric injector ‘on-demand’ and which do not appreciably evaporate in the sample volume. Lagrangian statistics on 1000 reconstructed tracks are presented. Although improved, uncertainty on the depth positions remains higher, as expected in in-line digital holography. An additional filter is used to reduce the effect of this uncertainty when calculating the droplet velocities and accelerations along this direction. The diameters measured along the trajectories remain constant within ±1.6%, thus indicating that accuracy on size is high enough for evaporation studies. The method is then tested with R114 freon droplets at an early stage of evaporation. The striking feature is the presence on each hologram of a thermal wake image, aligned with the relative velocity fluctuations ‘seen’ by the droplets (visualization of the Lagrangian fluid motion about the droplet). Its orientation compares rather well with that calculated by using a dynamical equation for describing the droplet motion. A decrease of size due to evaporation is measured for the droplet that remains longest in the turbulence domain.
Lewis, D M
2003-05-07
It is a well-established fact that encounter rates between different species of planktonic microorganism, either swimming, or passively advected by the flow, are enhanced in the presence of turbulence. However, due to the complexity of the various calculations involved, current encounter rate theories are based on a number of simplifying approximations, which do not reflect reality. In particular, a typical planktonic predator is usually assumed to have perfect 'all round vision', i.e. it can perceive a prey particle at any relative orientation, provided it lies within some given contact radius R. Unfortunately, there is a wide body of experimental evidence that this is not the case. In this study the encounter problem for a predator with a limited field of sensory perception, swimming in a turbulent flow, is examined from first principles and a number of new modelling ideas proposed. A wide range of kinematic simulations are also undertaken to test these predictions. Particular attention is paid to the swimming strategy such a predator might undertake to enhance its encounter rate. It turns out that the predicted optimum swimming strategies differ radically from the results of previous work. Empirical evidence is also presented which appears to support these new findings.
Modeling the turbulent kinetic energy equation for compressible, homogeneous turbulence
NASA Technical Reports Server (NTRS)
Aupoix, B.; Blaisdell, G. A.; Reynolds, William C.; Zeman, Otto
1990-01-01
The turbulent kinetic energy transport equation, which is the basis of turbulence models, is investigated for homogeneous, compressible turbulence using direct numerical simulations performed at CTR. It is shown that the partition between dilatational and solenoidal modes is very sensitive to initial conditions for isotropic decaying turbulence but not for sheared flows. The importance of the dilatational dissipation and of the pressure-dilatation term is evidenced from simulations and a transport equation is proposed to evaluate the pressure-dilatation term evolution. This transport equation seems to work well for sheared flows but does not account for initial condition sensitivity in isotropic decay. An improved model is proposed.
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.
Large Eddy Simulation of Homogeneous Rotating Turbulence
NASA Technical Reports Server (NTRS)
Squires, Kyle D.; Mansour, Nagi N.; Cambon, Claude; Chasnov, Jeffrey R.; Kutler, Paul (Technical Monitor)
1994-01-01
Study of turbulent flows in rotating reference frames has proven to be one of the more challenging areas of turbulence research. The large number of theoretical, experimental, and computational studies performed over the years have demonstrated that the effect of solid-body rotation on turbulent flows is subtle and remains exceedingly difficult to predict. Because of the complexities associated with non-homogeneous turbulence, it is worthwhile to examine the effect of steady system rotation on the evolution of an initially isotropic turbulent flow. The assumption of statistical homogeneity considerably simplifies analysis and computation; calculation of homogeneous turbulence is further motivated since it possesses the essential physics found in more complex rotating flows. The principal objectives of the present study have therefore been to increase our fundamental understanding of turbulent flows in rotating reference frames through an examination of the asymptotic state of homogeneous rotating turbulence; particularly as to the existence of an asymptotic state which is self similar. Knowledge of an asymptotic similarity state permits prediction of the ultimate statistical evolution of the flow without requiring detailed knowledge of the complex, and not well understood, non-linear transfer processes. Aside from examination of possible similarity states in rotating turbulence, of further interest in this study has been an examination of the degree to which solid-body rotation induces a two-dimensional state in an initially isotropic flow.
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.
Particle dynamics during the transition from isotropic to anisotropic turbulence
NASA Astrophysics Data System (ADS)
Lee, Chung-Min; Gylfason, Armann; Toschi, Federico
2016-11-01
Turbulent fluctuations play an important role on the dynamics of particles in turbulence, enhancing their dispersion and mixing. In recent years the statistical properties of particles in several statistically stationary turbulent flows have been the subject of many numerical and experimental studies. In many natural and industrial environments, however, one deals with turbulence in a transient state. As a prototype system, we investigate the transition from an isotropic to an anisotropic flow, namely looking at the influence of a developing mean flow on the dynamics of particles. We simulate, via direct numerical simulation, stationary homogeneous and isotropic turbulence and then suddenly impose a mean shear or strain. This allows us to quantify the effects of the mean flow on particle dynamics in these transient periods. Preliminary results on single particle properties, such as velocities and accelerations will be reported.
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.
Kinematical uniqueness of homogeneous isotropic LQC
NASA Astrophysics Data System (ADS)
Engle, Jonathan; Hanusch, Maximilian
2017-01-01
In a paper by Ashtekar and Campiglia, invariance under volume preserving residual diffeomorphisms has been used to single out the standard representation of the reduced holonomy-flux algebra in homogeneous loop quantum cosmology (LQC). In this paper, we use invariance under all residual diffeomorphisms to single out the standard kinematical Hilbert space of homogeneous isotropic LQC for both the standard configuration space {{{R}}\\text{Bohr}} , as well as for the Fleischhack one {R}\\sqcup {{{R}}\\text{Bohr}} . We first determine the scale invariant Radon measures on these spaces, and then show that the Haar measure on {{{R}}\\text{Bohr}} is the only such measure for which the momentum operator is hermitian w.r.t. the corresponding inner product. In particular, the measure is forced to be identically zero on {R} in the Fleischhack case, so that for both approaches, the standard kinematical LQC-Hilbert space is singled out.
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.
Leith diffusion model for homogeneous anisotropic turbulence
NASA Astrophysics Data System (ADS)
Rubinstein, Robert; Clark, Timothy; Kurien, Susan
2016-11-01
A new spectral closure model for homogeneous anisotropic turbulence is proposed. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.
Leith diffusion model for homogeneous anisotropic turbulence
Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan
2017-06-01
Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numericalmore » simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.« less
Leith diffusion model for homogeneous anisotropic turbulence
Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan
2016-07-19
Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.
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
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.
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.
NASA Astrophysics Data System (ADS)
Valente, Pedro C.; da Silva, Carlos B.; Pinho, Fernando T.
2013-11-01
We report a numerical study of statistically steady and decaying turbulence of FENE-P fluids for varying polymer relaxation times ranging from the Kolmogorov dissipation time-scale to the eddy turnover time. The total turbulent kinetic energy dissipation is shown to increase with the polymer relaxation time in both steady and decaying turbulence, implying a ``drag increase.'' If the total power input in the statistically steady case is kept equal in the Newtonian and the viscoelastic simulations the increase in the turbulence-polymer energy transfer naturally lead to the previously reported depletion of the Newtonian, but not the overall, kinetic energy dissipation. The modifications to the nonlinear energy cascade with varying Deborah/Weissenberg numbers are quantified and their origins investigated. The authors acknowledge the financial support from Fundação para a Ciência e a Tecnologia under grant PTDC/EME-MFE/113589/2009.
Scaling and intermittency in compressible isotropic turbulence
NASA Astrophysics Data System (ADS)
Wang, Jianchun; Gotoh, Toshiyuki; Watanabe, Takeshi
2017-05-01
Scaling and intermittency in compressible isotropic turbulence at the turbulent Mach number Mt ranging from 0.5 to 1.0 are studied by using numerical simulations with solenoidal forcing. Linear relations between the structure functions of the compressible velocity component and those of thermodynamic variables are modeled based on the shock jump conditions and are verified by numerical simulations. At a turbulent Mach number around 1.0, the relative scaling exponent of the structure functions saturates with an increase of the order. After proper normalization, the tails of the probability density functions (PDFs) of the increments of the compressible velocity component and thermodynamic variables overlap one another for different separations. Moreover, we study the conditional PDFs of the increments with respect to the shocklet. Linear relations between the tails of unconditional PDFs and conditional PDFs are established. The shocklet plays an important role in the determination of the PDF tails. The compressible velocity increment is decomposed into a negative component and a positive component. The negative component of the compressible velocity increment exhibits a scaling behavior with the saturation of the scaling exponent at high orders, which is similar to the Burgers turbulence, while the positive component of the compressible velocity increment exhibits a power-law scaling behavior, which is similar to the incompressible turbulence.
Small scale dynamics of isotropic viscoelastic turbulence
NASA Astrophysics Data System (ADS)
Nguyen, M. Quan; Delache, Alexandre; Simoëns, Serge; Bos, Wouter J. T.; El Hajem, Mamoud
2016-12-01
The comparison of the results of direct numerical simulations of isotropic turbulence of Newtonian and viscoelastic fluid provides evidence that viscoelasticity modifies qualitatively the behavior of the smallest scales: we observe a power law in the far dissipation range of the fluid kinetic energy spectrum and we show that it is a robust feature, roughly independent of the large scale dynamics. A detailed analysis of the energy transfer shows that at these scales energy is injected into the fluid flow through polymer relaxation. It is further shown that a part of the total energy is transferred among scales through an interaction of the velocity field with the polymer field.
Spectra and statistics in compressible isotropic turbulence
NASA Astrophysics Data System (ADS)
Wang, Jianchun; Gotoh, Toshiyuki; Watanabe, Takeshi
2017-01-01
Spectra and one-point statistics of velocity and thermodynamic variables in isotropic turbulence of compressible fluid are examined by using numerical simulations with solenoidal forcing at the turbulent Mach number Mt from 0.05 to 1.0 and at the Taylor Reynolds number Reλ from 40 to 350. The velocity field is decomposed into a solenoidal component and a compressible component in terms of the Helmholtz decomposition, and the compressible velocity component is further decomposed into a pseudosound component, namely, the hydrodynamic component associated with the incompressible field and an acoustic component associated with sound waves. It is found that the acoustic mode dominates over the pseudosound mode at turbulent Mach numbers Mt≥0.4 in our numerical simulations. At turbulent Mach numbers Mt≤0.4 , there exists a critical wave number kc beyond which the pseudosound mode dominates while the acoustic mode dominates at small wave numbers k
Near isotropic behavior of turbulent thermal convection
NASA Astrophysics Data System (ADS)
Nath, Dinesh; Pandey, Ambrish; Kumar, Abhishek; Verma, Mahendra K.
2016-10-01
We investigate the anisotropy in turbulent convection in a three-dimensional (3D) box using direct numerical simulation. We compute the anisotropic parameter A =u⊥2/(2 u∥2) , where u⊥ and u∥ are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number Pr ≈1 , but the anisotropy increases with the Prandtl number. For Pr =∞ ,A ≈0.3 , anisotropy is not very significant even in extreme cases. We also observe that u∥ feeds energy to u⊥ via pressure. The computation of shell-to-shell energy transfers reveals that the energy transfer in turbulent convection is local and forward, similar to hydrodynamic turbulence. These results are consistent with the Kolmogorov's spectrum observed by Kumar et al. [Phys. Rev. E 90, 023016 (2014), 10.1103/PhysRevE.90.023016] for turbulent convection.
On the Lighthill relationship and sound generation from isotropic turbulence
NASA Technical Reports Server (NTRS)
Zhou, YE; Praskovsky, Alexander; Oncley, Steven
1994-01-01
In 1952, Lighthill developed a theory for determining the sound generated by a turbulent motion of a fluid. With some statistical assumptions, Proudman applied this theory to estimate the acoustic power of isotropic turbulence. Recently, Lighthill established a simple relationship that relates the fourth-order retarded time and space covariance of his stress tensor to the corresponding second-order covariance and the turbulent flatness factor, without making statistical assumptions for a homogeneous turbulence. Lilley revisited Proudman's work and applied the Lighthill relationship to evaluate directly the radiated acoustic power from isotropic turbulence. After choosing the time separation dependence in the two-point velocity time and space covariance based on the insights gained from direct numerical simulations, Lilley concluded that the Proudman constant is determined by the turbulent flatness factor and the second-order spatial velocity covariance. In order to estimate the Proudman constant at high Reynolds numbers, we analyzed a unique data set of measurements in a large wind tunnel and atmospheric surface layer that covers a range of the Taylor microscale based on Reynolds numbers 2.0 x 10(exp 3) less than or equal to R(sub lambda) less than or equal to 12.7 x 10(exp 3). Our measurements demonstrate that the Lighthill relationship is a good approximation, providing additional support to Lilley's approach. The flatness factor is found between 2.7 - 3.3 and the second order spatial velocity covariance is obtained. Based on these experimental data, the Proudman constant is estimated to be 0.68 - 3.68.
Direct simulation of particle dispersion in a decaying isotropic turbulence
NASA Technical Reports Server (NTRS)
Elghobashi, S.; Truesdell, G. C.
1992-01-01
Results of a numerical investigation of the dispersion of solid particles in decaying isotropic turbulence are presented. The 3D time-dependent velocity field of a homogeneous nonstationary turbulence is computed using the method of direct numerical simulation (DNS). The dispersion characteristics of three different solid particles (corn, copper, and glass) injected in the flow are obtained by integrating the complete equation of particle motion along the instantaneous trajectories of 22-cubed particles for each particle type, and then by performing ensemble averaging. Good agreement was achieved between the present DNS results and the measured time development of the mean-square displacement of the particles. Questions of how and why the dispersion statistics of a solid particle differ from those of its corresponding fluid point and surrounding fluid and what influences inertia and gravity have on these statistics are also discussed.
Shocklet statistics in compressible isotropic turbulence
NASA Astrophysics Data System (ADS)
Wang, Jianchun; Gotoh, Toshiyuki; Watanabe, Takeshi
2017-02-01
Shocklet statistics in compressible isotropic turbulence are studied by using numerical simulations with solenoidal forcing, at the turbulent Mach number Mt ranging from 0.5 up to 1.0 and at the Taylor Reynolds number Reλ ranging from 110 to 250. A power-law region of the probability density function (PDF) of the shocklet strength Mn-1 (Mn is the normal shock Mach number) is observed. The magnitude of the power-law exponent is found to decrease with the increase of Mt. We show that the most probable shocklet strength is proportional to Mt3, and the shocklet thickness corresponding to the most probable shock Mach number is proportional to Mt-2 in our numerical simulations. The PDFs of the jumps of the velocity and thermodynamic variables across a shocklet exhibit a similar power-law scaling. The statistics of the jumps of the velocity and thermodynamic variables are further investigated by conditioned average. Nonlinear models for the conditional average of the jumps of the velocity and thermodynamic variables are developed and verified.
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.
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.
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.
Line segments in homogeneous scalar turbulence
NASA Astrophysics Data System (ADS)
Gauding, Michael; Goebbert, Jens Henrik; Hasse, Christian; Peters, Norbert
2015-09-01
The local structure of a turbulent scalar field in homogeneous isotropic turbulence is analyzed by direct numerical simulations (DNS) with different Taylor micro-scale based Reynolds numbers between 119 and 529. A novel signal decomposition approach is introduced where the signal of the scalar along a straight line is partitioned into segments based on the local extremal points of the scalar field. These segments are then parameterized by the distance ℓ between adjacent extremal points and the scalar difference Δϕ at the extrema. Both variables are statistical quantities and a joint distribution function of these quantities contains most information to statistically describe the scalar field. It is highlighted that the marginal distribution function of the length becomes independent of Reynolds number when normalized by the mean length ℓm. From a statistical approach, it is further shown that the mean length scales with the Kolmogorov length, which is also confirmed by DNS. For turbulent mixing, the scalar gradient plays a paramount role. Turbulent scalar fields are characterized by cliff-ramp-like structures manifesting the occurrence of localized large scalar gradients. To study turbulent mixing, a segment-based gradient is defined as Δϕ/ℓ. Joint statistics of the length and the segment-based gradient provide novel understanding of cliff-ramp-like structures. Ramp-like structures are unveiled by the asymmetry of the joint distribution function of the segment-based gradient and the length. Cliff-like structures are further analyzed by conditional statistics and it is shown from DNS that the width of cliffs scales with the Kolmogorov length scale.
The structure of the vorticity field in homogeneous turbulent flows
NASA Technical Reports Server (NTRS)
Rogers, Michael M.; Moin, Parviz
1987-01-01
The structures of the vorticity fields in several homogeneous irrotational straining flows and a homogeneous turbulent shear flow were examined using a database generated by direct numerical simulation of the unsteady Navier-Stokes equations. In all cases, strong evidence was found for the presence of coherent vortical structures. The initially isotropic vorticity fields were rapidly affected by imposed mean strain and the rotational component of mean shear and developed accordingly. In the homogeneous turbulent shear-flow cases, the roll-up of mean vorticity into characteristic hairpin vortices was clearly observed, supporting the view that hairpin vortices are an important vortical structure in all turbulent shear flows; the absence of mean shear in the homogeneous irrotational straining flows precludes the presence of hairpin-like vortices.
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.
The curvature of material surfaces in isotropic turbulence
NASA Astrophysics Data System (ADS)
Pope, S. B.; Yeung, P. K.; Girimaji, S. S.
1989-12-01
Direct numerical simulation is used to study the curvature of material surfaces in isotropic turbulence. The Navier-Stokes equation is solved by a 643 pseudospectral code for constant-density homogeneous isotropic turbulence, which is made statistically stationary by low-wavenumber forcing. The Taylor-scale Reynolds number is 39. An ensemble of 8192 infinitesimal material surface elements is tracked through the turbulence. For each element, a set of exact ordinary differential equations is integrated in time to determine, primarily, the two principal curvatures k1 and k2. Statistics are then deduced of the mean-square curvature M= (1)/(2) (k21+k22), and of the mean radius of curvature R=(k21+k22)-1/2. Curvature statistics attain an essentially stationary state after about 15 Kolmogorov time scales. Then the area-weighted expectation of R is found to be 12η, where η is the Kolmogorov length scale. For moderate and small radii (less than 10η) the probability density function (pdf) of R is approximately uniform, there being about 5% probability of R being less than η. The uniformity of the pdf of R, for small R, implies that the expectation of M is infinite. It is found that the surface elements with large curvatures are nearly cylindrical in shape (i.e., ‖k1‖≫‖k2‖ or ‖k2‖≫‖k1‖), consistent with the folding of the surface along nearly straight lines. Nevertheless the variance of the Gauss curvature K=k1k2 is infinite.
The radiated noise from isotropic turbulence revisited
NASA Technical Reports Server (NTRS)
Lilley, Geoffrey M.
1993-01-01
The noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers, as derived by Proudman (1952), was the first application of Lighthill's Theory of Aerodynamic Noise to a complete flow field. The theory presented by Proudman involves the assumption of the neglect of retarded time differences and so replaces the second-order retarded-time and space covariance of Lighthill's stress tensor, Tij, and in particular its second time derivative, by the equivalent simultaneous covariance. This assumption is a valid approximation in the derivation of the second partial derivative of Tij/derivative of t exp 2 covariance at low Mach numbers, but is not justified when that covariance is reduced to the sum of products of the time derivatives of equivalent second-order velocity covariances as required when Gaussian statistics are assumed. The present paper removes these assumptions and finds that although the changes in the analysis are substantial, the change in the numerical result for the total acoustic power is small. The present paper also considers an alternative analysis which does not neglect retarded times. It makes use of the Lighthill relationship, whereby the fourth-order Tij retarded-time covariance is evaluated from the square of similar second order covariance, which is assumed known. In this derivation, no statistical assumptions are involved. This result, using distributions for the second-order space-time velocity squared covariance based on the Direct Numerical Simulation (DNS) results of both Sarkar and Hussaini(1993) and Dubois(1993), is compared with the re-evaluation of Proudman's original model. These results are then compared with the sound power derived from a phenomenological model based on simple approximations to the retarded-time/space covariance of Txx. Finally, the recent numerical solutions of Sarkar and Hussaini(1993) for the acoustic power are compared with the results obtained from the analytic solutions.
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.
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.
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.
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.
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.
Preferential Rotation of Chiral Dipoles in Isotropic Turbulence.
Kramel, Stefan; Voth, Greg A; Tympel, Saskia; Toschi, Federico
2016-10-07
We introduce a new particle shape which shows preferential rotation in three dimensional homogeneous isotropic turbulence. We call these particles chiral dipoles because they consist of a rod with two helices of opposite handedness, one at each end. 3D printing is used to fabricate these particles with a length in the inertial range and their rotations are tracked in a turbulent flow between oscillating grids. High aspect ratio chiral dipoles preferentially align with their long axis along the extensional eigenvectors of the strain rate tensor, and the helical ends respond to the extensional strain rate with a mean spinning rate that is nonzero. We use Stokesian dynamics simulations of chiral dipoles in pure strain flow to quantify the dependence of spinning on particle shape. Based on the known response to pure strain, we build a model that gives the spinning rate of small chiral dipoles using velocity gradients along Lagrangian trajectories from high resolution direct numerical simulations. The statistics of chiral dipole spinning determined with this model show surprisingly good agreement with the measured spinning of much larger chiral dipoles in the experiments.
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.
Compressibility Effects on the Growth and Structure of Homogeneous Turbulent Shear Flow
NASA Technical Reports Server (NTRS)
Blaisdell, G. A.; Mansour, N. N.; Reynolds, W. C.
1993-01-01
Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure-dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.
On the effects of isotropic turbulence on the evaporation rate of a liquid droplet
NASA Astrophysics Data System (ADS)
Dodd, Michael; Ferrante, Antonino
2016-11-01
Our objective is to explain the effects of isotropic turbulence on the vaporization rate of a liquid droplet in conditions that are relevant to spray combustion applications. To this end, we have performed direct numerical simulation (DNS) of a single droplet in homogeneous isotropic turbulence using the volume-of-fluid method for resolving fully the process of momentum, heat, and mass transfer between the liquid droplet and the gas. The simulations were performed using 10243 grid points. The effect of turbulence on the droplet vaporization rate is investigated by varying the gas-phase Reynolds number based on the Taylor microscale, Reλ. Reλ is increased from 0 to 75 by increasing the r.m.s. velocity of the gas phase while keeping all other physical properties constant. We will present the droplet evaporation rate as a function of turbulence Reynolds number and investigate the physical mechanisms.
Electromagnetic cloaking of conducting cylinders using homogeneous and isotropic media
NASA Astrophysics Data System (ADS)
Gana, Usman M.
2017-08-01
Scattering characteristics of cloaked conducting cylinders is investigated. An attempt is made in replacing the difficult anisotropic material properties required of a cloack with simple ones. The anisotropic material parameters of the cylindrical cloaking shell was approximated by homogeneous, isotropic layers and effective medium approximation was employed in determining the parameters of the layers. Scattering of both polarized (TM & TE) and un-polarized plane electromagnetic waves was studied in the far field. Scattering cross sections of different kinds of cylindrical cloaks are presented and the merits of their structures outlined. Significant reductions in scattering cross sections, compared with bare cylinders, were realized by some of the structures studied.
Influence of initial mean helicity on homogeneous turbulent shear flow.
Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie
2011-11-01
Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A wavelet-based scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity.
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.
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.
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.
Cosmic-ray pitch-angle scattering in isotropic turbulence
NASA Technical Reports Server (NTRS)
Bieber, John W.; Smith, Charles W.; Matthaeus, William H.
1988-01-01
A dissipation range is incorporated in the turbulence model to reconcile the divergent conclusions from studies of cosmic-ray pitch-angle scattering in isotropic magnetic turbulence. The Fokker-Planck coefficient for pitch-angle scattering is calculated. It is shown that the slab form of the Fokker-Plank coefficient (Jokipii, 1966) is valid at very low energies, while the nonslab form (Fisk, 1974) is valid at intermediate energies.
Assessing the Structure of Isotropic and Anisotropic Turbulent Magnetic Fields
NASA Astrophysics Data System (ADS)
Fatuzzo, Marco; Holden, Lisa; Grayson, Lindsay; Wallace, Kirk
2016-10-01
Turbulent magnetic fields permeate our universe, impacting a wide range of astronomical phenomena across all cosmic scales. A clear example is the magnetic field that threads the interstellar medium (ISM), which impacts the motion of cosmic rays through that medium. Understanding the structure of magnetic turbulence within the ISM and how it relates to the physical quantities that characterize it can thus inform our analysis of particle transport within these regions. Toward that end, we probe the structure of magentic turbulence through the use of Lyapunov exponents for a suite of isotropic and nonisotropic Alfvénic turbulence profiles. Our results provide a means of calculating a “turbulence lengthscale” that can then be connected to how cosmic rays propagate through magentically turbulent environments, and we perform such an analysis for molecular cloud environments.
The decay of isotropic turbulence in a rapidly rotating frame
NASA Technical Reports Server (NTRS)
Speziale, C. G.; Mansour, N. N.; Rogallo, R. S.
1987-01-01
A direct numerical simulation of the decay of initially isotropic turbulence in a rapidly rotating frame was conducted. This 128 x 128 x 128 simulation was completed for a Reynolds number Re sub lambda = 15.3 and a Rossby number Ro sub lambda = 0.07 based on the initial turbulent kinetic energy and Taylor microscale. The numerical results indicate that the turbulence remains essentially isotropic during the major part of the decay (i.e., beyond the point where the turbulent kinetic energy has decayed to less than 10 percent of its initial value). The rapid rotation has the primary effect of shutting off the energy transfer so that the turbulence dissipation (and hence the rate of decay of the turbulent kinetic energy) is substantially reduced. Consequently, the anisotropy tensor remains essentially unchanged while the energy spectrum undergoes a nearly linear viscous decay (the same results that are predicted by Rapid Distortion Theory which is only formally valid for much shorter elapsed times. Surprisingly, no Taylor-Proudman reorganization of the flow to a two-dimensional state is observed. The implications that these results have on turbulence modeling are discussed briefly along with prospective future research.
Acoustoelastic Lamb Wave Propagation in a Homogeneous, Isotropic Aluminum Plate
NASA Astrophysics Data System (ADS)
Gandhi, Navneet; Michaels, Jennifer E.; Lee, Sang Jun
2011-06-01
The effect of stress on Lamb wave propagation is relevant to both nondestructive evaluation and structural health monitoring because of changes in received signals due to both the associated strain and the acoustoelastic effect. A homogeneous plate that is initially isotropic becomes anisotropic under uniaxial stress, and dispersion of propagating waves becomes directionally dependent. The problem is similar to Lamb wave propagation in an anisotropic plate, except the fourth order tensor in the resulting wave equation does not have the same symmetry as that for the unstressed anisotropic plate, and the constitutive equation relating incremental stress to incremental strain is more complicated. Here we consider the theory of acoustoelastic Lamb wave propagation and show how dispersion curves shift anisotropically for an aluminum plate under uniaxial tension. Theoretical predictions of changes in phase velocity as a function of propagation direction are compared to experimental results for a single wave mode.
Acoustoelastic lamb wave propagation in a homogeneous, isotropic aluminum plate
Gandhi, Navneet; Michaels, Jennifer E.; Lee, Sang Jun
2011-06-23
The effect of stress on Lamb wave propagation is relevant to both nondestructive evaluation and structural health monitoring because of changes in received signals due to both the associated strain and the acoustoelastic effect. A homogeneous plate that is initially isotropic becomes anisotropic under uniaxial stress, and dispersion of propagating waves becomes directionally dependent. The problem is similar to Lamb wave propagation in an anisotropic plate, except the fourth order tensor in the resulting wave equation does not have the same symmetry as that for the unstressed anisotropic plate, and the constitutive equation relating incremental stress to incremental strain is more complicated. Here we consider the theory of acoustoelastic Lamb wave propagation and show how dispersion curves shift anisotropically for an aluminum plate under uniaxial tension. Theoretical predictions of changes in phase velocity as a function of propagation direction are compared to experimental results for a single wave mode.
Uniqueness of the Representation in Homogeneous Isotropic LQC
NASA Astrophysics Data System (ADS)
Engle, Jonathan; Hanusch, Maximilian; Thiemann, Thomas
2017-08-01
We show that the standard representation of homogeneous isotropic loop quantum cosmology (LQC) is the GNS-representation that corresponds to the unique state on the reduced quantum holonomy-flux *-algebra that is invariant under residual diffeomorphisms— both when the standard algebra is used as well as when one uses the extended algebra proposed by Fleischhack. More precisely, we find that in both situations the GNS-Hilbert spaces coincide, and that in the Fleischhack case the additional algebra elements are just mapped to zero operators. In order for the residual diffeomorphisms to have a well-defined action on the quantum algebra, we have let them act on the fiducial cell as well as on the dynamical variables, thereby recovering covariance. Consistency with Ashtekar and Campilgia in the Bianchi case is also shown.
Dynamic Green's function for homogeneous and isotropic porous media
NASA Astrophysics Data System (ADS)
Sahay, Pratap N.
2001-12-01
The source terms that are meaningful in dynamic poroelasticity are those exciting the centre-of-mass field and the internal field. These fields are the sum of the mass weighted motion and the difference motion of the solid and fluid constituents, respectively. The corresponding homogeneous and isotropic Green's function valid for a uniform whole-space is obtained using Kupradze's method after the vector differential equations for these two fields are combined and expressed as a 6×6 matrix differential operator. The solution is quite amenable to numerical calculations and the results for a saturated Berea sandstone show that the fast P and S waves correspond to those usually detected by geophones at large distances from the source. The slow P wave, which is associated with fluid flow, is rapidly attenuated with distance from the source while the slow S wave, which is part of the solution, dies off rapidly in the near-neighbourhood of the source.
A spatially homogeneous and isotropic Einstein-Dirac cosmology
NASA Astrophysics Data System (ADS)
Finster, Felix; Hainzl, Christian
2011-04-01
We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.
Reynolds number scaling of velocity increments in isotropic turbulence
NASA Astrophysics Data System (ADS)
Iyer, Kartik P.; Sreenivasan, Katepalli R.; Yeung, P. K.
2017-02-01
Using the largest database of isotropic turbulence available to date, generated by the direct numerical simulation (DNS) of the Navier-Stokes equations on an 81923 periodic box, we show that the longitudinal and transverse velocity increments scale identically in the inertial range. By examining the DNS data at several Reynolds numbers, we infer that the contradictory results of the past on the inertial-range universality are artifacts of low Reynolds number and residual anisotropy. We further show that both longitudinal and transverse velocity increments scale on locally averaged dissipation rate, just as postulated by Kolmogorov's refined similarity hypothesis, and that, in isotropic turbulence, a single independent scaling adequately describes fluid turbulence in the inertial range.
Investigation of subgrid models in homogeneous incompressible turbulence
NASA Astrophysics Data System (ADS)
Teissedre, C.
1987-08-01
A data base of simulated homogeneous, incompressible turbulence in an anisotropic regime was derived using a direct simulation code on a parallel processing computer. The simulated distributions were used to validate subgrid models of the turbulent viscosity and similitude type (analogy between the near field of the cut-off and the subgrid field). The first type of model accounts for the evolution of turbulent kinetic energy well, while the second type, although it better represents the exact value of stress in the subgrid, seems to present a defect of nondissipation. Tests of a model of perturbation of nonlinear terms were performed in an isotropic situation with large structures. The results show the same kind of nondissipative behavior as for the similitude model.
A new framework for simulating forced homogeneous buoyant turbulent flows
NASA Astrophysics Data System (ADS)
Carroll, Phares L.; Blanquart, Guillaume
2015-06-01
This work proposes a new simulation methodology to study variable density turbulent buoyant flows. The mathematical framework, referred to as homogeneous buoyant turbulence, relies on a triply periodic domain and incorporates numerical forcing methods commonly used in simulation studies of homogeneous, isotropic flows. In order to separate the effects due to buoyancy from those due to large-scale gradients, the linear scalar forcing technique is used to maintain the scalar variance at a constant value. Two sources of kinetic energy production are considered in the momentum equation, namely shear via an isotropic forcing term and buoyancy via the gravity term. The simulation framework is designed such that the four dimensionless parameters of importance in buoyant mixing, namely the Reynolds, Richardson, Atwood, and Schmidt numbers, can be independently varied and controlled. The framework is used to interrogate fully non-buoyant, fully buoyant, and partially buoyant turbulent flows. The results show that the statistics of the scalar fields (mixture fraction and density) are not influenced by the energy production mechanism (shear vs. buoyancy). On the other hand, the velocity field exhibits anisotropy, namely a larger variance in the direction of gravity which is associated with a statistical dependence of the velocity component on the local fluid density.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Abdelsamie, Abouelmagd H.; Lee, Changhoon
2013-03-01
The current paper examines the heavy particle statistics modification by two-way interaction in particle-laden isotropic turbulence in an attempt to interpret their statistics modification using the information of modulated turbulence. Moreover, we clarify the distinctions of this modification between decaying and stationary turbulence as an extension of our previous work [A. H. Abdelsamie and C. Lee, "Decaying versus stationary turbulence in particle-laden isotropic turbulence: Turbulence modulation mechanism," Phys. Fluids 24, 015106 (2012), 10.1063/1.3678332]. Direct Numerical Simulation (DNS) was carried out using 1283 grid points at a Taylor micro-scale Reynolds number of Rλ ˜ 70. The effect of O(10^6) solid particles with a different Stokes number (St) was implemented as a point-force approximation in the Navier-Stokes equation. Various statistics associated with particle dispersion are investigated, and the auto-correlations models which was provided by Jung et al. ["Behavior of heavy particles in isotropic turbulence," Phys. Rev. E 77, 016307 (2008), 10.1103/PhysRevE.77.016307] are extended in the current paper. DNS results reveal that the two-way coupling interaction enhances the fluid and heavy particle auto-correlation functions and the alignment between their velocity vectors for all Stokes numbers in decaying and stationary turbulence, but for different reasons. The modification mechanisms of particle dispersion statistics in stationary turbulence are different from those in decaying turbulence depending on the Stokes number, particularly for St <1.
Coherent Eigenmodes in Homogeneous MHD Turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2010-01-01
The statistical mechanics of Fourier models of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence is discussed, along with their relevance for dissipative magnetofluids. Although statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation, i.e., we have coherent structure. We use eigenanalysis of the modal covariance matrices in the probability density function to 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 provide examples from 2-D and 3-D magnetohydrodynamic simulations of homogeneous turbulence, and show new results from long-time simulations of MHD turbulence with and without a mean magnetic field
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.
A new approach to Lagrangian investigations of isotropic turbulence
NASA Astrophysics Data System (ADS)
Barjona, Manuel; B. da Silva, Carlos; Idmec Team
2016-11-01
A new numerical approach is used in conjunction with direct numerical simulations (DNS) of statistically stationary (forced) isotropic turbulence to investigate the high Reynolds number scaling properties of turbulence characteristics in a Lagrangian frame. The new method provides an alternative route to the determination of the classical Lagrangian turbulence quantities, such as the second order Lagrangian velocity structure function and two point particle separation, at a much higher Reynolds number than as obtained in previous numerical simulations, and displays excellent agreement with the classical theoretical predictions and existing numerical simulations and experimental data. The authors acknowledge the Laboratory for Advanced Computing at University of Coimbra for providing HPC, computing, consulting resources that have contributed to the research results reported within this paper. URL http://www.lca.uc.pt.
Equilibrium states of homogeneous sheared compressible turbulence
NASA Astrophysics Data System (ADS)
Riahi, M.; Lili, T.
2011-06-01
Equilibrium states of homogeneous compressible turbulence subjected to rapid shear is studied using rapid distortion theory (RDT). The purpose of this study is to determine the numerical solutions of unsteady linearized equations governing double correlations spectra evolution. In this work, RDT code developed by authors solves these equations for compressible homogeneous shear flows. Numerical integration of these equations is carried out using a second-order simple and accurate scheme. The two Mach numbers relevant to homogeneous shear flow are the turbulent Mach number Mt, given by the root mean square turbulent velocity fluctuations divided by the speed of sound, and the gradient Mach number Mg which is the mean shear rate times the transverse integral scale of the turbulence divided by the speed of sound. Validation of this code is performed by comparing RDT results with direct numerical simulation (DNS) of [A. Simone, G.N. Coleman, and C. Cambon, Fluid Mech. 330, 307 (1997)] and [S. Sarkar, J. Fluid Mech. 282, 163 (1995)] for various values of initial gradient Mach number Mg0. It was found that RDT is valid for small values of the non-dimensional times St (St < 3.5). It is important to note that RDT is also valid for large values of St (St > 10) in particular for large values of Mg0. This essential feature justifies the resort to RDT in order to determine equilibrium states in the compressible regime.
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.
Spark ignition of aviation fuel in isotropic turbulence
NASA Astrophysics Data System (ADS)
Krisman, Alex; Lu, Tianfeng; Borghesi, Giulio; Chen, Jacqueline
2016-11-01
Turbulent spark ignition occurs in combustion engines where the spark must establish a viable flame kernel that leads to stable combustion. A competition exists between kernel growth, due to flame propagation, and kernel attenuation, due to flame stretch and turbulence. This competition can be measured by the Karlovitz number, Ka, and kernel viability decreases rapidly for Ka >> 1 . In this study, the evolution of an initially spherical flame kernel in a turbulent field is investigated at two cases: Ka- (Ka = 25) and Ka+ (Ka = 125) using direct numerical simulation (DNS). A detailed chemical mechanism for jet fuel (Jet-A) is used, which is relevant for many practical conditions, and the mechanism includes a pyrolysis sub-model which is important for the ignition of large hydrocarbon fuels. An auxiliary non-reacting DNS generates the initial field of isotropic turbulence with a turbulent Reynolds number of 500 (Ka-) and 1,500 (Ka+). The kernel is then imposed at the center of the domain and the reacting DNS is performed. The Ka- case survives and the Ka+ case is extinguished. An analysis of the turbulence chemistry interactions is performed and the process of extinction is described. Department of Energy - Office of Basic Energy Science under Award No. DE-SC0001198.
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.
NASA Astrophysics Data System (ADS)
Gopalan, Balaji; Katz, Joseph
2008-11-01
This study investigates experimentally, the effects of adding dispersants on the breakup of crude oil droplets in turbulent flows during oceanic spills. The current measurements are performed in a nearly homogeneous and isotropic turbulence facility, the central portion of which is characterized using 2-D PIV. Sample crude oil from Alaska National Slope is mixed with dispersant COREXIT 9527 and injected into the central portion of the turbulent facility. High speed, in-line digital holographic cinematography is utilized to visualize the breakup of droplets at high spatial and temporal resolution. We observe that, in some cases, after the droplet breaks up, the elongated portion of the droplet does not recoil, leaving an elongated tail, probably due to the low local surface tension. At high dispersant to oil ratios, extremely thin tails extend from the droplet, and are stretched by the flow. Breakup of these thin threads produces very small oil droplets, a desired effect during cleanup of oil spill.
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.
Effect of rotation on isotropic turbulence - Computation and modelling
NASA Technical Reports Server (NTRS)
Bardina, J.; Ferziger, J. H.; Rogallo, R. S.
1985-01-01
This paper uses numerical simulation to analyse the effects of uniform rotation on homogeneous turbulence. Both large-eddy and full simulations were made. The results indicate that the predominant effect of rotation is to decrease the rate of dissipation of the turbulence and increase the lengthscales, especially those along the axis of rotation. These effects are a consequence of the reduction, due to the generation of inertial waves, of the net energy transfer from large eddies to small ones. Experiments are also influenced by a more complicated interaction between the rotation and the wakes of the turbulence-generating grid which modifies the nominal initial conditions in the experiment. The latter effect is accounted for in simulations by modifying the initial conditions. Finally, a two-equation model is proposed that accounts for the effects of rotation and is able to reproduce the experimental decay of the turbulent kinetic energy.
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.
PDF Modeling of Evaporating Droplets in Isotropic Turbulence.
NASA Astrophysics Data System (ADS)
Mashayek, F.; Pandya, R. V. R.
2000-11-01
We use a statistical closure scheme of Van Kampen [1] to obtain an approximate equation for probability density function p(τ_d, t) to predict the time (t) evolution of statistical properties related to particle time constant τd of collisionless evaporating droplets suspended in isothermal isotropic turbulent flows. The resulting Fokker-Planck equation for p(τ_d, t) has non-linear, time-dependent drift and diffusion coefficients that depend on the statistical properties of droplet's slip velocity. Approximate analytical expressions for these properties are derived and the equation is solved numerically after implementing a numerical method based on path-integral formalism. Time evolution of various droplet diameter related statistical properties are then calculated and are compared with the data available from the stochastic and direct numerical simulations (DNS) studies performed by Mashayek[2]. A good agreement for temporal evolution of mean and standard deviation of particle diameter is observed with DNS results. Reference [1] Van Kampen, N.G., Stochastic Processes in Physics and Chemistry, Elsevier Science Publishers, North Holland, Amsterdam, 1992. [2] Mashayek, F., Stochastic Simulations of Particle-Laden Isotropic Turbulent Flow, Int. J. Multiphase Flow, 25(8):1575-1599 (1999).
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.
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.
Fluctuations of thermodynamic variables in compressible isotropic turbulence
NASA Astrophysics Data System (ADS)
Donzis, Diego; Jagannathan, Shriram
2014-11-01
A distinguishing feature of compressible turbulence is the appearance of fluctuations of thermodynamic variables. While their importance is well-known in understanding these flows, some of their basic characteristics such as the Reynolds and Mach number dependence are not well understood. We use a large database of Direct Numerical Simulation of stationary compressible isotropic turbulence on up to 20483 grids at Taylor Reynolds numbers up to 450 and a range of Mach numbers (Mt ~ 0 . 1 - 0 . 6) to examine statistical properties of thermodynamic variables. Our focus is on the PDFs and moments of pressure, density and temperature. While results at low Mt are consistent with incompressible results, qualitative changes are observed at higher Mt with a transition around Mt ~ 0 . 3 . For example, the PDF of pressure changes from negatively to positively skewed as Mt increases. Similar changes are observed for temperature and density. We suggest that large fluctuations of thermodynamic variables will be log-normal at high Mt. We also find that, relative to incompressible turbulence, the correlation between enstrophy and low-pressure regions is weakened at high Mt which can be explained by the dominance of the so-called dilatational pressure.
Hierarchy compensation of non-homogeneous intermittent atmospheric turbulence
NASA Astrophysics Data System (ADS)
Redondo, Jose M.; Mahjoub, Otman B.; Cantalapiedra, Inma R.
2010-05-01
In this work a study both the internal turbulence energy cascade intermittency evaluated from wind speed series in the atmospheric boundary layer, as well as the role of external or forcing intermittency based on the flatness (Vindel et al 2008)is carried out. The degree of intermittency in the stratified ABL flow (Cuxart et al. 2000) can be studied as the deviation, from the linear form, of the absolute scaling exponents of the structure functions as well as generalizing for non-isotropic and non-homogeneous turbulence, even in non-inertial ranges (in the Kolmogorov-Kraichnan sense) where the scaling exponents are not constant. The degree of intermittency, evaluated in the non-local quasi-inertial range, is explained from the variation with scale of the energy transfer as well as the dissipation. The scale to scale transfer and the structure function scaling exponents are calculated and from these the intermittency parametres. The turbulent diffusivity could also be estimated and compared with Richardson's law. Some two point correlations and time lag calculations are used to investigate the time and spatial integral length scales obtained from both Lagrangian and Eulerian correlations and functions, and we compare these results with both theoretical and laboratory data. We develop a theoretical description of how to measure the different levels of intermittency following (Mahjoub et al. 1998, 2000) and the role of locality in higher order exponents of structure function analysis. Vindel J.M., Yague C. and Redondo J.M. (2008) Structure function analysis and intermittency in the ABL. Nonlin. Processes Geophys., 15, 915-929. Cuxart J, Yague C, Morales G, Terradellas E, Orbe J, Calvo J, Fernández A, Soler M R, Infante C, Buenestado P, Espinalt A, Joergensen H E, Rees J M, Vilá J, Redondo J M, Cantalapiedra R and Conangla L (2000): Stable atmospheric boundary-layer experiment in Spain (Sables 98): a report, Boundary-Layer Meteorology 96, 337-370 Mahjoub O
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.
The modified cumulant expansion for two-dimensional isotropic turbulence
NASA Astrophysics Data System (ADS)
Tatsumi, T.; Yanase, S.
1981-09-01
The two-dimensional isotropic turbulence in an incompressible fluid is investigated using the modified zero fourth-order cumulant approximation. The dynamical equation for the energy spectrum obtained under this approximation is solved numerically and the similarity laws governing the solution in the energy-containing and enstrophy-dissipation ranges are derived analytically. At large Reynolds numbers the numerical solutions yield the k to the -3rd power inertial subrange spectrum which was predicted by Kraichnan (1967), Leith (1968) and Batchelor (1969), assuming a finite enstrophy dissipation in the inviscid limit. The energy-containing range is found to satisfy an inviscid similarity while the enstrophy-dissipation range is governed by the quasi-equilibrium similarity with respect to the enstrophy dissipation as proposed by Batchelor (1969). There exists a critical time which separates the initial period and the similarity period in which the enstrophy dissipation vanishes and remains non-zero respectively in the inviscid limit.
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.
Random shearing direction models for isotropic turbulent diffusion
NASA Astrophysics Data System (ADS)
Majda, Andrew J.
1994-06-01
Recently, a rigorous renormalization theory for various scalar statistics has been developed for special modes of random advection diffusion involving random shear layer velocity fields with long-range spatiotemporal correlations. New random shearing direction models for isotropic turbulent diffusion are introduced here. In these models the velocity field has the spatial second-order statistics of an arbitrary prescribed stationary incompressible isotropic random field including long-range spatial correlations with infrared divergence, but the temporal correlations have finite range. The explicit theory of renormalization for the mean and second-order statistics is developed here. With ɛ the spectral parameter, for -∞<ɛ<4 and measuring the strength of the infrared divergence of the spatial spectrum, the scalar mean statistics rigorously exhibit a phase transition from mean-field behavior for ɛ<2 to anomalous behavior for ɛ with 2<ɛ<4 as conjectured earlier by Avellaneda and the author. The universal inertial range renormalization for the second-order scalar statistics exhibits a phase transition from a covariance with a Gaussian functional form for ɛ with ɛ<2 to an explicit family with a non-Gaussian covariance for ɛ with 2<ɛ<4. These non-Gaussian distributions have tails that are broader than Gaussian as ɛ varies with 2<ɛ<4 and behave for large values like exp(- C c | x|4-ɛ), with C c an explicit constant. Also, here the attractive general principle is formulated and proved that every steady, stationary, zero-mean, isotropic, incompressible Gaussian random velocity field is well approximated by a suitable superposition of random shear layers.
Nematic - isotropic phase transition in turbulent thermal convection
NASA Astrophysics Data System (ADS)
Ahlers, Guenter; Weiss, Stephan
2013-11-01
The nematic-isotropic transition of a liquid crystal (LC) at a temperature TNI is an example of a soft phase transition, where fluid properties, although discontinuous, change only very little and where the latent heat is small. Understanding thermal convection in the presence of such a phase change is relevant to convection in Earth's mantle where discontinuous changes of the crystalline structure occur. We report on turbulent Rayleigh-Bénard convection of a nematic LC while it undergoes a transition from the nematic to the isotropic phase in a cylindrical convection cell with aspect ratio Γ (height over diameter) of 0.50. The difference between the top- and the bottom-plate temperature ΔT =Tb -Tt was held constant, while the average temperature Tm = (Tb +Tt) / 2 was varied. There was a significant increase of heat transport when TNI was between Tb and Tt. Measurements of the temperatures along the side wall as a function of Tm showed several ranges with qualitatively different behavior of quantities such as the time-averaged side-wall temperature, temperature gradient, or temperature fluctuations. We interpret these different ranges in terms of processes in the thermal boundary layers close to the top and bottom plates. SW acknowledges support by the Deutsche Forschungsgemeinschaft. This work was supported by the U.S. National Science Foundation through Grant No. DMR11-58514.
Scale Properties of Anisotropic and Isotropic Turbulence in the Urban Surface Layer
NASA Astrophysics Data System (ADS)
Liu, Hao; Yuan, Renmin; Mei, Jie; Sun, Jianning; Liu, Qi; Wang, Yu
2017-06-01
The scale properties of anisotropic and isotropic turbulence in the urban surface layer are investigated. A dimensionless anisotropic tensor is introduced and the turbulent tensor anisotropic coefficient, defined as C, where C = 3d3 + 1 (d3 is the minimum eigenvalue of the tensor) is used to characterize the turbulence anisotropy or isotropy. Turbulence is isotropic when C ≈ 1 , and anisotropic when C ≪ 1 . Three-dimensional velocity data collected using a sonic anemometer are analyzed to obtain the anisotropic characteristics of atmospheric turbulence in the urban surface layer, and the tensor anisotropic coefficient of turbulent eddies at different spatial scales calculated. The analysis shows that C is strongly dependent on atmospheric stability ξ = (z-zd)/L_{MO} , where z is the measurement height, zd is the displacement height, and L_{MO} is the Obukhov length. The turbulence at a specific scale in unstable conditions (i.e., ξ < 0 ) is closer to isotropic than that at the same scale under stable conditions. The maximum isotropic scale of turbulence is determined based on the characteristics of the power spectrum in three directions. Turbulence does not behave isotropically when the eddy scale is greater than the maximum isotropic scale, whereas it is horizontally isotropic at relatively large scales. The maximum isotropic scale of turbulence is compared to the outer scale of temperature, which is obtained by fitting the temperature fluctuation spectrum using the von Karman turbulent model. The results show that the outer scale of temperature is greater than the maximum isotropic scale of turbulence.
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
Coherent clusters of inertial particles in homogeneous turbulence
NASA Astrophysics Data System (ADS)
Baker, Lucia; Frankel, Ari; Mani, Ali; Coletti, Filippo
2016-11-01
Clustering of heavy particles in turbulent flows manifests itself in a broad spectrum of physical phenomena, including sediment transport, cloud formation, and spray combustion. However, a clear topological definition of particle cluster has been lacking, limiting our ability to describe their features and dynamics. Here we introduce a definition of coherent cluster based on self-similarity, and apply it to the distribution of heavy particles in direct numerical simulations of homogeneous isotropic turbulence. We consider a range of particle Stokes numbers, with and without the effect of gravity. Clusters show self-similarity at length scales larger than twice the Kolmogorov length, with a specific fractal dimension. In the absence of gravity, clusters demonstrate a tendency to sample regions of the flow where strain is dominant over vorticity, and to align themselves with the local vorticity vector; when gravity is present, the clusters tend to align themselves with gravity, and their fall speed is different from the average settling velocity. This approach yields observations which are consistent with findings obtained from previous studies while opening new avenues for analysis of the topology and evolution of particle clusters in a wealth of applications.
Isotropic blackbody cosmic microwave background radiation as evidence for a homogeneous universe.
Clifton, Timothy; Clarkson, Chris; Bull, Philip
2012-08-03
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.
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.
NASA Astrophysics Data System (ADS)
Carroll, Jonathan J.; Frank, Adam; Blackman, Eric G.
2010-10-01
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.
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
Large-deviation statistics of vorticity stretching in isotropic turbulence.
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 Re(λ)=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.
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.
Joint Statistics of Finite Time Lyapunov Exponents in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Johnson, Perry; Meneveau, Charles
2014-11-01
Recently, the notion of Lagrangian Coherent Structures (LCS) has gained attention as a tool for qualitative visualization of flow features. LCS visualize repelling and attracting manifolds marked by local ridges in the field of maximal and minimal finite-time Lyapunov exponents (FTLE), respectively. To provide a quantitative characterization of FTLEs, the statistical theory of large deviations can be used 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 (with finite-size correction). We generalize the formalism to characterize the joint distributions of the two independent FTLEs in 3D. The ``joint Cramér function of turbulence'' is measured from the Johns Hopkins Turbulence Databases (JHTDB) isotropic simulation at Reλ = 433 and results are compared with those computed using only the symmetric part of the velocity gradient tensor, as well as with those of instantaneous strain-rate eigenvalues. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude and the most likely ratio of FTLEs changes from 4:1:-5 to 8:3:-11, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. Supported by NSF Graduate Fellowship (DGE-1232825), a JHU graduate Fellowship, and NSF Grant CMMI-0941530. CM thanks Prof. Luca Biferale for useful discussions on the subject.
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
Energy transfer and dissipation in forced isotropic turbulence
NASA Astrophysics Data System (ADS)
Linkmann, Moritz; McComb, W. David; Berera, Arjun; Yoffe, Samuel
2014-11-01
A model for the Reynolds number dependence of the dimensionless dissipation rate Cɛ is derived from the dimensionless Kármán-Howarth equation, resulting in Cɛ =Cɛ , ∞ + C /RL , 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. The model equation is fitted to data from direct numerical simulations (DNS) of forced isotropic turbulence for integral scale Reynolds numbers up to RL = 5875 (Rλ = 435), which results in an asymptote for Cɛ in the infinite Reynolds number limit Cɛ , ∞ = 0 . 47 +/- 0 . 01 . Since the coefficients in the model equation are scale-dependent while the dimensionless dissipation rate is not, we modelled the scale dependences of the coefficients by an ad hoc profile function such that they cancel out, leaving the model equation scale-independent, as it must be. The profile function was compared to DNS data to very good agreement, provided we restrict the comparison to scales small enough to be well resolved in our simulations. This work has made use of the resources provided by the UK supercomputing service HECToR, made available through the Edinburgh Compute and Data Facility (ECDF). A.B. is supported by STFC, S.R.Y. and M.F.L. are funded by EPSRC.
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.
NASA Astrophysics Data System (ADS)
Fisanov, V. V.
2017-09-01
Analytical expressions for complex values of the wave number, refractive index, and the characteristic wave impedance of homogeneous electromagnetic plane waves propagating in a linear, homogeneous, isotropic medium with losses and gain are derived. Formulas for determining the type of normal wave as a function of the values of the real and imaginary parts of the permittivity and permeability are obtained, and conditions for the appearance of positive and negative refraction at the interface of two isotropic media are indicated. In the approach applied here, the concept of a negative refractive index is not used.
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.
Modeling inertial particle acceleration statistics in isotropic turbulence
NASA Astrophysics Data System (ADS)
Ayyalasomayajula, S.; Warhaft, Z.; Collins, L. R.
2008-09-01
Our objective is to explain recent Lagrangian acceleration measurements of inertial particles in decaying, nearly isotropic turbulence [Ayyalasomayajula et al., Phys. Rev. Lett. 97, 144507 (2006)]. These experiments showed that as particle inertial effects increased, the variance in the particle acceleration fluctuations was reduced, and the tails of the normalized particle acceleration probability density function (PDF) became systematically attenuated. We model this phenomenon using a base flow that consists of a two-dimensional array of evenly spaced vortices with signs and intensities that vary randomly in time. We simulate a large sample of inertial particles moving through the fluid without disturbing the flow (one-way coupling). Consistent with Bec et al. [J. Fluid Mech. 550, 349 (2006)], we find that our model exhibits preferential concentration or clustering of particles in regions located away from the vortex centers. That is, inertial particles selectively sample the flow field, oversampling regions with high strains and undersampling regions with high vorticities. At low Stokes numbers, this biased "sampling" of the flow is responsible for the reduction in the acceleration variance and partially explains the attenuation of the tails of the acceleration PDF. However, contrary to previous findings, we show that the tails of the PDF are also diminished by "filtering" induced by the attenuated response of the inertial particles to temporal variations in the fluid acceleration: Inertial particles do not respond to fluctuations with frequencies much higher than the inverse of the particle stopping time. We show that larger fluid acceleration events have higher frequencies and hence experience greater filtering by particle inertia. We contrast the vortex model with previous Lagrangian acceleration models by Sawford [Phys. Fluids A 3, 1577 (1991)] and Reynolds [Phys. Fluids 15, L1 (2003)] and show that although these models capture some aspects of the inertial
Compressibility Effects on the Passive Scalar Flux Within Homogeneous Turbulence
NASA Technical Reports Server (NTRS)
Blaisdell, G. A.; Mansour, N. N.; Reynolds, W. C.
1994-01-01
Compressibility effects on turbulent transport of a passive scalar are studied within homogeneous turbulence using a kinematic decomposition of the velocity field into solenoidal and dilatational parts. It is found that the dilatational velocity does not produce a passive scalar flux, and that all of the passive scalar flux is due to the solenoidal velocity.
A mathematical framework for forcing turbulence applied to horizontally homogeneous stratified flow
NASA Astrophysics Data System (ADS)
Rao, K. J.; de Bruyn Kops, S. M.
2011-06-01
It is often desirable to study turbulent flows at steady state even if the flow has no inherent source of turbulence kinetic energy. Doing so requires a forcing schema, and various methods applicable to laboratory experiments or numerical simulations have been studied extensively for turbulence that is isotropic and homogeneous in three dimensions. A review of existing schemata for simulations is used to form a framework for more general forcing methods. In this framework, the problem of developing a forcing method is abstracted into the two problems of (1) prescribing the spectrum of the input power and (2) specifying a force that has the desired characteristics and that adds energy to the flow with the correct spectrum. The framework is used to construct three forcing methods for simulating horizontally homogeneous and isotropic, vertically stratified turbulence. They are implemented in a pseudo-spectral large-eddy simulations and their characteristics are analyzed. The framework is then used to characterize existing laboratory experiments. While no exact analogy can be drawn between forcing in esoteric pseudo-spectral simulations and forcing in physical experiments, there are many similarities. It is suggested that the forcing framework can be applied to predict and systematically test the effects of configuration choices made in the design of simulations and laboratory experiments.
Experimental Study of Inertial Particle-Pair Relative Velocity in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Dou, Zhongwang
The investigation of turbulence-enhanced inertial particle collision in isotropic turbulence could improve our understanding and modeling of many particle-laden turbulent flows in engineering and nature. In this study, we investigate one of the most critical factors of particle collision - particle-pair relative velocity (RV) in three major steps. First, to generate a reliable homogeneous and isotropic turbulence (HIT) field, we have designed and implemented a high Reynolds number (R lambda), enclosed, fan-driven HIT chamber in the shape of 'soccer ball', conducive for studying inertial particle dynamics using whole-field imaging techniques. The characterization of turbulence in this near-zero-mean flow chamber was performed using a new two-scale particle imaging velocimetry (PIV) approach. The measurement results showed that turbulence in the apparatus achieved high homogeneity and isotropy in a large central region (48mm diameter) of the chamber with minimized gravity effect. A maximum Rlambda of 384 was achieved. Second, to measure particle-pair RV accurately, we have employed numerical experiments to systemically analyze the measurement error in the previous particle-pair RV measurement by holographic PIV. We found that accurate RV measurement requires high accuracy of both particle positioning and particle pairing. To meet these requirements, we have devised a novel planar 4-frame particle tracking velocimetry technique (4F-PTV) combining two PIV systems. It tracks particles in four consecutive frames in high speed to increase particle pairing accuracy. Furthermore, the particles are tracked only in a thin laser light sheet, thus negating the intrinsic position uncertainty in the depth direction in holographic PIV. In addition, we have studied the laser thickness effect on the RV measurement and attempted to use Monte Carlo analysis to correct this effect. Third, and most importantly, to better understand turbulence-enhanced inertial particle collision, we
On the dynamics of homogeneous turbulence near a surface
NASA Astrophysics Data System (ADS)
Flores, Oscar; Riley, James J.
2011-11-01
It is becoming increasing clear that stably-stratified flows can support a stratified turbulence k - 5 / 3 inertial range, different from Kolmogorov's. Stratification inhibits vertical motions, but the large-scale quasi-horizontal motions produce strong vertical shearing and small-scale instabilities. The result is a k - 5 / 3 horizontal spectrum for the horizontal velocities at scales larger than the Ozmidov scale, the largest scale that can overturn. For smaller scales, the classical Kolmogorov k - 5 / 3 applies. Inspired by data taken near the water surface in a tidal river, we here explore to what extent the dynamics of the nonlinear spectral energy transfer of near-surface turbulence with no mean shear (i.e., horizontally isotropic turbulence bounded by free-slip and no-slip surfaces) is analogous to stably stratified turbulence. To that end, we perform DNS of decaying isotropic turbulence with Reλ ~ 100 , but bounded by a non-slip surface and a free slip surface. The behavior of the flow near the free-slip surface is similar to stratified turbulence, with a tentative k - 5 / 3 range, but the same is not true for the no-slip surface at the present Reynolds numbers. This research was supported by ARO and NSF. Chickadel et al. (2011) to appear in IEEE Geosci. Remote Sens. Lett.
NASA Astrophysics Data System (ADS)
Buaria, Dhawal; Yeung, P. K.; Sawford, B. L.
2016-11-01
An efficient massively parallel algorithm has allowed us to obtain the trajectories of 300 million fluid particles in an 81923 simulation of isotropic turbulence at Taylor-scale Reynolds number 1300. Conditional single-particle statistics are used to investigate the effect of extreme events in dissipation and enstrophy on turbulent dispersion. The statistics of pairs and tetrads, both forward and backward in time, are obtained via post-processing of single-particle trajectories. For tetrads, since memory of shape is known to be short, we focus, for convenience, on samples which are initially regular, with all sides of comparable length. The statistics of tetrad size show similar behavior as the two-particle relative dispersion, i.e., stronger backward dispersion at intermediate times with larger backward Richardson constant. In contrast, the statistics of tetrad shape show more robust inertial range scaling, in both forward and backward frames. However, the distortion of shape is stronger for backward dispersion. Our results suggest that the Reynolds number reached in this work is sufficient to settle some long-standing questions concerning Lagrangian scale similarity. Supported by NSF Grants CBET-1235906 and ACI-1036170.
Design of diamond-shaped transient thermal cloaks with homogeneous isotropic materials
NASA Astrophysics Data System (ADS)
Li, Ting-Hua; Zhu, Dong-Lai; Mao, Fu-Chun; Huang, Ming; Yang, Jing-Jing; Li, Shou-Bo
2016-10-01
Transformation thermodynamics as a major extension of transformation optics has recently received considerable attention. In this paper, we present two-dimensional (2D) and three-dimensional (3D) diamond-shaped transient thermal cloaks with non-singular homogeneous material parameters. The absence of singularity in the parameters results from the fact that the linear coordinate transformation is performed by expanding a line segment rather than a point into a region, while the mechanism behind the homogeneity is the homogeneous stretching and compression along orthogonal directions during the transformation. Although the derived parameters remain anisotropic, we further show that this can be circumvented by considering a layered structure composed of only four types of isotropic materials based on the effective medium theory. Numerical simulation results confirm the good performance of the proposed cloaks.
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.
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.
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
Analysis of the decay of temperature fluctuations in isotropic turbulence
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1982-01-01
The Lagrangian dispersion theory of Durbin (1980) is used to analyze experiments by Warhaft and Lumley (1978) and by Sreenivasan et al. (1980) on temperature fluctuations in grid-generated turbulence. Both theory and experiment show that the decay exponent m depends on the ratio of the initial length scales of velocity and temperature, although when this ratio is greater than 2.5 such dependence is negligible. The theory shows that m is not truly constant, but within the range covered by the experiments it is nearly so. The agreement between theory and experiment lends credence to the idea that the decay of fluctuations is controlled largely by turbulent relative dispersion.
Direct numerical simulation of isotropic turbulence interacting with a weak shock wave
NASA Technical Reports Server (NTRS)
Lee, Sangsan; Lele, Sanjiva K.; Moin, Parviz
1993-01-01
Direct numerical simulations are used to investigate the interaction of isotropic quasi-incompressible turbulence with a weak shock wave. A linear analysis of the interaction is conducted for comparison with the simulations. Both the simulations and the analysis show that turbulence is enhanced during the interaction. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. It is suggested that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behavior not reproduced by the linear analysis. Analysis of the budget of the turbulent kinetic energy transport equation shows that this behavior can be attributed to the pressure transport term. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.
High-resolution simulations of forced compressible isotropic turbulence
NASA Astrophysics Data System (ADS)
Jagannathan, Shriram; Donzis, Diego
2011-11-01
Direct numerical simulations of compressible turbulent flows are several times more expensive than their incompressible counterparts. Therefore, using large computing resources efficiently is even more pressing when studying compressible turbulence. A highly scalable code is presented which is used to perform simulations aimed at understanding fundamental turbulent processes. The code, which is based on a 2D domain decomposition, is shown to scale well up to 128k cores. To attain a statistically stationary state a new scheme is developed which involves large-scale stochastic forcing (solenoidal or dilatational) and a procedure to keep mean internal energy constant. The resulting flows show characteristics consistent with results in the literature. The attainable Reynolds and turbulent Mach numbers for given computational resources depend on the number of grid points and the degree to which the smallest scales are resolved that are given by Kolmogorov scales. A systematic comparison of simulations at different resolutions suggests that the resolution needed depends on the particular statistic being considered. The resulting database is used to investigate small-scale universality, the scaling of spectra of velocity, density and temperature fields, structure functions and the trends towards high-Reynolds number asymptotes. Differences with incompressible results are highlighted.
NASA Astrophysics Data System (ADS)
Liu, Ya-Ming; Liu, Zhao-Hui; Han, Hai-Feng; Li, Jing; Wang, Han-Feng; Zheng, Chu-Guang
2009-06-01
The statistics of a passive scalar along inertial particle trajectory in homogeneous isotropic turbulence with a mean scalar gradient is investigated by using direct numerical simulation. We are interested in the influence of particle inertia on such statistics, which is crucial for further understanding and development of models in non-isothermal gas-particle flows. The results show that the scalar variance along particle trajectory decreases with the increasing particle inertia firstly; when the particle's Stokes number St is less than 1.0, it reaches the minimal value when St is around 1.0, then it increases if St increases further. However, the scalar dissipation rate along the particle trajectory shows completely contrasting behavior in comparison with the scalar variance. The mechanical-to-thermal time scale ratios averaged along particle,
Generating and controlling homogeneous air turbulence using random jet arrays
NASA Astrophysics Data System (ADS)
Carter, Douglas; Petersen, Alec; Amili, Omid; Coletti, Filippo
2016-12-01
The use of random jet arrays, already employed in water tank facilities to generate zero-mean-flow homogeneous turbulence, is extended to air as a working fluid. A novel facility is introduced that uses two facing arrays of individually controlled jets (256 in total) to force steady homogeneous turbulence with negligible mean flow, shear, and strain. Quasi-synthetic jet pumps are created by expanding pressurized air through small straight nozzles and are actuated by fast-response low-voltage solenoid valves. Velocity fields, two-point correlations, energy spectra, and second-order structure functions are obtained from 2D PIV and are used to characterize the turbulence from the integral-to-the Kolmogorov scales. Several metrics are defined to quantify how well zero-mean-flow homogeneous turbulence is approximated for a wide range of forcing and geometric parameters. With increasing jet firing time duration, both the velocity fluctuations and the integral length scales are augmented and therefore the Reynolds number is increased. We reach a Taylor-microscale Reynolds number of 470, a large-scale Reynolds number of 74,000, and an integral-to-Kolmogorov length scale ratio of 680. The volume of the present homogeneous turbulence, the largest reported to date in a zero-mean-flow facility, is much larger than the integral length scale, allowing for the natural development of the energy cascade. The turbulence is found to be anisotropic irrespective of the distance between the jet arrays. Fine grids placed in front of the jets are effective at modulating the turbulence, reducing both velocity fluctuations and integral scales. Varying the jet-to-jet spacing within each array has no effect on the integral length scale, suggesting that this is dictated by the length scale of the jets.
Transmission of acoustic waves through mixing layers and 2D isotropic turbulence
NASA Astrophysics Data System (ADS)
Juve, D.; Blanc-Benon, P.; Comte-Bellot, G.
Ray tracing and parabolic equation methods have been used to study the properties of acoustic waves transmitted through turbulent velocity fields. A numerical simulation permits individual realizations of the turbulent field, which then allow, if desired, an ensemble averaging of the fields. Two flows have been considered, 2D isotropic turbulence and a 2D mixing layer. The following complementary aspects are developed: the occurrence of caustics, the reinforced or weakened zones of the acoustic field, the eigenrays between a source and a receiver, and the associated travel times, variances, and scintillation index.
Depression of Nonlinearity in Decaying Isotropic MHD Turbulence
Servidio, S.; Matthaeus, W. H.; Dmitruk, P.
2008-03-07
Spectral method simulations show that undriven magnetohydrodynamic turbulence spontaneously generates coherent spatial correlations of several types, associated with local Beltrami fields, directional alignment of velocity and magnetic fields, and antialignment of magnetic and fluid acceleration components. These correlations suppress nonlinearity to levels lower than what is obtained from Gaussian fields, and occur in spatial patches. We suggest that this rapid relaxation leads to non-Gaussian statistics and spatial intermittency.
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.
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.
Dynamics of dissolved polymer chains in isotropic turbulence
NASA Astrophysics Data System (ADS)
Jin, Shi; Collins, Lance R.
2007-10-01
Polymers are remarkable molecules that have relaxation times that can span 15 orders of magnitude. The very longest of the relaxation times for high molecular weight polymers are sufficiently long to overlap with fluid mechanical times scales; under those circumstances, polymers can influence the flow. A well-known example that is still not fully understood is polymer drag reduction. It has been known since Toms (1949 Proc. 1st Int. Congress on Rheology 2 135-41) that parts per million (mass basis) concentrations of polymers can reduce the drag on a solid surface by as much as 80%. Understanding the mechanism of drag reduction requires an understanding of the dynamics of the dissolved polymer chain in response to local fluctuations in the turbulent flow field. We investigate this by using Brownian dynamics simulations of bead-spring models of polymers immersed in a turbulent solvent that is separately computed using direct numerical simulations. We observe that polymer chains with parameters that are effective for drag reduction generally remain stretched for long periods of time and only occasionally relax. The relatively restricted configuration space they sample makes it reasonable to represent their behavior with simpler dumbbell models. We also study the spatial structure of the polymer stresses using a Lagrangian strategy. The results explain the need for relatively high spatial resolution for numerical simulations of polymer flows.
NASA Astrophysics Data System (ADS)
Yu, Rixin; Lipatnikov, Andrei N.
2017-06-01
A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U' to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze=6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U' is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.
NASA Astrophysics Data System (ADS)
Kaufmann, A.; Moreau, M.; Simonin, O.; Helie, J.
2008-06-01
The purpose of this paper is to evaluate the accuracy of the mesoscopic approach proposed by Février et al. [P. Février, O. Simonin, K.D. Squires, Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, J. Fluid Mech. 533 (2005) 1-46] by comparison against the Lagrangian approach for the simulation of an ensemble of non-colliding particles suspended in a decaying homogeneous isotropic turbulence given by DNS. The mesoscopic Eulerian approach involves to solve equations for a few particle PDF moments: number density, mesoscopic velocity, and random uncorrelated kinetic energy (RUE), derived from particle flow ensemble averaging conditioned by the turbulent fluid flow realization. In addition, viscosity and diffusivity closure assumptions are used to compute the unknown higher order moments which represent the mesoscopic velocity and RUE transport by the uncorrelated velocity component. A detailed comparison between the two approaches is carried out for two different values of the Stokes number based on the initial fluid Kolmogorov time scale, St=0.17 and 2.2. In order to perform reliable comparisons for the RUE local instantaneous distribution and for the mesoscopic kinetic energy spectrum, the error due to the computation method of mesoscopic quantities from Lagrangian simulation results is evaluated and minimized. A very good agreement is found between the mesoscopic Eulerian and Lagrangian predictions for the small particle Stokes number case corresponding to the smallest particle inertia. For larger particle inertia, a bulk viscous term is included in the mesoscopic velocity governing equation to avoid spurious spatial oscillation that may arise due to the inability of the numerical scheme to resolve sharp number density gradients. As a consequence, for St=2.2, particle number density and RUE spatial distribution predicted by the
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
The minimum energy decay rate in quasi-isotropic grid turbulence
NASA Astrophysics Data System (ADS)
Davidson, P. A.
2011-08-01
We consider high Reynolds number, freely-decaying, isotropic turbulence in which the large scales evolve in a self-similar manner when normalized by the integral scales, u and ℓ. As it is well known, a range of possible behaviors may be observed depending on the form of the longitudinal velocity correlation at large separation, uf∞=u 2f(r →∞). We consider the cases u2f∞=cmr-m,2≤m ≤6, whose spectral counterpart is E(k →0)~cmkm -1 for m <6, with or without a lnk correction, and E(k →0)~I k4 for m =6. (I is Loitsyansky's integral.) It has long been known that the cmm=constant during the decay. This, in turn, sets the energy decay rate as u2~t-(1-p)2m /(m+2), where p is the power-law exponent for the normalized dissipation rate, εℓ/εℓu3u3~t-p, observed empirically to be a small positive number in grid turbulence. We systematically explore the properties of these different classes of turbulence and arrive at the following conclusions. (i) The invariance of cm is a direct consequence of linear momentum conservation for m ≤4, and angular momentum conservation for m =5. (ii) The classical spectra of Saffman, E(k →0)~c3k2, and Batchelor, E(k →0)~Ik4, are robust in the sense that they emerge from a broad class of initial conditions. In particular, it is necessary only that <ωi ω'j >∞ ≤O(r-8) at t =0. The non-classical spectra (m =2,4,5), on the other hand, require very specific initial conditions in order to be realized, of the form <ωiω'j>∞=O(r-(m +2)). (Note the equality rather than the inequality here.) This makes the non-classical spectra less likely to be observed in practice. (iii) The case of m =2, which is usually associated with the u2~t-1 decay law, is pathological in a number of respects. For example, its spectral tensor diverges as k →0, and the long-range correlations
Effects of an oscillating magnetic field on homogeneous ferrofluid turbulence.
Schumacher, Kristopher R; Riley, James J; Finlayson, Bruce A
2010-01-01
This paper presents the results from direct numerical simulations of homogeneous ferrofluid turbulence with a spatially uniform, applied oscillating magnetic field. Due to the strong coupling that exists between the magnetic field and the ferrofluid, we find that the oscillating field can affect the characteristics of the turbulent flow. The magnetic field does work on the turbulent flow and typically leads to an increased rate of energy loss via two dissipation modes specific to ferrofluids. However, under certain conditions this magnetic work results in injection, or a forcing, of turbulent kinetic energy into the flow. For the cases considered here, there is no mean shear and the mean components of velocity, vorticity, and particle spin rate are all zero. Thus, the effects shown are entirely due to the interactions between the turbulent fluctuations of the ferrofluid and the magnetic field. In addition to the effects of the oscillation frequency, we also investigate the effects of the choice of magnetization equation. The calculations focus on the approximate centerline conditions of the relatively low Reynolds number turbulent ferrofluid pipe flow experiments described previously [K. R. Schumacher, Phys. Rev. E 67, 026308 (2003)].
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).
A homogeneous and isotropic universe in Lorentz gauge theory of gravity
NASA Astrophysics Data System (ADS)
Borzou, Ahmad; Mirza, Behrouz
2017-07-01
Lorentz gauge theory of gravity was recently introduced. We study the homogeneous and isotropic universe of this theory. It is shown that some time after the matter in the universe is diluted enough, at z ∼ 0.6 , the decelerating expansion shifts spontaneously to an accelerating one without a dark energy. We discuss that Lorentz gauge theory puts no constraint on the total energy content of the universe at present time and therefore the magnitude of vacuum energy predicted by field theory is not contradictory anymore. It is demonstrated that in this theory the limit on the number of relativistic particles in the universe is much looser than in GR. An inflationary mechanism is discussed as well. We show that the theory, unlike GR, does not require the slow-roll or similar conditions to drive the inflation at the beginning of the universe.
Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
NASA Astrophysics Data System (ADS)
Barcaroli, Leonardo; Brunkhorst, Lukas K.; Gubitosi, Giulia; Loret, Niccoló; Pfeifer, Christian
2017-01-01
The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to present a Planck-scale deformation of the Hamiltonian of a particle in Friedman-Lemaître-Robertson-Walker (FLRW) geometry that is locally identical to the κ -Poincaré dispersion relation, in the same way as the dispersion relation of point particles in general relativity is locally identical to the one valid in special relativity. Studying the motion of particles subject to such a Hamiltonian, we derive the redshift and lateshift as observable consequences of the Planck-scale deformed FLRW universe.
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
Choi, Yeontaek; Kim, Byung-Gu; Lee, Changhoon
2009-07-01
We provide an observation suggesting a strong correlation between helicity and enstrophy in fluid turbulence. Helicity statistics were obtained in a direct numerical simulation of forced isotropic turbulence. An investigation of coherent structures revealed that intermittently large local helicity was found in the core region of the coherent rotational structures, thus showing a strong correlation with local enstrophy, not dissipation. Statistics regarding the relative helicity and the correlation between velocity and vorticity conditioned on different levels of enstrophy clearly suggest that velocity and vorticity tend to be aligned in the core of the coherent structures.
Bubble-induced turbulence study in homogeneous turbulent flow using DNS approach
NASA Astrophysics Data System (ADS)
Feng, Jinyong; Bolotnov, Igor
2015-11-01
The effect of a single bubble on the energy transfer to a homogeneous turbulent flow using DNS approach is investigated for various conditions. The single-phase turbulence is numerically generated by pressure-gradient driven uniform flow through a fully resolved turbulence generating grid. The turbulent intensity measured is uniform normal to the flow direction. The decay rate of the turbulent kinetic energy is validated against analytical power law. The collected instantaneous velocity is used as inflow condition for single-bubble simulations to study the bubble-induced turbulence (BIT). In interface-resolved two-phase simulation the bubble is kept at fixed positions by using a proportional-integral-derivative controller. This simulation set allows estimating the turbulent kinetic energy before and after the bubble, quantifying the BIT. Effects of bubble deformability, velocity and turbulent intensity are separately studied. We observe that for a nearly spherical bubble, the bubble-induced turbulence is positive, increasing the level of turbulent kinetic energy in the liquid phase. BIT is influenced by the other studied parameters and the presented work will contribute to the closure BIT model development in multiphase computational fluid dynamics modeling. The work is supported by NSF-CBET-Fluid Dynamics, Award #1333993.
ISOTROPIC TURBULENCE AND INERTIAL-RANGE STRUCTURE IN THE ABRIDGED LHDI APPROXIMATION
effective eddy viscosities, and Lagrangian spacetime statistics in stationary and decaying isotropic turbulence. The results are then specialized to the...of energy transfer, for Lagrangian spacetime structure functions, and for Lagrangian spacetime acceleration covariances. Inertial-range Eulerian... spacetime structure functions also are computed. The predicted absolute Kolmogorov spectrum in the inertial and dissipation ranges is compared with data of Grant, Stewart, and Moilliet, and of M. M. Gibson.
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)
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.
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.
On the Structure Orientation in Rotating and Sheared Homogeneous Turbulence
NASA Astrophysics Data System (ADS)
Aguirre, Joylene C.; Moreau, Adam F.; Jacobitz, Frank G.
2016-11-01
The results of direct numerical simulations are used to study the effect of rotation on the orientation of structures and the evolution of the turbulent kinetic energy in homogeneous sheared turbulence. Shear flows without rotation, with moderate rotation, and with strong rotation are considered and the rotation axis is either parallel or anti-parallel to the mean flow vorticity. In the case of moderate rotation, an anti-parallel configuration increases the growth rate of the turbulent kinetic energy, while a parallel configuration decreases the growth rate as compared to the flow without rotation. The orientation of turbulent structures present in the flows are characterized using the three-dimensional, two-point autocorrelation coefficient of velocity magnitude and vorticity magnitude. An ellipsoid is fitted to the surface defined by a constant autocorrelation coefficient value and the major and minor axes are used to determine the inclination angle of flow structures in the plane of shear. It was found that the inclination angle assumes a maximum value for the anti-parallel configuration with moderate rotation. Again, the inclination angle for the parallel configuration with moderate rotation is reduced as compared to the case without rotation. The smallest inclination angles are found for the strongly rotating cases. Hence, the inclination angle is directly related to the growth rate of the turbulent kinetic energy. University of San Diego Shiley-Marcos School of Engineering and McNair Scholars.
NASA Astrophysics Data System (ADS)
Horiuti, Kiyosi; Ozawa, Tetsuya
2011-03-01
The stretched spiral vortex [T. S. Lundgren, "Strained spiral vortex model for turbulent structures," Phys. Fluids 25, 2193 (1982)] is identified in turbulence in homogeneous shear flow and the spectral properties of this flow are studied using direct-numerical simulation data. The effects of mean shear on the genesis, growth, and annihilation processes of the spiral vortex are elucidated, and the role of the spiral vortex in the generation of turbulence is shown. As in homogeneous isotropic turbulence [K. Horiuti and T. Fujisawa, "The multi mode stretched spiral vortex in homogeneous isotropic turbulence," J. Fluid Mech. 595, 341 (2008)], multimodes of the spiral vortex are extracted. Two symmetric modes of configurations with regard to the vorticity alignment along the vortex tube in the core region and dual vortex sheets spiraling around the tube are often educed. One of the two symmetric modes is created by a conventional rolling-up of a single spanwise shear layer. Another one is created by the convergence of the recirculating flow or streamwise roll [F. Waleffe, "Homotopy of exact coherent structures in plane shear flows," Phys. Fluids 15, 1517 (2003)] caused by the upward and downward motions associated with the streaks. The vortex tube is formed by axial straining and lowering of pressure in the recirculating region. The spanwise shear layers are entrained by the tube and they form spiral turns. The latter symmetric mode tends to be transformed into the former mode with lapse of time due to the action of the pressure Hessian term. The power law in the inertial subrange energy spectrum is studied. The base steady spectrum fits the equilibrium Kolmogorov -5/3 spectrum, to which a nonequilibrium component induced by the fluctuation of the dissipation rate ɛ is added. This component is extracted using the conditional sampling on ɛ, and it is shown that it fits the -7/3 power in accordance with the statistical theory. The correlation between these spectra and
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.
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
Dispersion of finite size droplets and solid particles in isotropic turbulence
NASA Astrophysics Data System (ADS)
Rosso, Michele
Turbulent disperse two-phase flows, of either fluid/fluid or fluid/solid type, are common in natural phenomena and engineering devices. Notable examples are atmospheric clouds, i.e. dispersed liquid water droplets and ice particles in a complex turbulent flow, and spray of fuel droplets in the combustion chamber of internal combustion engines. However, the physics of the interaction between a dispersed phase and turbulence is not yet fully understood. The objective of this study is to compare the dispersion of deformable finite size droplets with that of solid particles in a turbulent flow in the absence of gravity, by performing Direct Numerical Simulation (DNS). The droplets and the particles have the same diameter, of the order of the Taylor's microscale of turbulence, and the same density ratio to the carrier flow. The solid particle-laden turbulence is simulated by coupling a standard projection method with the Immersed Boundary Method (IBM). The solid particles are fully resolved in space and time without considering particle/particle collisions (two-way coupling). The liquid droplet-laden turbulence is simulated by coupling a variable-density projection method with the Accurate Conservative Level Set Method (ACLSM). The effect of the surface tension is accounted for by using the Ghost Fluid Method (GFM) in order to avoid any numerical smearing, while the discontinuities in the viscous term of the Navier-Stokes equation are smoothed out via the Continuum Surface Force approach. Droplet/droplet interactions are allowed (four-way coupling). The results presented here show that in isotropic turbulence the dispersion of liquid droplets in a given direction is larger than that of solid particles due to the reduced decay rate of turbulence kinetic energy via the four-way coupling effects of the droplets.
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.
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.
Transport equation for plasmas in a stationary-homogeneous turbulence
Wang, Shaojie
2016-02-15
For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose symmetry has been proved, can be computed in a straightforward way when the fluctuating particle trajectories are provided. As an application, it has been shown that a mean parallel electric filed can drive a particle flux through the Stokes-Einstein relation, independent of the details of the fluctuations.
Fractally Fourier decimated homogeneous turbulent shear flow in noninteger dimensions.
Fathali, Mani; Khoei, Saber
2017-02-01
Time evolution of the fully resolved incompressible homogeneous turbulent shear flow in noninteger Fourier dimensions is numerically investigated. The Fourier dimension of the flow field is extended from the integer value 3 to the noninteger values by projecting the Navier-Stokes equation on the fractal set of the active Fourier modes with dimensions 2.7≤d≤3.0. The results of this study revealed that the dynamics of both large and small scale structures are nontrivially influenced by changing the Fourier dimension d. While both turbulent production and dissipation are significantly hampered as d decreases, the evolution of their ratio is almost independent of the Fourier dimension. The mechanism of the energy distribution among different spatial directions is also impeded by decreasing d. Due to this deficient energy distribution, turbulent field shows a higher level of the large-scale anisotropy in lower Fourier dimensions. In addition, the persistence of the vortex stretching mechanism and the forward spectral energy transfer, which are three-dimensional turbulence characteristics, are examined at changing d, from the standard case d=3.0 to the strongly decimated flow field for d=2.7. As the Fourier dimension decreases, these forward energy transfer mechanisms are strongly suppressed, which in turn reduces both the small-scale intermittency and the deviation from Gaussianity. Besides the energy exchange intensity, the variations of d considerably modify the relative weights of local to nonlocal triadic interactions. It is found that the contribution of the nonlocal triads to the total turbulent kinetic energy exchange increases as the Fourier dimension increases.
Fractally Fourier decimated homogeneous turbulent shear flow in noninteger dimensions
NASA Astrophysics Data System (ADS)
Fathali, Mani; Khoei, Saber
2017-02-01
Time evolution of the fully resolved incompressible homogeneous turbulent shear flow in noninteger Fourier dimensions is numerically investigated. The Fourier dimension of the flow field is extended from the integer value 3 to the noninteger values by projecting the Navier-Stokes equation on the fractal set of the active Fourier modes with dimensions 2.7 ≤d ≤3.0 . The results of this study revealed that the dynamics of both large and small scale structures are nontrivially influenced by changing the Fourier dimension d . While both turbulent production and dissipation are significantly hampered as d decreases, the evolution of their ratio is almost independent of the Fourier dimension. The mechanism of the energy distribution among different spatial directions is also impeded by decreasing d . Due to this deficient energy distribution, turbulent field shows a higher level of the large-scale anisotropy in lower Fourier dimensions. In addition, the persistence of the vortex stretching mechanism and the forward spectral energy transfer, which are three-dimensional turbulence characteristics, are examined at changing d , from the standard case d =3.0 to the strongly decimated flow field for d =2.7 . As the Fourier dimension decreases, these forward energy transfer mechanisms are strongly suppressed, which in turn reduces both the small-scale intermittency and the deviation from Gaussianity. Besides the energy exchange intensity, the variations of d considerably modify the relative weights of local to nonlocal triadic interactions. It is found that the contribution of the nonlocal triads to the total turbulent kinetic energy exchange increases as the Fourier dimension increases.
Hybrid Model for Homogenization of the Elastoplastic Properties of Isotropic Matrix Composites
NASA Astrophysics Data System (ADS)
Fedotov, A. F.
2017-07-01
A hybrid homogenization model for calculating the effective elastoplastic properties of isotropic matrix composites is suggested. The hybrid model combines the continuous deformation models of heterogeneous solid and porous materials. A distinctive feature of the model is the calculation of concentration coefficients of the average Hill strains in terms of the effective volumes of strain averaging. The effective volumes of averaging are determined by solving the boundary-value problem on plastic deformation of a simplified structural model of a two-phase composite considering the porous state of matrix. A comparison of calculation results with experimental data upon constructing deformation diagrams for polymer-matrix and metal-matrix composites is carried out. The possibility of changing the properties of the metal matrix in producing composites is mentioned. Therefore, the adequacy of analytical models greatly depends on the accuracy of identification of material constants of the matrix. On the whole, the new model described the plastic deformation of matrix composites more accurately than the Mori-Tanaka model. The analytical model proposed has a simpler sampling scheme, a simple computation algorithm, and ensured the same calculation accuracy for the deformation diagram of an aluminum-matrix composite as the numerical finite-element model created by the ABAQUS software.
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 Radiated Noise from Isotropic Turbulence with Applications to the Theory of Jet Noise
NASA Astrophysics Data System (ADS)
Lilley, G. M.
1996-02-01
Lighthill [1], in his Theory of Aerodynamic Noise, considered the noise from a pseudo-finite yet unbounded domain of compressible unsteady flow. The first application of this theory was given by Proudman [2] for the case of isotropic turbulence at low Mach numbers and high Reynolds numbers. More recently, Lilley [3] and Sarkar and Hussaini [4], using Direct Numerical Simulation (DNS), have reconsidered this problem, and evaluated for the first time the fourth order space-retarded time covariance which is central to Lighthill's theory for the determination of the acoustic radiated sound power. In this paper the previous work is extended to include the effects of a hot fluid in motion immersed in an external medium at rest. On the introduction of a simple hypothesis these results for the noise radiated from isotropic turbulence are used to predict the noise power radiated from a gaseous hot turbulent jet. The results are found to be qualitatively in agreement with far field experimental data on hot jets at subsonic and supersonic speeds, provided the jets are fully expanded and are devoid of shock waves. The theory has its origins in the 1950s following the publication of Lighthill's theory of aerodynamic noise, when Professor E. J. Richards, the author and their colleagues were striving to predict the noise from jet engines and establish methods for their noise reduction, without loss in performance.
Field Line Random Walk in Isotropic Magnetic Turbulence up to Infinite Kubo Number
NASA Astrophysics Data System (ADS)
Sonsrettee, W.; Wongpan, P.; Ruffolo, D. J.; Matthaeus, W. H.; Chuychai, P.; Rowlands, G.
2013-12-01
In astrophysical plasmas, the magnetic field line random walk (FLRW) plays a key role in the transport of energetic particles. In the present, we consider isotropic magnetic turbulence, which is a reasonable model for interstellar space. Theoretical conceptions of the FLRW have been strongly influenced by studies of the limit of weak fluctuations (or a strong mean field) (e.g, Isichenko 1991a, b). In this case, the behavior of FLRW can be characterized by the Kubo number R = (b/B0)(l_∥ /l_ \\bot ) , where l∥ and l_ \\bot are turbulence coherence scales parallel and perpendicular to the mean field, respectively, and b is the root mean squared fluctuation field. In the 2D limit (R ≫ 1), there has been an apparent conflict between concepts of Bohm diffusion, which is based on the Corrsin's independence hypothesis, and percolative diffusion. Here we have used three non-perturbative analytic techniques based on Corrsin's independence hypothesis for B0 = 0 (R = ∞ ): diffusive decorrelation (DD), random ballistic decorrelation (RBD) and a general ordinary differential equation (ODE), and compared them with direct computer simulations. All the analytical models and computer simulations agree that isotropic turbulence for R = ∞ has a field line diffusion coefficient that is consistent with Bohm diffusion. Partially supported by the Thailand Research Fund, NASA, and NSF.
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.
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.
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).
Calculation of velocity structure functions for vortex models of isotropic turbulence
NASA Astrophysics Data System (ADS)
Saffman, P. G.; Pullin, D. I.
1996-11-01
Velocity structure functions (up'-up)m are calculated for vortex models of isotropic turbulence. An integral operator is introduced which defines an isotropic two-point field from a volume-orientation average for a specific solution of the Navier-Stokes equations. Applying this to positive integer powers of the longitudinal velocity difference then gives explicit formulas for (up'-up)m as a function of order m and of the scalar separation r. Special forms of the operator are then obtained for rectilinear stretched vortex models of the Townsend-Lundgren type. Numerical results are given for the Burgers vortex and also for a realization of the Lundgren-strained spiral vortex, and comparison with experimental measurement is made. In an Appendix, we calculate values of the velocity-derivative moments for the Townsend-Burgers model.
Large-eddy simulations of viscoelastic isotropic turbulence with the FENE-P fluid
NASA Astrophysics Data System (ADS)
Pinho, Fernando T.; Ferreira, Pedro O.; B. da Silva, Carlos; Idmec/Feup Collaboration
2016-11-01
A new subgrid-scale (SGS) model developed for large-eddy simulations (LES) of dilute polymer solutions described by the Finitely Extensible Nonlinear Elastic constitutive equation closed with the Peterlin approximation (FENE-P), is presented. The filtered conformation tensor evolution equation uses the self-similarity of the polymer stretching terms, and the global equilibrium of the trace of the conformation tensor, while the SGS stresses are modelled with the classical Smagorinsky model. The new closure is assessed in direct numerical simulations (DNS) of forced isotropic turbulence using classical a-priori tests, and in a-posteriori (LES) showing excellent agreement with all the exact (filtered DNS) results.
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.
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.
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.
Cutoff radius effect of the isotropic periodic sum method in homogeneous system. II. Water.
Takahashi, Kazuaki; Narumi, Tetsu; Yasuoka, Kenji
2010-07-07
Molecular dynamics simulation has been applied for water to compare the isotropic periodic sum (IPS) method [X. Wu and B. R. Brooks, J. Chem. Phys. 122, 044107 (2005)] with the Ewald sum based on the diffusion coefficient and liquid structure. The IPS method gives a good estimation for the self-diffusion coefficient at a cutoff radius, r(c), greater than 2.2 nm; however, the radial distribution function g(r) has a notable deviation. The peak of this deviation appears at specific intermolecular distances which are near each cutoff radius and decrease in proportion to the inverse of the cube of r(c). Thus the deviation becomes insignificant (less than 1%) at r(c) greater than 2.2 nm. The distance dependent Kirkwood factor G(k)(r) was also calculated, and since the truncation of a long-range interaction of the cutofflike method (such as cutoff with or without the switch function and the reaction field) shows serious shortcomings for dipole-dipole correlations in bulk water systems, this was observed by comparing the shape to that of the Ewald sum [Y. Yonetani, J. Chem. Phys. 124, 204501 (2006); D. van der Spoel and P. J. van Maaren, J. Chem. Theory Comput. 2, 1 (2006)]. The G(k)(r) of cutofflike method greatly deviate from that of the Ewald sum. However, the discrepancy of G(k)(r) for the IPS method was found to be much less than that of other typical cutofflike methods. In conclusion, the IPS method is an adequately accurate technique for estimating transport coefficients and the liquid structure of water in a homogeneous system at long cutoff distances.
On the effects of density ratio on droplet-laden isotropic turbulence
NASA Astrophysics Data System (ADS)
Ferrante, Antonino; Dodd, Michael
2016-11-01
Our objective is to determine the effects of varying the droplet- to carrier-fluid density ratio (ρd /ρc) on the interaction of droplets with turbulence. We performed DNS of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor lengthscale and with 5% droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number Reλ = 83 . We varied ρd /ρc from 1 to 100 while keeping the Weber number and dynamic viscosity ratio constant, Werms=1 and μd /μc =1. We derived the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. We show that increasing ρd /ρc increases the decay rate of TKE in the two-fluid flow. The TKE budget shows that this increase is caused by an increase in the dissipation rate of TKE and a decrease in the power of the surface tension. The underlying physical mechanisms for these behaviors will be presented.
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.
Analysis of the behavior of bubbles and droplets in isotropic turbulence
NASA Astrophysics Data System (ADS)
Snyder, Murray R.
The behavior and scale-dependent dispersion of small air bubbles, and the rise of slightly buoyant oil droplets in water under isotropic turbulence conditions, are analyzed computationally. The flow field is simulated using a pseudo-spectral code, while the bubble dynamics are analyzed by integration of a Lagrangian equation of motion with buoyancy, virtual mass, pressure, drag and lift forces. Consistent with experimental data, bubble rise velocities are increasingly suppressed with increasing turbulence intensity. The role of the lift force in moving the bubbles to the down-flow side of turbulent eddies, and consequently retarding their rise, is observed. Analysis also reveals that the vertical bubble velocities are characterized by asymmetric probability density functions that are positive or negative-skewed dependent upon the non-dimensional turbulence intensity and the Taylor length scale. Lagrangian bubble trajectories are used to determine dispersion characteristics, following the theoretical development of Cushman and Moroni (2001). The dispersion of 40 mum bubbles exhibits transition to Fickian behavior, and the process is weakly affected by the turbulence level for the entire range considered. Larger, 400 mum bubbles are shown to be more sensitive to turbulence level, with transition to Fickian behavior delayed in low turbulence fields. Computations are also performed to investigate the puzzling behavior observed by Friedman and Katz (2002), that the rise velocity of slightly buoyant droplets smaller than 800 mum in diameter is enhanced by turbulence whereas the rise of larger droplets is retarded. Using the quasi-steady, empirically-determined drag and lift coefficients, the observed experimental behavior could not be reproduced. Further, analysis of the effect of lift and history forces also indicates that, within a broad range of uncertainty, these forces do not account for the experimentally observed mean droplet rise. Guided by correlations obtained
On the Two-Dimensionalization of Homogeneous Rotating Turbulence
NASA Technical Reports Server (NTRS)
Squires, K. D.; Cambon, C.; Mansor, N. N.; Rai, Man Mohan (Technical Monitor)
1994-01-01
Large-eddy simulation of the incompressible Navier-Stokes equations has been used to examine the long-time development of initially isotropic turbulence subjected to solid-body rotation. The simulations were carried out using a pseudo-spectral method with 128 x 128 x 512 collocation points in a computational domain that is four times larger along the rotation axis than in the other directions; subgrid-scale motions were parameterized using a spectral eddy viscosity model modified for system rotation. Simulation results show that the correlation length along the rotation am's of velocities orthogonal to the rotation vector exhibits rapid growth while the integral length-scale of velocities aligned with the rotation axis is relatively unaffected by rotation. Examination of the energy spectrum of two-dimensional, two-component motions indicates the presence of an inverse cascade of energy. System rotation also causes an alignment of vorticity along the rotation axis with relatively stronger cyclonic vorticity than anticyclonic. The onset of anisotropic effects are well characterized by Rossby numbers defined in terms of both macroscopic and microscopic quantities.
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.
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.
Stochastic estimation of organized turbulent structure - Homogeneous shear flow
NASA Technical Reports Server (NTRS)
Adrian, Ronald J.; Moin, Parviz
1988-01-01
A generalization of the conditional-eddy concept is proposed in which the conditional event specifies the local kinematic state in terms of the velocity and the deformation. Results are presented for stochastically estimated conditional eddies given the local kinematics. The equation governing the probability density function of a kinematic state has been derived for constant-property incompressible flow, providing a link between coherent flow structures corresponding to the conditional eddies and the modelling of turbulent transport. The primary contributions to the second-quadrant and fourth-quadrant Reynolds-stress events in homogeneous shear flow are shown to come from flow induced through the 'legs' and close to the 'heads' of upright and inverted 'hairpins', respectively.
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.
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.
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.
Refined similarity hypotheses in shell models of homogeneous turbulence and turbulent convection.
Ching, Emily S C; Guo, H; Lo, T S
2008-08-01
A major challenge in turbulence research is to understand from first principles the origin of the anomalous scaling of velocity fluctuations in high-Reynolds-number turbulent flows. One important idea was proposed by Kolmogorov [J. Fluid Mech. 13, 82 (1962)], which attributes the anomaly to variations of the locally averaged energy dissipation rate. Kraichnan later pointed out [J. Fluid Mech. 62, 305 (1973)] that the locally averaged energy dissipation rate is not an inertial-range quantity and a proper inertial-range quantity would be the local energy transfer rate. As a result, Kraichnan's idea attributes the anomaly to variations of the local energy transfer rate. These ideas, generally known as refined similarity hypotheses, can also be extended to study the anomalous scaling of fluctuations of an active scalar, such as the temperature in turbulent convection. We examine the validity of these refined similarity hypotheses and their extensions to an active scalar in shell models of homogeneous turbulence and turbulent convection. We find that Kraichnan's refined similarity hypothesis and its extension are valid.
NASA Astrophysics Data System (ADS)
Hackl, J. F.; Yeung, P. K.; Sawford, B. L.
2009-11-01
Numerical simulations at up to (4096^3) grid resolution have been conducted on machines with very large processor counts to obtain the statistics of Lagrangian particle pairs and tetrads in turbulent relative dispersion. Richardson-Obukhov scaling for mean-square pair separation adjusted for initial conditions is observed for intermediate initial separations, in support of prior estimates of about 0.6 for Richardson's constant. Simulations at (Rλ 650) have also been conducted for sufficient duration to obtain fully converged exit time statistics for independently moving particles at very large scales. The fact that all particle pairs reach such large scales of separation means the inertial subrange of exit times is also captured accurately. The results show Kolmogorov scaling for positive moments of exit time, but a strong dependence on initial separations for inverse moments. Inertial-range estimates of tetrad shape factors are reinforced by simulations at Taylor-scale Reynolds numbers up to about 1100. Tetrad shape parameters conditioned on cluster size are also examined in order to understand geometric features of turbulent dispersion in more detail.
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.
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.
A Lagrangian study of scalar diffusion in isotropic turbulence with chemical reaction
NASA Astrophysics Data System (ADS)
Mitarai, S.; Riley, J. J.; Kosály, G.
2003-12-01
Direct numerical simulations are performed of a single-step, nonpremixed, Arrhenius-type reaction developing in isotropic, incompressible, decaying turbulence, for conditions where flame extinction and re-ignition occur. The Lagrangian characteristics of scalar diffusion, information necessary for modeling approaches such as some implementations of probability density function (PDF) methods, are investigated by tracking fluid particles. Focusing on the mixture fraction and temperature as the scalar variables of interest, fluid particles are characterized as continuously burning or noncontinuously burning based upon their recent time history, and noncontinuously burning particles are further characterized based upon their initial regions relative to the flame zone. The behavior of the mixture fraction and temperature fields is contrasted for the different types of particles characterized. Significant differences among these characterized particles are found, for example, in the unclosed conditional expectations of scalar diffusion appearing in the composition PDF equations.
Anisotropic spectral modeling for unstably stratified homogeneous turbulence
NASA Astrophysics Data System (ADS)
Briard, Antoine; Iyer, Manasa; Gomez, Thomas
2017-04-01
In this work, a spectral model is derived to investigate numerically unstably stratified homogeneous turbulence (USHT) at large Reynolds numbers. The modeling relies on an earlier work for passive scalar dynamics [Briard et al., J. Fluid Mech. 799, 159 (2016), 10.1017/jfm.2016.362] and can handle both shear and mean scalar gradients. The extension of this model to the case of active scalar dynamics is the main theoretical contribution of this paper. This spectral modeling is then applied at large Reynolds numbers to analyze the scaling of the kinetic energy, scalar variance, and scalar flux spectra and to study as well the temporal evolution of the mixing parameter, the Froude number, and some anisotropy indicators in USHT. A theoretical prediction for the exponential growth rate of the kinetic energy, associated with our model equations, is derived and assessed numerically. Throughout the validation part, results are compared with an analogous approach, restricted to axisymmetric turbulence, which is more accurate in term of anisotropy description, but also much more costly in terms of computational resources [Burlot et al., J. Fluid Mech. 765, 17 (2015), 10.1017/jfm.2014.726]. It is notably shown that our model can qualitatively recover all the features of the USHT dynamics, with good quantitative agreement on some specific aspects. In addition, some remarks are proposed to point out the similarities and differences between the physics of USHT, shear flows, and passive scalar dynamics with a mean gradient, the two latter configurations having been addressed previously with the same closure. Moreover, it is shown that the anisotropic part of the pressure spectrum in USHT scales in k-11 /3 in the inertial range, similarly to the one in shear flows. Finally, at large Schmidt numbers, a different spectral range is found for the scalar flux: It first scales in k-3 around the Kolmogorov scale and then further in k-1 in the viscous-convective range.
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.
Calculation of velocity structure functions for vortex models of isotropic turbulence
Saffman, P.G.; Pullin, D.I.
1996-11-01
Velocity structure functions ({ital u}{sub {ital p}}{sup {prime}}{minus}{ital u}{sub {ital p}}){sup {ital m}} are calculated for vortex models of isotropic turbulence. An integral operator is introduced which defines an isotropic two-point field from a volume-orientation average for a specific solution of the Navier{endash}Stokes equations. Applying this to positive integer powers of the longitudinal velocity difference then gives explicit formulas for ({ital u}{sub {ital p}}{sup {prime}}{minus}{ital u}{sub {ital p}}){sup {ital m}} as a function of order {ital m} and of the scalar separation {ital r}. Special forms of the operator are then obtained for rectilinear stretched vortex models of the Townsend{endash}Lundgren type. Numerical results are given for the Burgers vortex and also for a realization of the Lundgren-strained spiral vortex, and comparison with experimental measurement is made. In an Appendix, we calculate values of the velocity-derivative moments for the Townsend{endash}Burgers model. {copyright} {ital 1996 American Institute of Physics.}
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.
NASA Astrophysics Data System (ADS)
Kassinos, S. C.
2000-11-01
A closed-form solution for the evolution of one-point statistics is derived for the case of initially two-dimensional three-component (2D-3C) homogeneous turbulence deformed by rapid shear in a rotating frame. Cases with and without stratification are considered. Except for small total shear, the analytical result is shown to be in good agreement with the numerical solution of the governing equations, linearized for rapid distortions, and solved for the more general initial case of 3D-3C isotropic homogeneous turbulence. Based on this agreement, we show that the closed-from solution provides insight into the stabilizing and destabilizing effects of frame rotation on homogeneous stratified shear flow, and provides a useful reference point for the one-point modeling of rotated and stratified shear flows. This analysis provides insights on the stability of stratified homogeneous shear flows that are missed by the standard two-dimensional two-component (2D-2C) treatment of stability issues in these flows.
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.
Direct numerical simulation of two-particle relative diffusion in isotropic turbulence
NASA Astrophysics Data System (ADS)
Yeung, P. K.
1994-10-01
The relative diffusion of fluid particle pairs in statistically stationary isotropic turbulence is studied by direct numerical simulation, at a Taylor-scale Reynolds number of about 90. The growth of two-particle separation exhibits asymptotic stages at small and large diffusion times. Through the two-particle separation, particle-pair velocity correlations are closely related to the Eulerian spatial structure of the turbulence. At large times, the square of the separation distance has a chi-square probability distribution. At the moderate Reynolds number of the simulations, for this asymptotic distribution to be reached before the particles begin to move independently of each other, the initial separation must be small compared to the Kolmogorov scale. In an inertial frame moving with the initial particle velocities, the velocity increments of two fluid particles become uncorrelated only if their initial velocities are uncorrelated, which requires their initial separation be large compared to the integral length scale. For sufficiently large initial separations, the relative velocity increments and mean-square dispersion in this moving frame display a resemblance to inertial range scaling, but with a proportionality constant that is much smaller than classical estimates. At large times, the degree of preferential alignment between the separation and relative velocity vectors is weak, but the product of the separation distance and the velocity component projected along the separation vector is sustained on average.
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.
NASA Astrophysics Data System (ADS)
Yu, Huidan; Meneveau, Charles
2010-11-01
We study the Lagrangian time evolution of velocity gradient dynamics near the Vieillefosse tail. The data are obtained from fluid particle tracking through the 1024^4 space-time DNS of forced isotropic turbulence at Reλ=433, using a web-based public database (http://turbulence.pha.jhu.edu). Examination of individual time-series of velocity gradient invariants R and Q show that they are punctuated by strong peaks of negative Q and positive R. Most of these occur very close to the Viellefosse tail along Q = - (3/2^2/3) R^2/3. It is found there that the magnitude of pressure Hessian has positive Lagrangian time-derivative, meaning that it increases in order to resist the rapid growth. We also observe a "phase delay" of the pressure Hessian signals compared to those of R and Q, indicative of an "overshoot" of the controlling mechanism. We also examine the trajectories in the recently proposed 3-D extension of the R-Q plane (see Lüthi B, Holzner M, Tsinober A. 2009, J. Fluid Mech. 641, 497-507). Finally, Lagrangian models of the velocity gradient tensor are examined in the same light to identify similarities and differences with the observed dynamics. Such comparisons supply informative guidance to model improvements.
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.
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
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.
Two-space, two-time similarity solution for decaying homogeneous turbulence
NASA Astrophysics Data System (ADS)
Byers, Clayton P.; Hultmark, Marcus; George, William K.
2017-02-01
A two-point, two-time similarity solution is derived for homogeneous decaying turbulence. This is the first known solution which includes the temporal decay at two-different times. It assumes that the turbulence is homogeneous in all three space dimensions, and finds that homogeneity holds across time. The solutions show that time is logarithmically "stretched" while the homogeneous spatial scales grow. This solution reduces to the two point, single time equation when the two times are set equal. The turbulence initially decays exponentially, then asymptotically as t-n where n ≥1 and equality is possible only if the initial energy is infinite. The methodology should be applicable to other non-equilibrium homogeneous turbulent flows.
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.
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.
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.
Turbulent properties in a homogeneous tidal bottom boundary layer
NASA Astrophysics Data System (ADS)
Sanford, Thomas B.; Lien, Ren-Chieh
1999-01-01
Profiles of mean and turbulent velocity and vorticity in a tidal bottom boundary layer are reported. Friction velocities estimated (1) by the profile method using the time mean streamwise velocity, (2) by the eddy-correlation method using the turbulent Reynolds stress, and (3) by the dissipation method using the turbulent kinetic energy dissipation rate ɛ are in good agreement. The mean streamwise velocity component exhibits two distinct log layers. In both layers, ɛ is inversely proportional to the distance from the bottom Z. The lower log layer occupies the bottom 3 m. In this layer, the turbulent Reynolds stress is nearly constant. The dynamics in the lower log layer are directly related to the stress induced by the seabed. The upper log layer spans 5 to 12 m above the bottom. In this layer, the turbulent Reynolds stress decreases toward the surface. The friction velocity estimated by the profile method in the upper log layer is about 1.8 times of that estimated in the lower log layer. Form drag might be important in the upper log layer. A detailed study of upstream topography is required for the bed stress estimate. The mean profile of vertical flux of spanwise vorticity is nearly uniform with Z and is at least a factor of 5 larger than the vertical divergence of turbulent Reynolds stress to which it may be compared. A new method of estimating the friction velocity is proposed that uses the vertical flux of turbulent spanwise vorticity. This is supported by the fact that the vertical eddy diffusivity for the turbulent vorticity is about equal in magnitude and vertical structure to the eddy viscosity for the turbulent momentum. The friction velocity calculated from the vorticity flux is equal to that estimated by the other three methods. Turbulent enstrophy, corrected for the sensor response function, is proportional to Z-1 for the entire water column. The relation between ɛ and enstrophy for high-Reynolds-number flows is confirmed by our observations.
Particle dispersion in homogeneous turbulence using the one-dimensional turbulence model
Sun, Guangyuan; Lignell, David O.; Hewson, John C.; ...
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
Intermittency in the isotropic component of helical and nonhelical turbulent flows
NASA Astrophysics Data System (ADS)
Martin, L. N.; Mininni, P. D.
2010-01-01
We analyze the isotropic component of turbulent flows spanning a broad range or Reynolds numbers. The aim is to identify scaling laws and their Reynolds number dependence in flows under different mechanical forcings. To this end, we applied an SO(3) decomposition to data stemming from direct numerical simulations with spatial resolutions ranging from 643 to 10243 grid points, and studied the scaling of high order moments of the velocity field. The study was carried out for two different flows obtained forcing the system with a Taylor-Green vortex or the Arn’old-Beltrami-Childress flow. Our results indicate that helicity has no significant impact on the scaling exponents as obtained from the generalized structure functions. Intermittency effects increase with the Reynolds number in the range of parameters studied, and in some cases are larger than what can be expected from several models of intermittency in the literature. The observed dependence of intermittency with the Reynolds number decreases if extended self-similarity is used to estimate the exponents.
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)
Rani, Sarma; Koch, Donald
2012-11-01
In this study, we derived the Fokker-Planck equation governing the PDF of pair separation and relative velocity vectors of high St particles. The PDF equation contains a particle-pair diffusion coefficient in relative velocity space. We developed an analytical theory to predict this relative velocity-space pair diffusion coefficient in the limit of high St . Using the diffusion coefficient, Langevin-equation-based stochastic simulations were performed to evolve pair separation and velocity vectors in isotropic turbulence for particle Stokes numbers, St = 1 , 2 , 4 , 10 ,and, 20 and a Taylor micro-scale Reynolds number, Reλ = 75 . The most significant finding from the Langevin simulations is that our pair diffusivity theory successfully captures the transition of relative velocity PDF from a Gaussian PDF at separations of the order of integral length scale to a non-Gaussian PDF at smaller separations. The pair radial distribution functions (RDFs) computed using our theory show that as the Stokes number increased, particles preferentially accumulate even at integral length scale separations. Another significant finding of our approach is that the slope of RDF at Kolmogorov length scale separations for higher St particles is not zero.
NASA Astrophysics Data System (ADS)
Sun, P.; Jokipii, J. R.; Giacalone, J.
2016-12-01
Anisotropies in astrophysical turbulence has been proposed and observed for a long time. And recent observations adopting the multi-scale analysis techniques provided a detailed description of the scale-dependent power spectrum of the magnetic field parallel and perpendicular to the scale-dependent magnetic field line at different scales in the solar wind. In the previous work, we proposed a multi-scale method to synthesize non-isotropic turbulent magnetic field with pre-determined power spectra of the fluctuating magnetic field as a function of scales. We present the effect of test particle transport in the resulting field with a two-scale algorithm. We find that the scale-dependent turbulence anisotropy has a significant difference in the effect on charged par- ticle transport from what the isotropy or the global anisotropy has. It is important to apply this field synthesis method to the solar wind magnetic field based on spacecraft data. However, this relies on how we extract the power spectra of the turbulent magnetic field across different scales. In this study, we propose here a power spectrum synthesis method based on Fourier analysis to extract the large and small scale power spectrum from a single spacecraft observation with a long enough period and a high sampling frequency. We apply the method to the solar wind measurement by the magnetometer onboard the ACE spacecraft and regenerate the large scale isotropic 2D spectrum and the small scale anisotropic 2D spectrum. We run test particle simulations in the magnetid field generated in this way to estimate the transport coefficients and to compare with the isotropic turbulence model.
Self-similar spiral flow structure in low Reynolds number isotropic and decaying turbulence
NASA Astrophysics Data System (ADS)
Vassilicos, J. C.; Brasseur, James G.
1996-07-01
It is rigorously proved for axisymmetric incompressible flows with bounded axial vorticity at infinity that if a spiral-helical streamline has a Kolmogorov capacity (box-counting dimension) DK>~1, then the velocity field must have a singularity at the axis of symmetry. Furthermore, certain types of singularity with DK=1 can be excluded. The Burgers and the Lundgren vortices are examples of strained vortices with different types of near-singular structure, and in both cases sections of streamlines have a well-defined DK>~1. However, the strain severely limits the region in space where DK is larger than 1. An algorithm is developed which detects streamlines with persistently strong curvature and calculates both the DK of the streamlines and the lower bound scale δmin of the range of self-similar scaling defined by DK. Error bounds on DK are also computed. The use of this algorithm partly relies on the fact that two to three turns of a spiral are enough to determine a spiral's DK. We detect well-defined self-similar scaling in the geometry of streamlines around vortex tubes in decaying isotropic direct numerical simulation turbulence with exceptionally fine small-scale resolution and Reλ around 20. The measured values of DK vary from DK=1 to DK~=1.60, and in general the self-similar range of length scales over which DK is well defined extends over one decade and ends at one of two well-defined inner scales, one just above and the other just below the Kolmogorov microscale η. We identify two different types of accumulation of length scales with DK>~1 on streamlines around the vortex tubes in the simulated turbulence: an accumulation of the streamline towards a central axis of the vortex tube in a spiral-helical fashion, and a helical and axial accumulation of the streamline towards a limit circle at the periphery of the vortex tube. In the latter case, the limit circle lies in a region along the axis of the vortex tube where there is a rapid drop in enstrophy. The
NASA Astrophysics Data System (ADS)
Hartlep, Thomas; Cuzzi, Jeffrey N.; Weston, Brian
2017-03-01
Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into subvolumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, Re, finding good agreement with the asymptotic, infinite Re inertial range theory of Zaichik and Alipchenkov [New J. Phys. 11, 103018 (2009), 10.1088/1367-2630/11/10/103018]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.
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
Compressibility effects on the growth and structure of homogeneous turbulent shear flow
NASA Technical Reports Server (NTRS)
Blaisdell, G. A.; Reynolds, W. C.; Mansour, N. N.
1991-01-01
Direct numerical simulations of compressible homogeneous turbulent shear flow are used to provide insight into compressibility effects on turbulence. The simulations show a reduction in the growth rate of the turbulence compared to the incompressible case. Examination of the turbulent kinetic energy budget shows that the reduced growth rate is due to an increase in the dissipation rate due to the divergence of the velocity and to the pressure-dilatation correlation which acts to transfer energy between internal energy and kinetic energy. The structure of the turbulence is also examined. Visualizations of the flowfields reveal the presence of eddy shocklets. These shock structures are important contributors to the increased dissipation of compressible turbulence. A mechanism for the generation of the shocks is suggested.
NASA Astrophysics Data System (ADS)
Lin, Chuangxin; Saleh, Ramin; Milkereit, Bernd; Liu, Qinya
2017-07-01
Sonic log records, including measurements of wave speeds in boreholes, provide critical input to the geological, geophysical, and petrophysical studies of a region under exploration. 1D background models are routinely built based on sonic log records for applications such as seismic imaging of hydrocarbon reservoirs and microseismic source inversions. Smoothing or `upscaling' techniques are required to produce models in coarser scales than the very fine layers in the raw log data. In this paper, we follow the recently popular homogenization theory, derive its application to the special case of 1D TI models for both P-SV and SH waves, and show that it is consistent with the Backus averaging technique commonly used to upscale 1D fine-layered models. We examine a study case of sonic log data from a well in the Horn River Basin in northeastern British Columbia, a region known for its tight shale-gas deposit. We demonstrate the computational accuracy and efficiency gained by proper upscaling procedures for spectral-element simulations of seismic wave propagation, and discuss the effect of control parameters on wavefield recovery.
A formal derivation of the local energy transfer (LET) theory of homogeneous turbulence
NASA Astrophysics Data System (ADS)
McComb, W. D.; Yoffe, S. R.
2017-09-01
A statistical closure of the Navier-Stokes hierarchy which leads to equations for the two-point, two-time covariance of the velocity field for stationary, homogeneous isotropic turbulence is presented. It is a generalisation of the self-consistent field method due to Edwards (1964) for the stationary, single-time velocity covariance. The probability distribution functional P≤ft[\\mathbf{u},t\\right] is obtained, in the form of a series, from the Liouville equation by means of a perturbation expansion about a Gaussian distribution, which is chosen to give the exact two-point, two-time covariance. The triple moment is calculated in terms of an ensemble-averaged infinitesimal velocity-field propagator, and shown to yield the Edwards result as a special case. The use of a Gaussian zero-order distribution has been found to justify the introduction of a fluctuation-response relation, which is in accord with modern dynamical theories. In a sense this work completes the analogy drawn by Edwards between turbulence and Brownian motion. Originally Edwards had shown that the noise input was determined by the correlation of the velocity field with the externally applied stirring forces but was unable to determine the system response. Now we find that the system response is determined by the correlation of the velocity field with internal quasi-entropic forces. This analysis is valid to all orders of perturbation theory, and allows the recovery of the local energy transfer (LET) theory, which had previously been derived by more heuristical methods. The LET theory is known to be in good agreement with experimental results. It is also unique among two-point statistical closures in displaying an acceptable (i.e. non-Markovian) relationship between the transfer spectrum and the system response, in accordance with experimental results. As a result of the latter property, it is compatible with the Kolmogorov (K41) spectral phenomenology. In memory of Professor Sir Sam Edwards F
Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence.
Bragg, Andrew D; Ireland, Peter J; Collins, Lance R
2015-08-01
In this paper, we consider the physical mechanism for the clustering of inertial particles in the inertial range of isotropic turbulence. We analyze the exact, but unclosed, equation governing the radial distribution function (RDF) and compare the mechanisms it describes for clustering in the dissipation and inertial ranges. We demonstrate that in the limit Str≪1, where Str is the Stokes number based on the eddy turnover time scale at separation r, the clustering in the inertial range can be understood to be due to the preferential sampling of the coarse-grained fluid velocity gradient tensor at that scale. When Str≳O(1) this mechanism gives way to a nonlocal clustering mechanism. These findings reveal that the clustering mechanisms in the inertial range are analogous to the mechanisms that we identified for the dissipation regime [see New J. Phys. 16, 055013 (2014)]. Further, we discuss the similarities and differences between the clustering mechanisms we identify in the inertial range and the "sweep-stick" mechanism developed by Coleman and Vassilicos [Phys. Fluids 21, 113301 (2009)]. We show that the idea that initial particles are swept along with acceleration stagnation points is only approximately true because there always exists a finite difference between the velocity of the acceleration stagnation points and the local fluid velocity. This relative velocity is sufficient to allow particles to traverse the average distance between the stagnation points within the correlation time scale of the acceleration field. We also show that the stick part of the mechanism is only valid for Str≪1 in the inertial range. We emphasize that our clustering mechanism provides the more fundamental explanation since it, unlike the sweep-stick mechanism, is able to explain clustering in arbitrary spatially correlated velocity fields. We then consider the closed, model equation for the RDF given in Zaichik and Alipchenkov [Phys. Fluids 19, 113308 (2007)] and use this
Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence
Bragg, Andrew D.; Ireland, Peter J.; Collins, Lance R.
2015-08-27
In this study, we consider the physical mechanism for the clustering of inertial particles in the inertial range of isotropic turbulence. We analyze the exact, but unclosed, equation governing the radial distribution function (RDF) and compare the mechanisms it describes for clustering in the dissipation and inertial ranges. We demonstrate that in the limit St_{r} <<1, where St_{r} is the Stokes number based on the eddy turnover time scale at separation r, the clustering in the inertial range can be understood to be due to the preferential sampling of the coarse-grained fluid velocity gradient tensor at that scale. When St_{r}≳O(1) this mechanism gives way to a nonlocal clustering mechanism. These findings reveal that the clustering mechanisms in the inertial range are analogous to the mechanisms that we identified for the dissipation regime. Further, we discuss the similarities and differences between the clustering mechanisms we identify in the inertial range and the “sweep-stick” mechanism developed by Coleman and Vassilicos. We show that the idea that initial particles are swept along with acceleration stagnation points is only approximately true because there always exists a finite difference between the velocity of the acceleration stagnation points and the local fluid velocity. This relative velocity is sufficient to allow particles to traverse the average distance between the stagnation points within the correlation time scale of the acceleration field. We also show that the stick part of the mechanism is only valid for St_{r}<<1 in the inertial range. We emphasize that our clustering mechanism provides the more fundamental explanation since it, unlike the sweep-stick mechanism, is able to explain clustering in arbitrary spatially correlated velocity fields. We then consider the closed, model equation for the RDF given in Zaichik and Alipchenkov and use this, together with the results from our analysis, to predict the
Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence
Bragg, Andrew D.; Ireland, Peter J.; Collins, Lance R.
2015-08-27
In this study, we consider the physical mechanism for the clustering of inertial particles in the inertial range of isotropic turbulence. We analyze the exact, but unclosed, equation governing the radial distribution function (RDF) and compare the mechanisms it describes for clustering in the dissipation and inertial ranges. We demonstrate that in the limit Str <<1, where Str is the Stokes number based on the eddy turnover time scale at separation r, the clustering in the inertial range can be understood to be due to the preferential sampling of the coarse-grained fluid velocity gradient tensor at that scale. When Str≳O(1)more » this mechanism gives way to a nonlocal clustering mechanism. These findings reveal that the clustering mechanisms in the inertial range are analogous to the mechanisms that we identified for the dissipation regime. Further, we discuss the similarities and differences between the clustering mechanisms we identify in the inertial range and the “sweep-stick” mechanism developed by Coleman and Vassilicos. We show that the idea that initial particles are swept along with acceleration stagnation points is only approximately true because there always exists a finite difference between the velocity of the acceleration stagnation points and the local fluid velocity. This relative velocity is sufficient to allow particles to traverse the average distance between the stagnation points within the correlation time scale of the acceleration field. We also show that the stick part of the mechanism is only valid for Str<<1 in the inertial range. We emphasize that our clustering mechanism provides the more fundamental explanation since it, unlike the sweep-stick mechanism, is able to explain clustering in arbitrary spatially correlated velocity fields. We then consider the closed, model equation for the RDF given in Zaichik and Alipchenkov and use this, together with the results from our analysis, to predict the analytic form of the RDF in the
Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence
NASA Astrophysics Data System (ADS)
Bragg, Andrew D.; Ireland, Peter J.; Collins, Lance R.
2015-08-01
In this paper, we consider the physical mechanism for the clustering of inertial particles in the inertial range of isotropic turbulence. We analyze the exact, but unclosed, equation governing the radial distribution function (RDF) and compare the mechanisms it describes for clustering in the dissipation and inertial ranges. We demonstrate that in the limit Str≪1 , where Str is the Stokes number based on the eddy turnover time scale at separation r , the clustering in the inertial range can be understood to be due to the preferential sampling of the coarse-grained fluid velocity gradient tensor at that scale. When Str≳O (1 ) this mechanism gives way to a nonlocal clustering mechanism. These findings reveal that the clustering mechanisms in the inertial range are analogous to the mechanisms that we identified for the dissipation regime [see New J. Phys. 16, 055013 (2014), 10.1088/1367-2630/16/5/055013]. Further, we discuss the similarities and differences between the clustering mechanisms we identify in the inertial range and the "sweep-stick" mechanism developed by Coleman and Vassilicos [Phys. Fluids 21, 113301 (2009), 10.1063/1.3257638]. We show that the idea that initial particles are swept along with acceleration stagnation points is only approximately true because there always exists a finite difference between the velocity of the acceleration stagnation points and the local fluid velocity. This relative velocity is sufficient to allow particles to traverse the average distance between the stagnation points within the correlation time scale of the acceleration field. We also show that the stick part of the mechanism is only valid for Str≪1 in the inertial range. We emphasize that our clustering mechanism provides the more fundamental explanation since it, unlike the sweep-stick mechanism, is able to explain clustering in arbitrary spatially correlated velocity fields. We then consider the closed, model equation for the RDF given in Zaichik and
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.
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.
The Theory of Nearly Incompressible Magnetohydrodynamic Turbulence: Homogeneous Description
NASA Astrophysics Data System (ADS)
Zank, G. P.; Adhikari, L.; Hunana, P.; Shiota, D.; Bruno, R.; Telloni, D.; Avinash, K.
2017-09-01
The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed to understand the apparent incompressibility of the solar wind and other plasma environments, particularly the relationship of density fluctuations to incompressible manifestations of turbulence in the solar wind and interstellar medium. Of interest was the identification of distinct leading-order incompressible descriptions for plasma beta β ≫ 1 and β ∼ 1 or ≪ 1 environments. In the first case, the “dimensionality” of the MHD description is 3D whereas for the latter two, there is a collapse of dimensionality in that the leading-order incompressible MHD description is 2D in a plane orthogonal to the large-scale or mean magnetic field. Despite the success of NI MHD in describing fluctuations in a low-frequency plasma environment such as the solar wind, a basic turbulence description has not been developed. Here, we rewrite the NI MHD system in terms of Elsässer variables. We discuss the distinction that emerges between the three cases. However, we focus on the β ∼ 1 or ≪ 1 regimes since these are appropriate to the solar wind and solar corona. In both cases, the leading-order turbulence model describes 2D turbulence and the higher-order description corresponds to slab turbulence, which forms a minority component. The Elsäasser β ∼ 1 or ≪ 1 formulation exhibits the nonlinear couplings between 2D and slab components very clearly, and shows that slab fluctuations respond in a passive scalar sense to the turbulently evolving majority 2D component fluctuations. The coupling of 2D and slab fluctuations through the β ∼ 1 or ≪ 1 NI MHD description leads to a very natural emergence of the “Goldreich-Sridhar” critical balance scaling parameter, although now with a different interpretation. Specifically, the critical balance parameter shows that the energy flux in wave number space is a consequence of the intensity of Alfvén wave sweeping versus passive scalar
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.
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.
Critical assessment of Reynolds stress turbulence models using homogeneous flows
NASA Astrophysics Data System (ADS)
Shabbir, Aamir; Shih, Tsan-Hsing
1992-12-01
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.
NASA Astrophysics Data System (ADS)
Tryka, S.
2014-07-01
The multidomain integral equation method is used to calculate fluxes of radiation from various on- and off-axis point sources passing through two different homogeneous isotropic media and striking a surface of a circular disc perpendicular to the optical axes of these sources. This method is dedicated to radiation passing through attenuating or nonattenuating media with a Fresnel interface and is applicable for arbitrary radiation patterns of point sources. The paper presents, firstly, the generalized multidomain integral equation method, expressed by double iterated integrals, for calculating radiant fluxes from arbitrary emitting point sources. This generalized method is simplified then to the form of multidomain single integral equation method applicable for rotationally symmetrical radiation patterns with optical axes perpendicular to the disc. Next, the simplified method is used for computer simulation of radiant fluxes incident on the disc from small Lambertian and Gaussian sources represented by point source models. All numerical results obtained from this simulation have shown high accuracy and efficiency of the presented method. Selected results are illustrated graphically and validated by Optical Software for Layout and Optimization (OSLO) from Lambda Research Corporation. Potential applications of the presented method include optical sensing and metrology, optical coupling, immersion microscopes, light-extraction problems and creative lighting design.
NASA Astrophysics Data System (ADS)
Pavlov, V. M.
2009-10-01
A new method is proposed for calculating synthetic seismograms caused by a force in a plane-parallel medium consisting of homogeneous elastic isotropic layers. The matrix impedance, i.e., the matrix function of depth, by which motion vector must be multiplied in order to obtain the stress vector, is introduced for solving a system of ordinary differential equations with respect to the motion-stress vector, which appears during the separation of variables. An independent nonlinear equation is obtained for the impedance. The propagator for the motion vector is constructed with the aid of the impedance. The closed analytical formulas, which do not contain any exponents with positive indices, are obtained both for the impedance and for the motionvector propagator. The algorithm for the calculation of seismograms, free of limitations on the number and thickness of layers, as well as on the frequency range of interest, is constructed on the basis of these formulas. The algorithm is tested with the aid of an analytical solution.
NASA Astrophysics Data System (ADS)
Ferreira, Pedro O.; Pinho, Fernando T.; da Silva, Carlos B.
2016-12-01
A new subgrid-scale (SGS) model developed for large-eddy simulations (LES) of dilute polymer solutions, described by the finitely extensible nonlinear elastic constitutive equation closed with the Peterlin approximation, is presented. In this distortion similarity model (DSIM) the filtered conformation tensor evolution equation is based on the self-similarity of the polymer stretching terms, and on a global equilibrium of the trace of the conformation tensor, which is proportional to the elastic energy stored in the polymer molecules, while the SGS stresses are modelled with the classical Smagorinsky model. The DSIM closure is assessed in direct numerical simulations (DNS) of forced isotropic turbulence using classical a priori tests, and in a posteriori (LES) showing very good agreement with all the exact (filtered DNS) results. The DSIM model is simple to implement and computationally inexpensive and represents a major step forward in the numerical simulation of turbulent flows of Newtonian fluids with polymer additives.
NASA Astrophysics Data System (ADS)
Venkatachari, Balaji Shankar; Chang, Chau-Lyan
2016-11-01
The focus of this study is scale-resolving simulations of the canonical normal shock- isotropic turbulence interaction using unstructured tetrahedral meshes and the space-time conservation element solution element (CESE) method. Despite decades of development in unstructured mesh methods and its potential benefits of ease of mesh generation around complex geometries and mesh adaptation, direct numerical or large-eddy simulations of turbulent flows are predominantly carried out using structured hexahedral meshes. This is due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for unstructured meshes that can resolve multiple physical scales and flow discontinuities simultaneously. The CESE method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to accurately simulate turbulent flows using tetrahedral meshes. As part of the study, various regimes of the shock-turbulence interaction (wrinkled and broken shock regimes) will be investigated along with a study on how adaptive refinement of tetrahedral meshes benefits this problem. The research funding for this paper has been provided by Revolutionary Computational Aerosciences (RCA) subproject under the NASA Transformative Aeronautics Concepts Program (TACP).
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.
Wouchuk, J G; Huete Ruiz de Lira, C; Velikovich, A L
2009-06-01
An exact analytical model for the interaction between an isolated shock wave and an isotropic turbulent vorticity field is presented. The interaction with a single-mode two-dimensional (2D) divergence-free vorticity field is analyzed in detail, giving the time and space evolutions of the perturbed quantities downstream. The results are generalized to study the interaction of a planar shock wave with an isotropic three-dimensional (3D) or 2D preshock vorticity field. This field is decomposed into Fourier modes, and each mode is assumed to interact independently with the shock front. Averages of the downstream quantities are made by integrating over the angles that define the orientation of the upstream velocity field. The ratio of downstream/upstream kinetic energies is in good agreement with existing numerical and experimental results for both 3D and 2D preshock vorticity fields. The generation of sound and the sonic energy flux radiated downstream from the shock front is also discussed in detail, as well as the amplification of transverse vorticity across the shock front. The anisotropy is calculated for the far downstream fields of both velocity and vorticity. All the quantities characteristic of the shock-turbulence interaction are reduced to closed-form exact analytical expressions. They are presented as explicit functions of the two parameters that govern the dynamics of the interaction: the adiabatic exponent gamma and the shock Mach number M1 . These formulas are further reduced to simpler exact asymptotic expressions in the limits of weak and strong shock waves (M_{1}-11, M_{1}1) and high shock compressibility of the gas (gamma-->1) .
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.
The asymptotic state of rotating homogeneous turbulence at high Reynolds numbers
NASA Technical Reports Server (NTRS)
Squires, Kyle D.; Chasnov, Jeffrey R.; Mansour, Nagi N.; Cambon, Claude
1994-01-01
The long-time, asymptotic state of rotating homogeneous turbulence at high Reynolds numbers has been examined using large-eddy simulation of the incompressible Navier-Stokes equations. The simulations were carried out using 128 x 128 x 512 collocation points in a computational domain that is four times longer along the rotation axis than in the other directions. Subgrid-scale motions in the simulations were parameterized using a spectral eddy viscosity modified for system rotation. Simulation results show that in the asymptotic state the turbulence kinetic energy undergoes a power-law decay with an exponent which is independent of rotation rate, depending only on the low-wavenumber form of the initial energy spectrum. Integral lengthscale growth in the simulations is also characterized by power-law growth; the correlation length of transverse velocities exhibiting much more rapid growth than observed in non-rotating turbulence.
A study of compressibility effects on structure of homogeneous sheared turbulence
NASA Astrophysics Data System (ADS)
Riahi, M.; Chouchane, L.; Lili, T.
2007-07-01
A study of compressibility effects on structure and evolution of a sheared homogeneous turbulent flow is carried out using rapid distortion theory (RDT). The focus of this paper consists in validating RDT code by considering the direct numerical simulation (DNS) and RDT results of Simone [Simone, Coleman and Cambon, Fluid Mech. 330, 307 (1997)]. We will use this theory to clarify the physics of the compressible turbulent flows. An analysis of the behavior of different terms appearing in the turbulent kinetic energy and the Reynolds stress equations permit to well identify compressibility effects which allow us to analyze performance of the compressible model of Fujiwara and Arakawa concerning the pressure-dilatation correlation. The evaluation of this model stays in the field of RDT validity.
Generation of large-scale vorticity in a homogeneous turbulence with a mean velocity shear.
Elperin, Tov; Kleeorin, Nathan; Rogachevskii, Igor
2003-07-01
An effect of a mean velocity shear on a turbulence and on the effective force which is determined by the gradient of the Reynolds stresses is studied. Generation of a mean vorticity in a homogeneous incompressible nonhelical turbulent flow with an imposed mean velocity shear due to an excitation of a large-scale instability is found. The instability is caused by a combined effect of the large-scale shear motions ("skew-induced" deflection of equilibrium mean vorticity) and "Reynolds stress-induced" generation of perturbations of mean vorticity. Spatial characteristics of the instability, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This instability and the dynamics of the mean vorticity are associated with Prandtl's turbulent secondary flows.
NASA Astrophysics Data System (ADS)
Dou, Zhongwang; Bragg, Andrew; Hammond, Adam; Liang, Zach; Collins, Lance; Meng, Hui
2016-11-01
Effects of Reynolds number (Rλ) and Stokes number (St) on particle-pair relative velocity (RV) were studied using four-frame particle tracking in an enclosed turbulence chamber. Two tests were performed: varying Rλ between 246 and 357 at six St values, and varying St between 0.02 and 4.63 at five Rλ values. By comparing experimental and DNS results of mean inward particle-pair RV,
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.
Asymptotic stability of spectral-based PDF modeling for homogeneous turbulent flows
NASA Astrophysics Data System (ADS)
Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca
2015-11-01
Engineering models of turbulence, based on one-point statistics, neglect spectral information inherent in a turbulence field. It is well known, however, that the evolution of turbulence is dictated by a complex interplay between the spectral modes of velocity. For example, for homogeneous turbulence, the pressure-rate-of-strain depends on the integrated energy spectrum weighted by components of the wave vectors. The Interacting Particle Representation Model (IPRM) (Kassinos & Reynolds, 1996) and the Velocity/Wave-Vector PDF model (Van Slooten & Pope, 1997) emulate spectral information in an attempt to improve the modeling of turbulence. We investigate the evolution and asymptotic stability of the IPRM using three different approaches. The first approach considers the Lagrangian evolution of individual realizations (idealized as particles) of the stochastic process defined by the IPRM. The second solves Lagrangian evolution equations for clusters of realizations conditional on a given wave vector. The third evolves the solution of the Eulerian conditional PDF corresponding to the aforementioned clusters. This last method avoids issues related to discrete particle noise and slow convergence associated with Lagrangian particle-based simulations.
NASA Astrophysics Data System (ADS)
Xia, Zhenhua; Shi, Yipeng; Chen, Shiyi
2015-11-01
In this paper, two-way interactions between heavy point particles and forced compressible homogenous turbulence are simulated by using a localized artificial diffusivity scheme and an Eulerian-Lagrangian approach. The initial turbulent Mach number is around 1.0 and the Taylor Reynolds number is around 110. Seven different simulations of 106 particles with different particle densities (or Stokes number) are considered. The statistics of the compressible turbulence, such as the turbulence Mach number, kinetic energy, dilatation, and the kinetic energy spectra, from different simulations are compared with each other, and with the one-way undisturbed case. Our results show that the turbulence is suppressed if the two-way coupling backward interactions are considered, and the effect is more obvious if the density of particles is higher. The kinetic energy spectrum at larger Stokes number (higher density) exhibits a reduction at low wave numbers and an augmentation at high wave numbers, which is similar to those obtained in incompressible cases. The probability density functions of dilatation, and normal upstream Mach number of shocklets also show that the modulation to the shocklet statistics is more apparent for particles with higher density. We acknowledge the financial support provided by National Natural Science Foundation of China (Grants Nos. 11302006, and U1330107).
On the modification of particle dispersion in isotropic turbulence by free rotation of particle
NASA Astrophysics Data System (ADS)
Park, Yongnam; Lee, Changhoon
2008-11-01
Effect of a particle's spin is investigated numerically by considering the effect of lift occurring due to difference of rotations of a particle and of fluid such as the Saffman lift and Magnus force. These lift forces have been neglected in many previous works on particle-laden turbulence. The trajectory of particles can be changed by the lift forces, resulting in significant modification of the stochastic characteristics of heavy particles. Probability density functions and autocorrelations are examined of velocity, acceleration of solid particle and acceleration of fluid at the position of solid particle. Changes in velocity statistics are negligible but statistics related with acceleration are a little bit changed by particle's rotation. When a laden particle encounters with coherent structures during the motion, the particle's rotation might significantly affects the motion due to intermittently large fluid acceleration near coherent structures. The result can be used for development of stochastic model for particle dispersion. Detailed physical interpretation will be presented in the meeting.
Shy, S.S.; Yang, S.I.; Lin, W.J.; Su, R.C.
2005-10-01
This paper presents turbulent burning velocities, S{sub T}, of several premixed CH{sub 4}/diluent/air flames at the same laminar burning velocity S{sub L}=0.1 m/s for two equivalence ratios f=0.7 and 1.4 near flammability limits with consideration of radiation heat losses from small (N{sub 2} diluted) to large (CO{sub 2} diluted). Experiments are carried out in a cruciform burner, in which the long vertical vessel is used to provide a downward propagating premixed flame and the large horizontal vessel equipped with a pair of counterrotating fans and perforated plates can be used to generate an intense isotropic turbulence in the central region between the two perforated plates. Turbulent flame speeds are measured by four different arrangements of pairs of ion-probe sensors at different positions from the top to the bottom of the central region in the burner. It is found that the effect of gas velocity on S{sub T} measured in the central region can be neglected. Simultaneous measurements using the pressure transducer and ion-probe sensors show that the pressure rise due to turbulent burning has little influence on S{sub T}. These measurements prove the accuracy of the S{sub T} data. At f=0.7, the percentage of [(S{sub T}/S{sub L}){sub CO{sub 2}}-(S{sub T}/S{sub L}){sub N{sub 2}}]/(S{sub T}/S{sub L}){sub N{sub 2}} decreases gradually from -4 to -17% when values of u{sup '}/S{sub L} increase from 4 to 46, while at f=1.4 such decrease is much more abrupt from -19 to -53% when values of u{sup '}/S{sub L} only increase from 4 to 18. The larger the radiation losses, the smaller the values of S{sub T}. This decreasing effect is augmented by increasing u{sup '}/S{sub L} and is particularly pronounced for rich CH{sub 4} flames. When u{sup '}/S{sub L}=18, lean CO{sub 2} and/or N{sub 2}-diluted CH{sub 4} flames have much higher, 3.6 and/or 1.8 times higher, values of S{sub T}/S{sub L} than rich CO{sub 2} and/or N{sub 2}-diluted CH{sub 4} flames, respectively. It is found that
NASA Astrophysics Data System (ADS)
Linkmann, Moritz; Berera, Arjun; Goldstraw, Erin E.
2017-01-01
This paper examines the behavior of the dimensionless dissipation rate Cɛ for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for Cɛ applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote Cɛ ,∞ lie between 0.193 ≤Cɛ ,∞≤0.268 for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure Cɛ ,∞=0.223 .
Linkmann, Moritz; Berera, Arjun; Goldstraw, Erin E
2017-01-01
This paper examines the behavior of the dimensionless dissipation rate C_{ɛ} for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for C_{ɛ} applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote C_{ɛ,∞} lie between 0.193≤C_{ɛ,∞}≤0.268 for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure C_{ɛ,∞}=0.223.
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.
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.
Eulerian formulation of the interacting particle representation model of homogeneous turbulence
NASA Astrophysics Data System (ADS)
Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca
2016-10-01
The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the confines of a one-point model. In the original formulation [Kassinos and Reynolds, Center for Turbulence Research: Annual Research Briefs, 31-51 (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is reformulated in an Eulerian framework, and evolution equations are developed for the marginal probability density functions (PDFs). Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. A specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.
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 Technical Reports Server (NTRS)
Madnia, C. K.; Frankel, S. H.; Givi, P.
1992-01-01
The presently obtained closed-form analytical expressions, which predict the limiting rate of mean reactant conversion in homogeneous turbulent flows under the influence of a binary reaction, are derived via the single-point pdf method based on amplitude mapping closure. With this model, the maximum rate of the mean reactant's decay can be conveniently expressed in terms of definite integrals of the parabolic cylinder functions. The results obtained are shown to be in good agreement with data generated by direct numerical simulations.
An Analytical Model for the Three-Point Third-Order Velocity Correlation in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Chang, Henry; Moser, Robert
2006-11-01
In turbulent flows, the three-point third-order velocity correlation Tijk(r,r') =
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.
Turbulent intermittent structure in non-homogeneous non-local flows
NASA Astrophysics Data System (ADS)
Mahjoub, O. B.; Castilla, R.; Vindel, J. M.; Redondo, J. M.
2010-05-01
Data from SABLES98 experimental campaign have been used in order to study the influence of stability (from weak to strong stratification) on intermittency [1]. Standard instrumentation, 14 thermocouples and 3 sonic anemometers at three levels (5.8, 13.5 and 32 m) were available in September 1998 and calculations are done in order to evaluate structure functions and the scale to scale characteristics. Using BDF [2-4] as well as other models of cascades, the spectral equilibrium values were used to calculate fluxes of momentum and heat as well as non-homogeneous models and the turbulent mixing produced. The differences in structure and higher order moments between stable, convective and neutral turbulence were used to identify differences in turbulent intermittent mixing and velocity PDF's. The intermittency of atmospheric turbulence in strongly stable situations affected by buoyancy and internal waves are seen to modify the structure functions exponents and intermittency, depending on the modulus of the Richardson's number,Ri, as well as of the Monin-Obukhov and Ozmidov lengthscales. The topological aspects of the turbulence affected by stratification reduce the vertical length-scales to a maximum described by the Thorpe and the Ozmidov lenth-scales, but intermittency, Kurtosis and other higher order descriptors of the turbulence based on spectral wavelet analysis are also affected in a complex way [5,6]. The relationship between stratification, intermittency, µ(Ri) and the fractal dimension of the stable flows and between the dispersion, the fractal dimension are discussed. The data analyzed is from the campaign SABLES-98 at the north-west Iberian Peninsula plateau.(Cuxart et al. 2000). Conditional statistics of the relationship between µ(Ri) are confirmed as in (Vindel et al 2008)[4] and compared with laboratory experiments and with 2D-3D aspects of the turbulence cascade. The use of BDF [3] model comparing the corresponding relative scaling exponents which are
NASA Astrophysics Data System (ADS)
Dizaji, Farzad F.; Marshall, Jeffrey S.
2016-11-01
Modeling the response of interacting particles, droplets, or bubbles to subgrid-scale fluctuations in turbulent flows is a long-standing challenge in multiphase flow simulations using the Reynolds-Averaged Navier-Stokes approach. The problem also arises for large-eddy simulation for sufficiently small values of the Kolmogorov-scale particle Stokes number. This paper expands on a recently proposed stochastic vortex structure (SVS) method for modeling of turbulence fluctuations for colliding or otherwise interacting particles. An accelerated version of the SVS method was developed using the fast multipole expansion and local Taylor expansion approach, which reduces computation speed by two orders of magnitude compared to the original SVS method. Detailed comparisons are presented showing close agreement of the energy spectrum and probability density functions of various fields between the SVS computational model, direct numerical simulation (DNS) results, and various theoretical and experimental results found in the literature. Results of the SVS method for particle collision rate and related measures of particle interaction exhibit excellent agreement with DNS predictions for homogeneous turbulent flows. The SVS method was also used with adhesive particles to simulate formation of particle agglomerates with different values of the particle Stokes and adhesion numbers, and various measures of the agglomerate structure are compared to the DNS results.
Stochastic modeling of fluid-particle flows in homogeneous cluster-induced turbulence
NASA Astrophysics Data System (ADS)
Innocenti, Alessio; Chibbaro, Sergio; Fox, Rodney; Salvetti, Maria Vittoria
2016-11-01
Inertial particles in turbulent flows are characterized by preferential concentration and segregation and, at sufficient mass loading, dense clusters may spontaneously generate due to momentum coupling between the phases. These clusters in turn can generate and sustain turbulence in the fluid phase, which we refer to as cluster-induced turbulence (CIT). In the present work, we tackle the problem of homogeneous gravity driven CIT in the framework of a stochastic model, based on a Lagrangian formalism which includes naturally the Eulerian one. A rigorous formalism has been put forward focusing in particular on the terms responsible of the two-way coupling in the carrier phase, which is the key mechanism in this type of flow. Moreover, the decomposition of the particle-phase velocity into the spatially correlated and uncorrelated components has been used allowing to identify the contributions to the correlated fluctuating energy and to the granular temperature. Tests have been performed taking into account also the effects of collisions between particles. Results are compared against DNS, and they show a good accuracy in predicting first and second order moments of particle velocity and fluid velocity seen by particles.
Dynamic multiscaling in magnetohydrodynamic turbulence.
Ray, Samriddhi Sankar; Sahoo, Ganapati; Pandit, Rahul
2016-11-01
We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Low, B.-C.
1972-01-01
The generation of a magnetic field by statistically homogeneous, stationary velocity turbulence is considered. The generation of rms magnetic fluctuation is explicitly demonstrated in the limit of short turbulence correlation time. It is shown that the fluctuation associated with a growing or stationary mean field grows with time such that the ratio of the fluctuation and the square of the mean field tends to a steady value, which is a monotonically decreasing function of the growth rate of the mean field.
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 Astrophysics Data System (ADS)
Buzzicotti, Michele; Bhatnagar, Akshay; Biferale, Luca; Lanotte, Alessandra S.; Sankar Ray, Samriddhi
2016-11-01
We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or homogeneous Fourier set. We find a strong sensitivity (reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree of mode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by a tendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales and frequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are still connected by a dimensional bridge-relation which is independent of the degree of Fourier-mode decimation.
Pressure spectra for vortex models of fine-scale homogeneous turbulence
NASA Astrophysics Data System (ADS)
Pullin, D. I.
1995-04-01
Pressure spectra at large wave numbers are calculated for Lundgren-Townsend vortex models of the fine scales of homogeneous turbulence. Specific results are given for the Burgers vortex and also for the Lundgren-strained spiral vortex. For the latter case, it is found that the contribution to the shell-summed spectrum produced by the interaction between the axisymmetric and nonaxisymmetric components of the velocity field is proportional to k-7/3 (k=‖k‖ is the modulus of the wave number) in agreement with Kolmogorov-type dimensional arguments. Numerical estimates of the dimensionless prefactors for this component are obtained in Kolmogorov scaling variables and comparisons are made with results from the Batchelor-Kolmogorov theory, and with experimental measurement.
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)
Merino-Aceituno, Sara
2016-12-01
The isotropic 4-wave kinetic equation is considered in its weak formulation using model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at most linear. We also consider finite stochastic particle systems undergoing instantaneous coagulation-fragmentation phenomena and give conditions in which this system approximates the solution of the equation (mean-field limit).
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.
Yoshimatsu, Katsunori; Kawahara, Yasuhiro; Schneider, Kai; Okamoto, Naoya; Farge, Marie
2011-09-15
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 512{sup 3} 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.
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.
Kong, Bo; Fox, Rodney O.; Feng, Heng; ...
2017-02-16
An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less
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.
Experimental evidence of homogeneous superfluid turbulence in large-pore porous media
Maddocks, J.R.; Van Sciver, S.W. )
1994-09-01
Experimental results are presented for counterflow and isothermal coflow through large-pore porous materials, with porosities greater than 90% and permeabilities of order 10[sup [minus]11] m[sup 2]. Counterflow velocities ranging from 0.06 to 0.14 m/s were obtained. Because of the large-pore geometry, and the velocity range investigated, the superfluid is fully turbulent. The counterflow data are well described by the two-fluid model using the Schwarz model of homogeneous mutual friction, with a larger, empirically-modified, mutual friction coefficient. The same mutual friction model is applied to the coflow results, assuming that dissipation due to superfluid vortex interaction with the wall of the porous media is negligible. In this case, the normal-fluid and superfluid velocities are coupled through the mutual friction, and relative velocities in the range 0.00 to 0.10 m/s, the authors calculate relative velocities up to 0.07 m/s, and normal-fluid velocities in excess of 0.04 m/s. An interesting feature of the coflow pressure drop, as a function of the normal-fluid velocity, is that it is larger than the counterflow pressure drop by the ratio of the total density to the normal-fluid density.
NASA Astrophysics Data System (ADS)
Masterlark, Timothy
2003-11-01
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 the1995 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.
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.
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.
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.
On the Lundgren-Townsend model of turbulent fine scales
NASA Astrophysics Data System (ADS)
Pullin, D. I.; Saffman, P. G.
1993-01-01
Vorticity and velocity-derivative moments for homogeneous isotropic turbulence are calculated using the strained-spiral vortex model of turbulent fine scales given by Lundgren (1982). 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.
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.
NASA Astrophysics Data System (ADS)
Pratt, J.; Busse, A.; Müller, W.-C.; Watkins, N. W.; Chapman, S. C.
2017-06-01
We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average disperse most efficiently in the form of extreme value statistics and flow anisotropy via the geometric properties of the convex hulls. We use the convex hull surface geometry to examine the anisotropy that occurs in turbulent convection. Applying extreme value theory, we show that the maximal square extensions of convex hull vertices are well described by a classic extreme value distribution, the Gumbel distribution. During turbulent convection, intermittent convective plumes grow and accelerate the dispersion of Lagrangian tracers. Convex hull analysis yields information that supplements standard Lagrangian analysis of coherent turbulent structures and their influence on the global statistics of the flow.
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.
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 Astrophysics Data System (ADS)
Jin, Guodong; Zhang, Jian; He, Guo-Wei; Wang, Lian-Ping
2010-12-01
Particle-laden turbulent flow is a typical non-equilibrium process characterized by particle relaxation time τp and the characteristic timescale of the flows τf, in which the turbulent mixing of heavy particles is related to different scales of fluid motions. The preferential concentration (PC) of heavy particles could be strongly affected by fluid motion at dissipation-range scales, which presents a major challenge to the large-eddy simulation (LES) approach. The errors in simulated PC by LES are due to both filtering and the subgrid scale (SGS) eddy viscosity model. The former leads to the removal of the SGS motion and the latter usually results in a more spatiotemporally correlated vorticity field. The dependence of these two factors on the flow Reynolds number is assessed using a priori and a posteriori tests, respectively. The results suggest that filtering is the dominant factor for the under-prediction of the PC for Stokes numbers less than 1, while the SGS eddy viscosity model is the dominant factor for the over-prediction of the PC for Stokes numbers between 1 and 10. The effects of the SGS eddy viscosity model on the PC decrease as the Reynolds number and Stokes number increase. LES can well predict the PC for particle Stokes numbers larger than 10. An SGS model for particles with small and intermediate Stokes numbers is needed to account for the effects of the removed SGS turbulent motion on the PC.
Lim, Jong-Min; Swami, Archana; Gilson, Laura M; Chopra, Sunandini; Choi, Sungyoung; Wu, Jun; Langer, Robert; Karnik, Rohit; Farokhzad, Omid C
2014-06-24
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.
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
NASA Astrophysics Data System (ADS)
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
Energy and dissipation range spectra in the inertial range of homogeneous turbulence
NASA Astrophysics Data System (ADS)
Yakhot, V.; She, Z.-S.; Orszag, S. A.
A study is conducted of deviations from Kolmogorov's inertial-range scaling behavior using the dynamical 'renormalization group' (RNG) analysis of turbulence; RNG has been found to yield good predictions for inertial-range statistics including the Kolmogorov and the Batchelor-Obukhov-Corrsin constants. Attention is given to the implications of the deviations for higher-order statistics of small-scale turbulence. It was established by Edwards (1964) that the relation between the exponent of the inertial range energy spectrum and that of the Gaussian force correlation spectrum is independent of the perturbation expansion. It is presently shown that this relationship holds even for higher-order correlation functions.
Comparison of a correlation term-discard closure for decaying homogeneous turbulence with experiment
NASA Technical Reports Server (NTRS)
Deissler, R. G.
1979-01-01
Turbulence decay is calculated by using experimental initial conditions and discarding quadruple-correlation terms in the correlation equations. Agreement with experiment is good only for moderately small times, but there are no perceptible negative spectral energies even at large times.
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.
NASA Technical Reports Server (NTRS)
Kerr, R. M.
1985-01-01
The classical approach to the investigation of small-scale intermittency in turbulence is based on the higher-order derivative correlations such as skewness and flatness factors. In the study of the small scales, numerial simulations can provide more detail than experiments. In the present paper, a variety of velocity- and scalar-derivative correlations are calculated over a range of Reynolds numbers. Particular attention is given to third- and fourth-order correlations, taking into account also some fifth- and sixth-order correlations to allow comparisons with the phenomenological models. The governing equations are the incompresssible Navier-Stokes equation for the velocity and transport equation for a passive scalar. Two numerical codes are used for the simulations presented. Attention is given to details regarding the numerical method used, forcing, simulation parameters, spectra and skewnesses, and graphics.
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
Solar turbulent magnetic fields: surprisingly homogeneous distribution during the solar minimum
NASA Astrophysics Data System (ADS)
Kleint, L.; Berdyugina, S. V.; Shapiro, A. I.; Bianda, M.
2010-12-01
Context. Small-scale, weak magnetic fields are ubiquitous in the quiet solar atmosphere. Yet their properties and temporal and spatial variations are not well known. Aims: We have initiated a synoptic program, carried out at the Istituto Ricerche Solari Locarno (IRSOL), to investigate both turbulent, mixed-polarity magnetic fields and nearly horizontal, directed fields and their variation with the solar cycle. Methods: Through spectropolarimetric observations we monitor linear and circular polarization at the solar limb (5” on the disk) at five positional angles (N, NW, S, SW, W) with the sensitivity of ~10-5. In addition, we analyzed measurements taken at different limb distances. We measure signatures in the 5141 Å region including two C2 triplets and three Fe i lines. Linear polarization in these lines arises from scattering and can be modified via the Hanle effect in the presence of turbulent magnetic fields. Through the application of the differential Hanle effect to the C2 R-triplet line ratios and the use of a simplified line formation model, we are able to infer a strength of turbulent magnetic fields while using the P-triplet to further restrict it. A Zeeman analysis of Fe i Stokes V/I is used to evaluate flux densities of horizontally directed fields. Results: We conclude that weak fields were evenly distributed over the Sun during this solar minimum. The turbulent field strength was at least 4.7 ± 0.2 G, and it did not vary during the last two years. This result was complemented with earlier, mainly unpublished measurements in the same region, which extend our set to nearly one decade. A statistical analysis of these all data suggests that there could be a very small variation of the turbulent field strength (3σ-limit) since the solar maximum in 2000. The Zeeman analysis of Fe i Stokes V/I reveals weak horizontal flux densities of 3-8 G. Conclusions: Our results demonstrate the potential of long-term observations of small-scale magnetic fields
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.
Inflow Turbulence Generation Methods
NASA Astrophysics Data System (ADS)
Wu, Xiaohua
2017-01-01
Research activities on inflow turbulence generation methods have been vigorous over the past quarter century, accompanying advances in eddy-resolving computations of spatially developing turbulent flows with direct numerical simulation, large-eddy simulation (LES), and hybrid Reynolds-averaged Navier-Stokes-LES. The weak recycling method, rooted in scaling arguments on the canonical incompressible boundary layer, has been applied to supersonic boundary layer, rough surface boundary layer, and microscale urban canopy LES coupled with mesoscale numerical weather forecasting. Synthetic methods, originating from analytical approximation to homogeneous isotropic turbulence, have branched out into several robust methods, including the synthetic random Fourier method, synthetic digital filtering method, synthetic coherent eddy method, and synthetic volume forcing method. This article reviews major progress in inflow turbulence generation methods with an emphasis on fundamental ideas, key milestones, representative applications, and critical issues. Directions for future research in the field are also highlighted.
Premixed autoignition in compressible turbulence
NASA Astrophysics Data System (ADS)
Konduri, Aditya; Kolla, Hemanth; Krisman, Alexander; Chen, Jacqueline
2016-11-01
Prediction of chemical ignition delay in an autoignition process is critical in combustion systems like compression ignition engines and gas turbines. Often, ignition delay times measured in simple homogeneous experiments or homogeneous calculations are not representative of actual autoignition processes in complex turbulent flows. This is due the presence of turbulent mixing which results in fluctuations in thermodynamic properties as well as chemical composition. In the present study the effect of fluctuations of thermodynamic variables on the ignition delay is quantified with direct numerical simulations of compressible isotropic turbulence. A premixed syngas-air mixture is used to remove the effects of inhomogeneity in the chemical composition. Preliminary results show a significant spatial variation in the ignition delay time. We analyze the topology of autoignition kernels and identify the influence of extreme events resulting from compressibility and intermittency. The dependence of ignition delay time on Reynolds and turbulent Mach numbers is also quantified. Supported by Basic Energy Sciences, Dept of Energy, United States.
Rapid distortion analysis of high speed homogeneous turbulence subject to periodic shear
NASA Astrophysics Data System (ADS)
Bertsch, Rebecca L.; Girimaji, Sharath S.
2015-12-01
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.
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
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.
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.
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.
Helicity fluctuations in incompressible turbulent flows
NASA Technical Reports Server (NTRS)
Rogers, Michael M.; Moin, Parviz
1987-01-01
Results from direct numerical simulations of several homogeneous flows and fully developed turbulent channel flow indicate that the probability distribution function (pdf) of relative helicity density exhibits at most a 20 percent deviation from a flat distribution. Isotropic flows exhibit a slight helical nature but the presence of mean strain in homogeneous turbulence suppresses helical behavior. All the homogeneous turbulent flows studied show no correlation between relative helicity density and the dissipation of turbulent kinetic energy. The channel flow simulations indicate that, except for low-dissipation regions near the outer edge of the buffer layer, there is no tendency for the flow to be helical. The strong peaks in the relative helicity density pdf and the association of these peaks with regions of low dissipation found in previous simulations by Pelz et al.(1985) are not observed.
Development and application of an improved subgrid model for homogeneous turbulence
NASA Astrophysics Data System (ADS)
Chasnov, Jeffrey Robert
1990-08-01
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 used an eddy viscosity to simulate the net subgrid scale energy transfer. 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.
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.
NASA Astrophysics Data System (ADS)
Nesrullajev, Arif
2017-03-01
The thermo-optical properties of various types of textures (the homeotropic, planar, and tilted aligned and non-aligned textures) in liquid crystalline materials with smectic A mesophase have been investigated. Investigations have been carried out for large temperature interval and at the direct smectic A mesophase-isotropic liquid (SmA-I) and isotropic liquid-smectic A mesophase (I-SmA) phase transitions that have been carried out. Homogeneous mixtures of 4-n-octyl-4'-cyanobiphenyl with 4-n-decyl-4'-cyanobiphenyl were the objects of the investigations. Temperature dependences of the optical transmission for aligned and non-aligned textures have been measured. Temperature widths of the heterophase regions for the SmA-I and I-SmA phase transitions have been determined. The temperature shift in the optical transmission dependences to low temperatures for the reverse I-SmA phase transition temperatures and the thermal hysteresis has been found for the aligned and non-aligned textures.
NASA Astrophysics Data System (ADS)
Nesrullajev, Arif
2017-06-01
The thermo-optical properties of various types of textures (the homeotropic, planar, and tilted aligned and non-aligned textures) in liquid crystalline materials with smectic A mesophase have been investigated. Investigations have been carried out for large temperature interval and at the direct smectic A mesophase-isotropic liquid (SmA-I) and isotropic liquid-smectic A mesophase (I-SmA) phase transitions that have been carried out. Homogeneous mixtures of 4-n-octyl-4'-cyanobiphenyl with 4-n-decyl-4'-cyanobiphenyl were the objects of the investigations. Temperature dependences of the optical transmission for aligned and non-aligned textures have been measured. Temperature widths of the heterophase regions for the SmA-I and I-SmA phase transitions have been determined. The temperature shift in the optical transmission dependences to low temperatures for the reverse I-SmA phase transition temperatures and the thermal hysteresis has been found for the aligned and non-aligned textures.
NASA Astrophysics Data System (ADS)
Soulard, Olivier; Gréa, Benoît-Joseph
2017-07-01
The purpose of this work is to study the anisotropic properties of the inertial range of Rayleigh-Taylor and unstably stratified homogeneous (USH) turbulence. More precisely, we aim to understand the role played by the so-called zero-modes, i.e., modes that nullify the anisotropic part of transfer terms. To this end, we determine several characteristic properties of zero-modes using an eddy-damped quasinormal Markovianized (EDQNM) model. Then we perform a high-Reynolds-number EDQNM simulation of a USH flow and check whether the predicted zero-mode properties are indeed observed in this idealized setting. Finally, we carry out a large-eddy simulation of a Rayleigh-Taylor flow and verify if zero-modes can also be identified in this configuration. Among the main findings of this work, we show that the small-scale anisotropy of the velocity and concentration spectra is dominated by the nonlocal contribution of zero-modes rather than by the local action of buoyancy forces. As a result, we predict inertial scaling exponents close to -7 /3 (rather than -3 ) for the second-order harmonics of the velocity and concentration spectra. By contrast, the concentration flux spectrum remains controlled by buoyancy forces. Still, we show that the zero-mode contribution vanishes slowly as the Reynolds number increases. This translates into a slow convergence of the scaling exponent of the second-order harmonic of the concentration flux to -7 /3 .
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.
Homogeneous Quantum Electrodynamic Turbulence.
1992-10-01
classical Noether invariants of the system. Then the numerical method will be described, and numerical results will be presented. 2 In addition to...is also achieved by scattering particles whose ’interaction time’ is at least 10-21 seconds, i.e., ’resonant’ particles. 3. Noether Invariants The...well, fluctuating no more than 0.04 % during the run. 10 Thus, the Noether invariants of nomalization (i. e., total charge, probability, or particle
Anisotropic Particles in Turbulence
NASA Astrophysics Data System (ADS)
Voth, Greg A.; Soldati, Alfredo
2017-01-01
Anisotropic particles are common in many industrial and natural turbulent flows. When these particles are small and neutrally buoyant, they follow Lagrangian trajectories while exhibiting rich orientational dynamics from the coupling of their rotation to the velocity gradients of the turbulence field. This system has proven to be a fascinating application of the fundamental properties of velocity gradients in turbulence. When particles are not neutrally buoyant, they experience preferential concentration and very different preferential alignment than neutrally buoyant tracer particles. A vast proportion of the parameter range of anisotropic particles in turbulence is still unexplored, with most existing research focusing on the simple foundational cases of axisymmetric ellipsoids at low concentrations in homogeneous isotropic turbulence and in turbulent channel flow. Numerical simulations and experiments have recently developed a fairly comprehensive picture of alignment and rotation in these cases, and they provide an essential foundation for addressing more complex problems of practical importance. Macroscopic effects of nonspherical particle dynamics include preferential concentration in coherent structures and drag reduction by fiber suspensions. We review the models used to describe nonspherical particle motion, along with numerical and experimental methods for measuring particle dynamics.
A dynamic subgrid-scale model for compressible turbulence and scalar transport
NASA Technical Reports Server (NTRS)
Moin, P.; Squires, K.; Cabot, W.; Lee, S.
1991-01-01
The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.
Interaction of turbulence with a detonation wave
NASA Technical Reports Server (NTRS)
Jackson, T. L.; Hussaini, M. Y.; Ribner, H. S.
1993-01-01
This paper addresses a specific reactive-flow configuration, namely, the interaction of a detonation wave with convected homogeneous isotropic weak turbulence (which can be constructed by a Fourier synthesis of small-amplitude vorticity waves). The effect of chemical heat release on the rms fluctuations downstream of the detonation is presented as a function of Mach number. In addition, for the particular case of the von Karman spectrum, the one-dimensional power spectra of these flow quantities are given.
Interaction of turbulence with a detonation wave
NASA Technical Reports Server (NTRS)
Jackson, T. L.; Hussaini, M. Y.; Ribner, H. S.
1993-01-01
This paper addresses a specific reactive-flow configuration, namely, the interaction of a detonation wave with convected homogeneous isotropic weak turbulence (which can be constructed by a Fourier synthesis of small-amplitude vorticity waves). The effect of chemical heat release on the rms fluctuations downstream of the detonation is presented as a function of Mach number. In addition, for the particular case of the von Karman spectrum, the one-dimensional power spectra of these flow quantities are given.
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}.
Characterizing Wake Turbulence with Staring Lidar Measurements
NASA Astrophysics Data System (ADS)
Bastine, D.; Wächter, M.; Peinke, J.; Trabucchi, D.; Kühn, M.
2015-06-01
Lidar measurements in the German offshore wind farm Alpha Ventus were performed to investigate the turbulence characteristics of wind turbine wakes. In particular, we compare measurements of the free flow in the surroundings of the wind turbines with measurements in the inner region of a wake flow behind one turbine. Our results indicate that wind turbines modulate the turbulent structures of the flow on a wide range of scales. For the data of the wake flow, the power spectrum as well as the multifractal intermittency coefficient reveal features of homogeneous isotropic turbulence. Thus, we conjecture that on scales of the rotor a new turbulent cascade is initiated, which determines the features of the turbulent wake flow quite independently from the more complex wind flow in the surroundings of the turbine.
Lagrangian and Eulerian statistics in homogeneous, anisotropic flows
NASA Astrophysics Data System (ADS)
Iyer, Kartik; Bonaccorso, Fabio; Toschi, Federico; Biferale, Luca
2016-11-01
We report results from highly resolved direct numerical simulations of anisotropic homogeneous flows using up to 20483 collocations points. We examine a turbulent Kolmogorov flow with randomly correlated phases in order to recover space homogeneity on average. We present Eulerian and Lagrangian measurements concerning the universality of isotropic and anisotropic contributions using a systematic decomposition based on the eigenfunctions of the SO (3) group of rotations in three dimensions. Additionally, we discuss absolute dispersion statistics of particles in flows subjected to different large-scale anisotropies. ERC ADG NewTURB 2013.
Shielded Superconducting Linear Motor for Towed-Grid Studies of Quantum Turbulence
Liu Shuchen; Zhou Yihui; Ihas, Gary G.
2006-09-07
A motor is described which can pull a grid through a channel of pure superfluid 4He to produce homogeneous isotropic turbulence. The motor is composed of a superconducting solenoid inside a superconducting shield to minimize Joule and eddy current heating of the liquid helium. Computer simulations show the design to be feasible.
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.
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
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.
Study of Lagrangian characteristic times using direct numerical simulation of turbulence
NASA Technical Reports Server (NTRS)
Lee, C. H.; Bertoglio, J.-P.; Squires, K.; Ferziger, J. H.
1987-01-01
Direct numerical simulations and large eddy simulations of homogeneous isotropic turbulence are used to compute Lagrangian statistics of turbulence and, in particular, its time scales. The computed time scales are compared with the spectral times scales that are frequently used in Eddy Damped Quasi-Normal Markovian calculations of the spectrum. The time scale models are rather good at high wavenumber and the results point to directions for improvement of the time scales at low wavenumber.
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.
NASA Astrophysics Data System (ADS)
Zhang, Chi; Chernyshenko, Sergei
2016-11-01
A formal definition to the two hypotheses of the quasi-steady and quasi-homogeneous (QSQH) theory was proposed. The theory is supposed to explain the phenomenon of the large-scale structures influencing the small-scale structures in a turbulent boundary layer. Multi-objective optimisations were performed to find the optimal cut-off parameters for the new large-scale filters. The new filters were proved to obtain much more clear large-scale structures than the filter suggested by the previous studies. Calculations and comparisons for a set of statistical flow properties extracted from the databases of the direct numerical simulations of a plane channel flow were conducted. The accuracy of the predictions based on the QSQH theory was observed improving when the Reynolds number increases. Extrapolations of urms and two-points correlation from medium to high Reynolds number based on the QSQH approach were preformed and about 10 % accuracy was reported. The more interesting thing is that the QSQH theory implies a dependence of the mean profile log-law constants on the Reynolds number. The main overall result of the present work is the validations of the two hypotheses of the quasi-steady quasi-homogeneous theory in near-wall turbulent flows.
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.
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.
Vorticity spectra in high Reynolds number anisotropic turbulence
NASA Astrophysics Data System (ADS)
Morris, Scott C.; Foss, John F.
2005-08-01
Assuming a turbulent flow to be homogeneous and isotropic allows for significant theoretical simplification in the description of its motions. The validity of these assumptions, first put forth by Kolmogorov [A. N. Kolmogorov, "The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers," C. R. Acad. Sci. URSS 30, 301 (1941)], has been the subject of considerable analytical development and extensive research as they are applied to actual flows. The present investigation describes the one-dimensional vorticity spectra of two flow fields: a single stream shear layer and the near surface region of an atmospheric boundary layer. Both flow fields exhibit a power-law region with a slope of -1 in the one-dimensional spectra of the spanwise component of vorticity in the same wave-number range for which the velocity spectra indicated the isotropic behavior. This is in strong disagreement with the isotropic prediction, which does not exhibit a power-law behavior.
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.
Propagation of multi-Gaussian Schell-model vortex beams in isotropic random media.
Tang, Miaomiao; Zhao, Daomu
2015-12-14
The effect of isotropic and homogeneous random media on propagation characteristics of recently introduced multi-Gaussian Schell-model (MGSM) vortex beams is investigated. The analytical formula for the cross-spectral density function of such a beam propagating in random turbulent media is derived and used to explore the evolution of the spectral density, the degree of coherence and the turbulence-induced spreading. An example illustrates the fact that, at sufficiently large distance from the source, the source correlations modulation of the spectral distribution in free space is shown to be suppressed by the uniformly correlated turbulence. The impacts, arising from the index M, the correlation width of the source and the properties of the medium on such characteristics are analyzed in depth.
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.
Shell models of magnetohydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Plunian, Franck; Stepanov, Rodion; Frick, Peter
2013-02-01
Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models. In this review we set up a general mathematical framework allowing the description of any MHD shell model. The variety of the latter, with their advantages and weaknesses, is introduced. Finally we consider a number of applications, dealing with free-decaying MHD turbulence, dynamo action, Alfvén waves and the Hall effect.
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.
Shock-turbulence interactions in a reacting flow
NASA Technical Reports Server (NTRS)
Jackson, T. L.; Hussaini, M. Y.; Ribner, H. S.
1992-01-01
A specific reactive flow configuration, the interaction of a detonation wave with convected homogeneous isotropic weak turbulence (which can be constructed by a Fourier synthesis of small amplitude shear waves) is addressed. The effect of chemical heat release on the rms fluctuations downstream of the detonation is presented as a function of Mach number. In addition, for the particular case of the von Karman spectrum, the one dimensional power spectra of these flow quantities is given.
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.
Evaporation of polydispersed droplets in a highly turbulent channel flow
NASA Astrophysics Data System (ADS)
Cochet, M.; Bazile, Rudy; Ferret, B.; Cazin, S.
2009-09-01
A model experiment for the study of evaporating turbulent two-phase flows is presented here. The study focuses on a situation where pre-atomized and dispersed droplets vaporize and mix in a heated turbulent flow. The test bench consists in a channel flow with characteristics of homogeneous and isotropic turbulence where fluctuations levels reach very high values (25% in the established zone). An ultrasonic atomizer allows the injection of a mist of small droplets of acetone in the carrier flow. The large range diameters ensure that every kind of droplet behavior with regards to turbulence is possible. Instantaneous concentration fields of the vaporized phase are extracted from fluorescent images (PLIF) of the two phase flow. The evolution of the mixing of the acetone vapor is analyzed for two different liquid mass loadings. Despite the high turbulence levels, concentration fluctuations remain significant, indicating that air and acetone vapor are not fully mixed far from the injector.
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.
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.
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)
Xing, Yu; Liu, Peiqing; Guo, Hao
2017-03-01
In this paper, we explain why the Bolgiano-Obukhov (BO) scaling behavior is unavailable by the SabraT model proposed for turbulent thermal convection in the range of 1 < δ < 2, which is extended from the Sabra model by coupling temperature with velocity in the equations of motion as an external forcing, i.e., buoyancy. Numerical studies show that SabraT model is mainly governed by the enstrophy budget equation, at which the buoyancy is not always relevant to the statistical properties and the effect of buoyancy is dependent on the parameter γ that measures the ratio of enstrophy to energy. When buoyancy is important, BO scaling is expected using theoretical arguments, such as dimensional analysis. Instead of BO scaling, a new γ-dependent scaling behavior is setup in the buoyancy relevant regime, which is found to equivalently deviate from the enstrophy cascade scaling and BO scaling. This deviation is mainly discussed by two dimensionless parameters, which respectively measure the deviation of the energy/enstrophy transfer flux rate and the injected energy/enstrophy due to buoyancy from dimensional analysis. The introduced buoyancy plays as a relative small perturbed forcing on the Sabra model without changing much its intrinsical statistical properties, i.e., dimensional analysis is not always validated in both Sabra and SabraT models.
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.
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.
Modeling Rotating Turbulent Flows with the Body Force Potential Model.
NASA Astrophysics Data System (ADS)
Bhattacharya, Amitabh; Perot, Blair
2000-11-01
Like a Reynolds Stress Transport equation model, the turbulent potential model has an explicit Coriolis acceleration term that appears in the model that accounts for rotation effects. In this work the additional secondary effects that system rotation has on the dissipation rate, return-to-isotropy, and fast pressure strain terms are also included in the model. The resulting model is tested in the context of rotating isotropic turbulence, rotating homogeneous shear flow, rotating channel flow, and swirling pipe flow. Many of the model changes are applicable to Reynolds stress transport equation models. All model modifications are frame indifferent.
Three-dimensional time dependent computation of turbulent flow
NASA Technical Reports Server (NTRS)
Kwak, D.; Reynolds, W. C.; Ferziger, J. H.
1975-01-01
The three-dimensional, primitive equations of motion are solved numerically for the case of isotropic box turbulence and the distortion of homogeneous turbulence by irrotational plane strain at large Reynolds numbers. A Gaussian filter is applied to governing equations to define the large scale field. This gives rise to additional second order computed scale stresses (Leonard stresses). The residual stresses are simulated through an eddy viscosity. Uniform grids are used, with a fourth order differencing scheme in space and a second order Adams-Bashforth predictor for explicit time stepping. The results are compared to the experiments and statistical information extracted from the computer generated data.
Turbulent solutions of the equations of fluid motion
NASA Technical Reports Server (NTRS)
Deissler, R. G.
1984-01-01
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. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used in most of the work considered. 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. Thus randomness or turbulence can arise as a consequence of the structure of the Navier-Stokes equations. The cases considered include turbulence which is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A mean shear is present in some cases. 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.
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.
NASA Technical Reports Server (NTRS)
Wang, Chi R.; Yeh, Frederick C.
1987-01-01
A theoretical analysis and numerical calculations for the turbulent flow field and for the effect of free-stream turbulence on the surface heat transfer rate of a stagnation flow are presented. The emphasis is on the modeling of turbulence and its augmentation of surface heat transfer rate. The flow field considered is the region near the forward stagnation point of a circular cylinder in a uniform turbulent mean flow. The free stream is steady and incompressible with a Reynolds number of the order of 10 to the 5th power and turbulence intensity of less than 5 percent. For this analysis, the flow field is divided into three regions: (1) a uniform free-stream region where the turbulence is homogeneous and isotropic; (2) an external viscid flow region where the turbulence is distorted by the variation of the mean flow velocity; and, (3) an anisotropic turbulent boundary layer region over the cylinder surface. The turbulence modeling techniques used are the kappa-epsilon two-equation model in the external flow region and the time-averaged turbulence transport equation in the boundary layer region. The turbulence double correlations, the mean velocity, and the mean temperature within the boundary layer are solved numerically from the transport equations. The surface heat transfer rate is calculated as functions of the free-stream turbulence longitudinal microlength scale, the turbulence intensity, and the Reynolds number.
NASA Technical Reports Server (NTRS)
Frost, W.; Lin, M. C.
1983-01-01
Statistical properties of atmospheric turbulence near the Earth's surface are presented. Emphasis is placed on the probability density distribution two point spatial correlation, length scale, and two point and single point spectrum. Comparison of the data with isotropic homogeneous models is made. In general, agreement with the models is poor. For the design of aircraft during operations in the lower levels associated with approach, takeoff, and terrain following, it appears necessary to improve existing models or develop new nonisotropic turbulence models.
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.
Regimes of turbulence without an energy cascade
NASA Astrophysics Data System (ADS)
Barenghi, C. F.; Sergeev, Y. A.; Baggaley, A. W.
2016-10-01
Experiments and numerical simulations of turbulent 4He and 3He-B have established that, at hydrodynamic length scales larger than the average distance between quantum vortices, the energy spectrum obeys the same 5/3 Kolmogorov law which is observed in the homogeneous isotropic turbulence of ordinary fluids. The importance of the 5/3 law is that it points to the existence of a Richardson energy cascade from large eddies to small eddies. However, there is also evidence of quantum turbulent regimes without Kolmogorov scaling. This raises the important questions of why, in such regimes, the Kolmogorov spectrum fails to form, what is the physical nature of turbulence without energy cascade, and whether hydrodynamical models can account for the unusual behaviour of turbulent superfluid helium. In this work we describe simple physical mechanisms which prevent the formation of Kolmogorov scaling in the thermal counterflow, and analyze the conditions necessary for emergence of quasiclassical regime in quantum turbulence generated by injection of vortex rings at low temperatures. Our models justify the hydrodynamical description of quantum turbulence and shed light into an unexpected regime of vortex dynamics.
Regimes of turbulence without an energy cascade
Barenghi, C. F.; Sergeev, Y. A.; Baggaley, A. W.
2016-01-01
Experiments and numerical simulations of turbulent 4He and 3He-B have established that, at hydrodynamic length scales larger than the average distance between quantum vortices, the energy spectrum obeys the same 5/3 Kolmogorov law which is observed in the homogeneous isotropic turbulence of ordinary fluids. The importance of the 5/3 law is that it points to the existence of a Richardson energy cascade from large eddies to small eddies. However, there is also evidence of quantum turbulent regimes without Kolmogorov scaling. This raises the important questions of why, in such regimes, the Kolmogorov spectrum fails to form, what is the physical nature of turbulence without energy cascade, and whether hydrodynamical models can account for the unusual behaviour of turbulent superfluid helium. In this work we describe simple physical mechanisms which prevent the formation of Kolmogorov scaling in the thermal counterflow, and analyze the conditions necessary for emergence of quasiclassical regime in quantum turbulence generated by injection of vortex rings at low temperatures. Our models justify the hydrodynamical description of quantum turbulence and shed light into an unexpected regime of vortex dynamics. PMID:27761005
Chaotic Lagrangian models for turbulent relative dispersion
NASA Astrophysics Data System (ADS)
Lacorata, Guglielmo; Vulpiani, Angelo
2017-04-01
A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.
Chaotic Lagrangian models for turbulent relative dispersion.
Lacorata, Guglielmo; Vulpiani, Angelo
2017-04-01
A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.
EDQNM closure: A homogeneous simulation to support it. A quasi-homogeneous simulation to disprove it
NASA Technical Reports Server (NTRS)
Bertoglio, J. P.; Squires, K.; Ferziger, J. H.
1987-01-01
It is known that two-point closures are useful tools for understanding and predicting turbulence. Among the various closures, the Eddy Damped Quasi-Normal Markovian (EDQNM) approach is one of the simplest and, at the same time, most useful. Direct numerical simulations (DNS) can provide information that can be used to test the validity of two-point theories. It is the purpose of the present work to use DNS to validate, or improve upon, EDQNM. A case was selected for which EDQNM is known to give satisfactory results: homogeneous isotropic turbulence. Quantities were then evaluated which may be used to test the assumptions of two-point closure approximations: spectral Lagrangian time scales. The goal was to make a careful and refined study to validate the EDQNM theory. A reference case was built for which EDQNM is likely to give poor results. An attempt to generate a quasi-homogeneous turbulent field containing organized structures, was built by artifically injecting them in the initial conditions. The results of direct simulations using such initial conditions are expected to provide a challenge for EDQNM since this kind of field is simple enough to allow comparisons with two-point theories, but at the same time contains coherent structures which cannot be expected to be accurately accounted for by closures based on expansions about Gaussianity.
Investigation of the asymptotic state of rotating turbulence using large-eddy simulation
NASA Technical Reports Server (NTRS)
Squires, Kyle D.; Chasnov, Jeffrey R.; Mansour, Nagi N.; Cambon, Claude
1993-01-01
Study of turbulent flows in rotating reference frames has long been an area of considerable scientific and engineering interest. Because of its importance, the subject of turbulence in rotating reference frames has motivated over the years a large number of theoretical, experimental, and computational studies. The bulk of these previous works has served to demonstrate that the effect of system rotation on turbulence is subtle and remains exceedingly difficult to predict. A rotating flow of particular interest in many studies, including the present work, is examination of the effect of solid-body rotation on an initially isotropic turbulent flow. One of the principal reasons for the interest in this flow is that it represents the most basic turbulent flow whose structure is altered by system rotation but without the complicating effects introduced by mean strains or flow inhomogeneities. The assumption of statistical homogeneity considerably simplifies analysis and computation. The principal objective of the present study has been to examine the asymptotic state of solid-body rotation applied to an initially isotropic, high Reynolds number turbulent flow. Of particular interest has been to determine the degree of two-dimensionalization and the existence of asymptotic self-similar states in homogeneous rotating turbulence.
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.
Spatiotemporal velocity-velocity correlation function in fully developed turbulence
NASA Astrophysics Data System (ADS)
Canet, Léonie; Rossetto, Vincent; Wschebor, Nicolás; Balarac, Guillaume
2017-02-01
Turbulence is a ubiquitous phenomenon in natural and industrial flows. Since the celebrated work of Kolmogorov in 1941, understanding the statistical properties of fully developed turbulence has remained a major quest. In particular, deriving the properties of turbulent flows from a mesoscopic description, that is, from the Navier-Stokes equation, has eluded most theoretical attempts. Here, we provide a theoretical prediction for the functional space and time dependence of the velocity-velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to the Navier-Stokes equation with stochastic forcing. This prediction, which goes beyond Kolmogorov theory, is the analytical fixed point solution of nonperturbative renormalization group flow equations, which are exact in the limit of large wave numbers. This solution is compared to two-point two-times correlation functions computed in direct numerical simulations. We obtain a remarkable agreement both in the inertial and in the dissipative ranges.
The use of direct numerical simulation data in turbulence modeling
NASA Technical Reports Server (NTRS)
Mansour, N. N.
1991-01-01
Direct numerical simulations (DNS) of turbulent flows provide a complete data base to develop and to test turbulence models. In this article, the progress made in developing models for the dissipation rate equation is reviewed. New scaling arguments for the various terms in the dissipation rate equation were tested using data from DNS of homogeneous shear flows. Modifications to the epsilon-equation model that take into account near-wall effects were developed using DNS of turbulent channel flows. Testing of new models for flows under mean compression was carried out using data from DNS of isotropically compressed turbulence. In all of these studies the data from the simulations was essential in guiding the model development. The next generation of DNS will be at higher Reynolds numbers, and will undoubtedly lead to improved models for computations of flows of practical interest.
Can we remove the systematic error due to isotropic inhomogeneities?
NASA Astrophysics Data System (ADS)
Negishi, Hiroyuki; Nakao, Ken-ichi
2017-01-01
Usually, we assume that there is no inhomogeneity isotropic in terms of our location in our Universe. This assumption has not been observationally confirmed yet in sufficient accuracy, and we need to consider the possibility that there are non-negligible large-scale isotropic inhomogeneities in our Universe. The existence of large-scale isotropic inhomogeneities affects the determination of cosmological parameters. In particular, from only the distance-redshift relation, we cannot distinguish the inhomogeneous isotropic universe model from the homogeneous isotropic one, because of the ambiguity in the cosmological parameters. In this paper, in order to avoid such ambiguity, we consider three observables—the distance-redshift relation, the fluctuation spectrum of the cosmic microwave background radiation, and the scale of the baryon acoustic oscillation—and compare these observables in two universe models. One is the inhomogeneous isotropic universe model with the cosmological constant, and the other is the homogeneous isotropic universe model with dark energy other than the cosmological constant. We show that these two universe models cannot predict the same observational data of all three observables but the same ones of only two of three, as long as the perturbations are adiabatic. In principle, we can distinguish the inhomogeneous isotropic universe from the homogeneous isotropic one through the appropriate three observables, if the perturbations are adiabatic.
Schwartz, M.W.
1981-04-30
A probabilistic safety criterion for isotropic flywheel rotors is established based on the tolerated noncontainment failure rates of commercial aircraft turbojet engine rotors. A technique is developed combining reliability with fracture mechanics, and a sample calculation provided, to show the energy-storage levels that isotropic flywheel rotors could achieve within the constraints of this safety criterion.
NASA Astrophysics Data System (ADS)
Palmore, John; Desjardins, Olivier
2014-11-01
Low waveshell spectral forcing has been proven to be a simple and effective manner to generate isotropic turbulence in a periodic domain. This simplicity is lost for flow problems with complex boundary conditions such as resolved particle flows, fluid-fluid flows with interfaces, and wall-bounded flows. Lundgren's linear forcing in physical space is a straightforward and easy-to-implement method to tackle these problems; however, the use of this method results in a halving of the large turbulence length scale. The technique that will be presented in this talk applies a low-pass filter to the source term used in linear forcing. It is shown to recover the scale resolution of low waveshell spectral forcing which translates to an approximately 60 percent increase in the attainable Reynolds number for a given computation domain. The characteristics of homogeneous isotropic turbulence generated using filtered linear forcing will be discussed. Finally, extension of this idea to scalar forcing will be presented.
Regularization of turbulence - a comprehensive modeling approach
NASA Astrophysics Data System (ADS)
Geurts, B. J.
2011-12-01
Turbulence readily arises in numerous flows in nature and technology. The large number of degrees of freedom of turbulence poses serious challenges to numerical approaches aimed at simulating and controlling such flows. While the Navier-Stokes equations are commonly accepted to precisely describe fluid turbulence, alternative coarsened descriptions need to be developed to cope with the wide range of length and time scales. These coarsened descriptions are known as large-eddy simulations in which one aims to capture only the primary features of a flow, at considerably reduced computational effort. Such coarsening introduces a closure problem that requires additional phenomenological modeling. A systematic approach to the closure problem, know as regularization modeling, will be reviewed. Its application to multiphase turbulent will be illustrated in which a basic regularization principle is enforced to physically consistently approximate momentum and scalar transport. Examples of Leray and LANS-alpha regularization are discussed in some detail, as are compatible numerical strategies. We illustrate regularization modeling to turbulence under the influence of rotation and buoyancy and investigate the accuracy with which particle-laden flow can be represented. A discussion of the numerical and modeling errors incurred will be given on the basis of homogeneous isotropic turbulence.
Intermittency and universality in fully developed inviscid and weakly compressible turbulent flows.
Benzi, Roberto; Biferale, Luca; Fisher, Robert T; Kadanoff, Leo P; Lamb, Donald Q; Toschi, Federico
2008-06-13
We perform high-resolution numerical simulations of homogenous and isotropic compressible turbulence, with an average 3D Mach number close to 0.3. We study the statistical properties of intermittency for velocity, density, and entropy. For the velocity field, which is the only quantity that can be compared to the isotropic incompressible case, we find no statistical differences in its behavior in the inertial range due either to the slight compressibility or to the different dissipative mechanism. For the density field, we find evidence of "frontlike" structures, although no shocks are produced by the simulation.
Structure of the velocity gradient tensor in turbulent shear flows
NASA Astrophysics Data System (ADS)
Pumir, Alain
2017-07-01
The expected universality of small-scale properties of turbulent flows implies isotropic properties of the velocity gradient tensor in the very large Reynolds number limit. Using direct numerical simulations, we determine the tensors formed by n =2 and 3 velocity gradients at a single point in turbulent homogeneous shear flows and in the log-layer of a turbulent channel flow, and we characterize the departure of these tensors from the corresponding isotropic prediction. Specifically, we separate the even components of the tensors, invariant under reflexion with respect to all axes, from the odd ones, which identically vanish in the absence of shear. Our results indicate that the largest deviation from isotropy comes from the odd component of the third velocity gradient correlation function, especially from the third moment of the derivative along the normal direction of the streamwise velocity component. At the Reynolds numbers considered (Reλ≈140 ), we observe that these second- and third-order correlation functions are significantly larger in turbulent channel flows than in homogeneous shear flow. Overall, our work demonstrates that a mean shear leads to relatively simple structure of the velocity gradient tensor. How isotropy is restored in the very large Reynolds limit remains to be understood.
Infinite Products of Random Isotropically Distributed Matrices
NASA Astrophysics Data System (ADS)
Il'yn, A. S.; Sirota, V. A.; Zybin, K. P.
2017-01-01
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
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.
The effects of particle loading on turbulence structure and modelling
NASA Technical Reports Server (NTRS)
Squires, Kyle D.; Eaton, J. K.
1989-01-01
The objective of the present research was to extend the Direct Numerical Simulation (DNS) approach to particle-laden turbulent flows using a simple model of particle/flow interaction. The program addressed the simplest type of flow, homogeneous, isotropic turbulence, and examined interactions between the particles and gas phase turbulence. The specific range of problems examined include those in which the particle is much smaller than the smallest length scales of the turbulence yet heavy enough to slip relative to the flow. The particle mass loading is large enough to have a significant impact on the turbulence, while the volume loading was small enough such that particle-particle interactions could be neglected. Therefore, these simulations are relevant to practical problems involving small, dense particles conveyed by turbulent gas flows at moderate loadings. A sample of the results illustrating modifications of the particle concentration field caused by the turbulence structure is presented and attenuation of turbulence by the particle cloud is also illustrated.
Clustering of settling charged particles in turbulence: theory and experiments
NASA Astrophysics Data System (ADS)
Lu, Jiang; Nordsiek, Hansen; Shaw, Raymond A.
2010-12-01
Atmospheric clouds, electrosprays and protoplanetary nebula (dusty plasma) contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. We have developed a theoretical description of the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions (RDFs) to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb 'terminal' speed to the turbulence dissipation velocity scale) and the settling parameter (the ratio of the gravitational terminal speed to the turbulence dissipation velocity scale). The theory is compared to measured RDFs for water particles in homogeneous, isotropic air turbulence. The RDFs are obtained from particle positions measured in three dimensions using digital holography. The measurements verify the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of 'gravity' is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity.
Physical Mechanisms of Two-Dimensional Turbulence
NASA Astrophysics Data System (ADS)
Ecke, Robert
2004-03-01
Turbulence has slowly yielded its mysteries through over 100 years of persistent effort. Recently experimental techniques and computation power have reached the stage where significant progress has been made on this very challenging problem. Two dimensional turbulence offers some real advantages in terms of reduced degrees of freedom such that the problem can now be thoroughly explored from many perspectives. Further, two-dimensional turbulence exhibits the basic phenomena of direct-enstrophy and inverse-energy cascades thought to apply to oceanic and atmospheric systems. We have investigated the properties of turbulence in two spatial dimensions using experimental measurements of the grid turbulence in a flowing soap film^1 and of the electromagnetically-forced turbulence in a thin salt layer floating on a dense immiscible fluid underlayer. We have also explored 2D turbulence using several different direct numerical simulations of homogeneous, isotropic turbulence in a periodic box^2. The data for both consist of high resolution fields of velocity; some are statistically independent sets and others are temporally resolved for dynamics. From this data we construct conventional Eulerian statistics, directly measure energy and enstrophy transfer^1, identify coherent structures in the flow, determine Lagrangian quantities, and calculate stretching fields. This comprehensive experimental and numerical characterization elucidates the physical mechanisms of two-dimensional turbulence. ^1 M.K. Rivera, W.B. Daniel and R.E. Ecke, Phys. Rev. Lett. 90, 104502 (2003). ^2 S. Chen, R.E. Ecke, G. Eyink, X. Wang, and Z. Xiao, Phys. Rev. Lett. 91, 214501 (2003).
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.
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.
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.
Development of renormalization group analysis of turbulence
NASA Technical Reports Server (NTRS)
Smith, L. M.
1990-01-01
The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.
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.
Development of renormalization group analysis of turbulence
NASA Technical Reports Server (NTRS)
Smith, L. M.
1990-01-01
The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.
A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing
Schwarzkopf, J. D.; Livescu, D.; Baltzer, 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
NASA Astrophysics Data System (ADS)
Korotkova, O.; Salem, M.; Dogariu, A.; Wolf, E.
2005-08-01
During the last few years, changes in the state of polarization of a class of random electromagnetic beams (so-called electromagnetic Gaussian Schell-model beams), propagating ill free space have been investigated. Ill the present paper, we extend the analysis to propagation of such beams in homogeneous, isotropic, non-absorbing atmospheric turbulence. We find that the effects Of turbulence Oil the State Of polarization are most significant when the atmospheric fluctuations are weak or moderate, whereas in a strong regime of atmospheric fluctuations the state of polarization of the beam returns to its original state. Our results might find possible useful applications for sensing, imaging and communication through the atmosphere.
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.
Small-scale anisotropy in turbulent shearless mixing.
Tordella, Daniela; Iovieno, Michele
2011-11-04
The generation of small-scale anisotropy in turbulent shearless mixing is numerically investigated. Data from direct numerical simulations at Taylor Reynolds' numbers between 45 and 150 show not only that there is a significant departure of the longitudinal velocity derivative moments from the values found in homogeneous and isotropic turbulence but that the variation of skewness has an opposite sign for the components across the mixing layer and parallel to it. The anisotropy induced by the presence of a kinetic energy gradient has a very different pattern from the one generated by an homogeneous shear. The transversal derivative moments in the mixing are in fact found to be very small, which highlights that smallness of the transversal moments is not a sufficient condition for isotropy.
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.
Turbulent swirling layer with free surface
NASA Astrophysics Data System (ADS)
Bardet, Philippe; Peterson, Per; Savas, Omer
2007-11-01
A turbulent annular liquid wall jet, or vortex tube, generated by helical injection inside a tube was characterized experimentally. The resulting hollow confined swirling layer is proposed for use in a thick liquid first-wall chamber concept for inertial fusion power plants. The velocity fields were measured with a single camera split-screen stereoscopic particle image velocimetry scheme. The flow was studied at 5 stations between 1.5 and 4.5 ``vortex tube'' diameters downstream of the injection nozzle in a horizontal plane that coincides with the tube axis. Up to 1024 independent realizations were recorded and analyzed for Reynolds numbers ranging from 3,200 to 14,000 at each station. The turbulent structures are non-isotropic and non-homogeneous. Gradients in average velocity and Reynolds stress result in turbulent kinetic energy production. Between 1.5 and 3.5 diameters, the average azimuthal velocity profile alone is non uniform away from the wall. Persistent large vortical structures are observed. The turbulent kinetic energy decreases slowly with distance while the dissipation decreases rapidly. At 4.5 diameters, the wall effect influences strongly the average velocity profiles. The vortical structures disappear and the turbulent kinetic energy increases.
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.
Decay of Finite Temperature Superfluid Helium-4 Turbulence
NASA Astrophysics Data System (ADS)
Kivotides, Demosthenes
2015-10-01
A mesoscopic model of superfluid helium-4, that describes the dynamics of individual topological defects of the ground state (superfluid vortices) and their (self-consistent) interactions with its quasi-particle excitations (normal-fluid), is solved numerically in order to analyse the physics of decaying homogeneous, isotropic turbulence. The calculations predict several temporal decay regimes not present in classical turbulence decay, the corresponding superfluid and normal-fluid energy spectra, and the experimentally observed scaling for the superfluid vortex line density at large times. The results demonstrate that the origin of this scaling is the energy spent by the superfluid in order to sustain a fluctuating low Reynolds number flow in the normal-fluid, and not the locking of turbulent superfluid and normal-fluid vorticities.
A modified restricted Euler equation for turbulent flows with mean velocity gradients
NASA Technical Reports Server (NTRS)
Girimaji, Sharath S.; Speziale, Charles G.
1994-01-01
The restricted Euler equation captures many important features of the behavior of the velocity gradient tensor observed in direct numerical simulations (DNS) of isotropic turbulence. However, in slightly more complex flows the agreement is not good, especially in regions of low dissipation. In this paper, it is demonstrated that the Reynolds-averaged restricted Euler equation violates the balance of mean momentum for virtually all homogeneous turbulent flows with only two major exceptions: isotropic and homogeneously-sheared turbulence. A new model equation which overcomes this shortcoming and is more widely applicable is suggested. This modele is derived from the Navier-Stokes equation with a restricted Euler type approximation made on the fluctuating velocity gradient field. Analytical solutions of the proposed modified restricted Euler equation appear to be difficult to obtain. Hence, a strategy for numerically calculating the velocity gradient tensor is developed. Preliminary calculations tend to indicate that the modified restricted Euler equation captures many important aspects of the behavior of the fluctuating velocity gradients in anisotropic homogeneous turbulence.
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.
Compressible turbulence and shock-capturing using a variational multiscale method
NASA Astrophysics Data System (ADS)
Garai, Anirban; Burgess, Nicholas; Murman, Scott; Diosady, Laslo
2016-11-01
We have previously developed a dynamic extension of Hughes' variational multiscale method which is implemented in an entropy-stable Discontinuous-Galerkin spectral-element solver. This solver and sub-grid model have been examined on standard low-speed benchmark flows, e.g. homogeneous turbulence, channel flow, etc. Here we extend the approach to higher speeds where compressibility effects are no longer insignificant, and the flowfields develop unsteady shocklets and shock waves. Homogeneous isotropic turbulence at high turbulent Mach number is tested for two cases - decaying and passing through a normal shock. Numerical simulations using the multiscale sub-grid model, no sub-grid model, and a variation of Barter and Darmofal's shock-capturing scheme are examined in isolation and combination. The computed results are compared against theoretical observations and previous computational results.
Fully-resolved DNS of finite-size particles exposed to a turbulent stream
NASA Astrophysics Data System (ADS)
Botto, Lorenzo; Prosperetti, Andrea
2008-11-01
A field of homogeneous isotropic turbulence is convected with a mean velocity past a group of fixed, finite-size particles and the structure and intensity of the resulting downstream turbulence are compared to the particle-free case. The diameter of the particles is larger than the Kolmogorov scale and is of the order of the Taylor micro-scale. The results illustrate the central role played by the particle wakes in destroying the isotropy and homogeneity of the incident turbulence. Furthermore, as a result of wake interactions, the time-dependent hydrodynamic forces on the downstream and upstream spheres are correlated. The numerical simulations are carried out on a uniform grid by employing the ``Physalis'' method which can be regarded as a combination of an immersed boundary and spectral method. Among other advantages, it does not require interpolation and its spectral convergence permits computations with relatively few grid nodes per particle.
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.
Space-Time Correlations and Dynamic Coupling in Turbulent Flows
NASA Astrophysics Data System (ADS)
He, Guowei; Jin, Guodong; Yang, Yue
2017-01-01
Space-time correlation is a staple method for investigating the dynamic coupling of spatial and temporal scales of motion in turbulent flows. In this article, we review the space-time correlation models in both the Eulerian and Lagrangian frames of reference, which include the random sweeping and local straining models for isotropic and homogeneous turbulence, Taylor's frozen-flow model and the elliptic approximation model for turbulent shear flows, and the linear-wave propagation model and swept-wave model for compressible turbulence. We then focus on how space-time correlations are used to develop time-accurate turbulence models for the large-eddy simulation of turbulence-generated noise and particle-laden turbulence. We briefly discuss their applications to two-point closures for Kolmogorov's universal scaling of energy spectra and to the reconstruction of space-time energy spectra from a subset of spatial and temporal signals in experimental measurements. Finally, we summarize the current understanding of space-time correlations and conclude with future issues for the field.
Turbulence comes in bursts in stably stratified flows
NASA Astrophysics Data System (ADS)
Rorai, C.; Mininni, P. D.; Pouquet, A.
2014-04-01
There is a clear distinction between simple laminar and complex turbulent fluids; however, in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity that disappear slowly in time. This phenomenon is ill understood and poorly modeled and yet it is central to our understanding of weather and climate dynamics. We present here data from direct numerical simulations of stratified turbulence on grids of 20483 points that display the somewhat paradoxical result of measurably stronger events for more stable flows, not only in the temperature and vertical velocity derivatives as commonplace in turbulence, but also in the amplitude of the fields themselves, contrary to what happens for homogenous isotropic turbulent flows. A flow visualization suggests that the extreme values take place in Kelvin-Helmoltz overturning events and fronts that develop in the field variables. These results are confirmed by the analysis of a simple model that we present. The model takes into consideration only the vertical velocity and temperature fluctuations and their vertical derivatives. It indicates that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid nonlinear amplification of energy stored in waves and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations in a range of parameters corresponding to the well-known saturation regime of stratified 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
Magnifying absolute instruments for optically homogeneous regions
Tyc, Tomas
2011-09-15
We propose a class of magnifying absolute optical instruments with a positive isotropic refractive index. They create magnified stigmatic images, either virtual or real, of optically homogeneous three-dimensional spatial regions within geometrical optics.
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.
Richardson's pair diffusion and the stagnation point structure of turbulence.
Dávila, J; Vassilicos, J C
2003-10-03
DNS and laboratory experiments show that the spatial distribution of straining stagnation points in homogeneous isotropic 3D turbulence has a fractal structure with dimension D(s)=2. In kinematic simulations the exponent gamma in Richardson's law and the fractal dimension D(s) are related by gamma=6/D(s). The Richardson constant is found to be an increasing function of the number density of straining stagnation points in agreement with pair diffusion occurring in bursts when pairs meet such points in the flow.
Hierarchical structures in fully developed turbulence
NASA Astrophysics Data System (ADS)
Liu, Li
Analysis of the probability density functions (PDFs) of the velocity increment dvl and of their deformation is used to reveal the statistical structure of the intermittent energy cascade dynamics of turbulence. By analyzing a series of turbulent data sets including that of an experiment of fully developed low temperature helium turbulent gas flow (Belin, Tabeling, & Willaime, Physica D 93, 52, 1996), of a three-dimensional isotropic Navier-Stokes simulation with a resolution of 2563 (Cao, Chen, & She, Phys. Rev. Lett. 76, 3711, 1996) and of a GOY shell model simulation (Leveque & She, Phys. Rev. E 55, 1997) of a very big sample size (up to 5 billions), the validity of the Hierarchical Structure model (She & Leveque, Phys. Rev. Lett. 72, 366, 1994) for the inertial-range is firmly demonstrated. Furthermore, it is shown that parameters in the Hierarchical Structure model can be reliably measured and used to characterize the cascade process. The physical interpretations of the parameters then allow to describe differential changes in different turbulent systems so as to address non-universal features of turbulent systems. It is proposed that the above study provides a framework for the study of non-homogeneous turbulence. A convergence study of moments and scaling exponents is also carried out with detailed analysis of effects of finite statistical sample size. A quantity Pmin is introduced to characterize the resolution of a PDF, and hence the sample size. The fact that any reported scaling exponent depends on the PDF resolution suggests that the validation (or rejection) of a model of turbulence needs to carry out a resolution dependence analysis on its scaling prediction.
The isotropic Hamiltonian formalism
Vaisman, Izu
2011-02-10
A Hamiltonian formalism is a procedure that allows to associate a dynamical system to a function and that includes classical Hamiltonian mechanics as a particular case. The present, expository paper gives a survey of the Hamiltonian formalism defined by an isotropic subbundle of TM+T*M, in particular, by a Dirac structure. We discuss reduction and geometric quantization of the Hamiltonian dynamical systems provided by this formalism.
DNS of turbulent flows of dense gases
NASA Astrophysics Data System (ADS)
Sciacovelli, L.; Cinnella, P.; Gloerfelt, X.; Grasso, F.
2017-03-01
The influence of dense gas effects on compressible turbulence is investigated by means of numerical simulations of the decay of compressible homogeneous isotropic turbulence (CHIT) and of supersonic turbulent flows through a plane channel (TCF). For both configurations, a parametric study on the Mach and Reynolds numbers is carried out. The dense gas considered in these parametric studies is PP11, a heavy fluorocarbon. The results are systematically compared to those obtained for a diatomic perfect gas (air). In our computations, the thermodynamic behaviour of the dense gases is modelled by means of the Martin-Hou equation of state. For CHIT cases, initial turbulent Mach numbers up to 1 are analyzed using mesh resolutions up to 5123. For TCF, bulk Mach numbers up to 3 and bulk Reynolds numbers up to 12000 are investigated. Average profiles of the thermodynamic quantities exhibit significant differences with respect to perfect-gas solutions for both of the configurations. For high-Mach CHIT, compressible structures are modified with respect to air, with weaker eddy shocklets and stronger expansions. In TCF, the velocity profiles of dense gas flows are much less sensitive to the Mach number and collapse reasonably well in the logarithmic region without any special need for compressible scalings, unlike the case of air, and the overall flow behaviour is midway between that of a variable-property liquid and that of a gas.
Detailed thermodynamic analyses of high-speed compressible turbulence
NASA Astrophysics Data System (ADS)
Towery, Colin; Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter
2016-11-01
Interactions between high-speed turbulence and flames (or chemical reactions) are important in the dynamics and description of many different combustion phenomena, including autoignition and deflagration-to-detonation transition. The probability of these phenomena to occur depends on the magnitude and spectral content of turbulence fluctuations, which can impact a wide range of science and engineering problems, from the hypersonic scramjet engine to the onset of Type Ia supernovae. In this talk, we present results from new direct numerical simulations (DNS) of homogeneous isotropic turbulence with turbulence Mach numbers ranging from 0 . 05 to 1 . 0 and Taylor-scale Reynolds numbers as high as 700. A set of detailed analyses are described in both Eulerian and Lagrangian reference frames in order to assess coherent (structural) and incoherent (stochastic) thermodynamic flow features. These analyses provide direct insights into the thermodynamics of strongly compressible turbulence. Furthermore, presented results provide a non-reacting baseline for future studies of turbulence-chemistry interactions in DNS with complex chemistry mechanisms. This work was supported by the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-14-1-0273, and the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) under a Frontier project award.
TURBULENT AMPLIFICATION AND STRUCTURE OF THE INTRACLUSTER MAGNETIC FIELD
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.
Local isotropy in buoyancy-generated turbulence
NASA Astrophysics Data System (ADS)
Chasnov, Jeffrey R.
1991-12-01
Batchelor et al. (1992) recently considered the turbulent motion generated by buoyancy forces acting on random fluctuations in the density of an infinite fluid. This homogeneous buoyancy-generated flow field with zero mean density gradient was conceived as an idealized system which, like isotropic turbulence, may be useful as a vehicle for the general study of turbulence. The Batchelor et al. study relied partly on theoretical analysis and partly on direct and large-eddy numerical simulations of the flow field. To this mix, we add here a two-point closure study based on the eddy-damped quasi-normal Markovian (EDQNM) closure model applied to axisymmetric turbulence. The EDQNM model has been shown to yield reasonably accurate quantitative results for a variety of problems in homogeneous turbulence (Lesieur 1987). The main advantage here in applying EDQNM to the buoyancy-driven flow field is the wide range of wavenumbers over which a solution of the EDQNM equations may be solved. Whereas a typical large-eddy simulation using 128(exp 3) grid points has a wavenumber range of only 60, the EDQNM calculation can be easily run with a wavenumber range of several decades. Because of the growth in length scales in the buoyancy-driven flow field, this large wavenumber range allows for a solution of the flow field well into its asymptotic regime. Recent comparisons between large-eddy simulations and closure theory (Herring 1990) indicate that a time longer than that attainable by current large-eddy simulations is required to reach flow asymptotics and that conclusions based on large-eddy simulation results may be based only on an intermediate transient state. We briefly introduce the EDQNM equations for the buoyancy-generated flow field. We then present a Kolmogorov-like theoretical argument on the scaling of the small-scale spectra. This scaling is then confirmed by numerical solution of the EDQNM equations. We briefly conclude with possible future research directions.
Lagrangian statistics in turbulent channel flow: implications for Lagrangian stochastic models
NASA Astrophysics Data System (ADS)
Stelzenmuller, Nickolas; Polanco, Juan Igancio; Vinkovic, Ivana; Mordant, Nicolas
2016-11-01
Lagrangian acceleration and velocity correlations in statistically one-dimesional turbulence are presented in the context of the development of Lagrangian stochastic models of inhomogeneous turbulent flows. These correlations are measured experimentally by 3D PTV in a high aspect ratio water channel at Reτ = 1450 , and numerically from DNS performed at the same Reynolds number. Lagrangian timescales, key components of Lagrangian stochastic models, are extracted from acceleration and velocity autocorrelations. The evolution of these timescales as a function of distance to the wall is presented, and compared to similar quantities measured in homogeneous isotropic turbulence. A strong dependance of all Lagrangian timescales on wall distance is present across the width of the channel. Significant cross-correlations are observed between the streamwise and wall-normal components of both acceleration and velocity. Lagrangian stochastic models of this flow must therefore retain dependance on the wall-normal coordinate and the components of acceleration and velocity, resulting in significantly more complex models than those used for homogeneous isotropic turbulence. We gratefully acknowledge funding from the Agence Nationale de la Recherche, LabEx Tec 21, and CONICYT Becas Chile.
Critical issues encountered in experiments and measurements involving optical turbulence
NASA Astrophysics Data System (ADS)
Eaton, Frank D.
2007-02-01
The successful design and operation of high energy laser (HEL) and laser communication systems require a comprehensive and thorough knowledge of the real turbulent atmosphere coupled with high-fidelity realistic laser beam propagation models. To date, modeling and simulation of laser beam propagation through atmospheric turbulence have relied upon a traditional theoretical basis that assumes the existence of homogeneous, isotropic, stationary, and Kolmogorov turbulence. The real impact of the refractive index structure parameter ( C2 n ) on laser beam propagation including effects of non-classical turbulence as well as inner (l °) and outer scale (L °) effects will be examined. Observations clearly show turbulence is often layered and is produced by wave activity and episodic events such as Kelvin-Helmholtz instabilities. Other critical turbulence issues involve the relationship between mechanical and optical turbulence and the effect of path variability of turbulence and inner scale on optical turbulence parameters over long paths. These issues will be examined from data obtained from five systems: a) a new measurement platform using a free-flying balloon that lifts a ring with a boom upon which are mounted several fine wire (1-μm diameter) sensors to measure high-speed temperature and velocity fluctuations, b) a new system using a kite/tethered blimp platform that obtains both profile and measurements at a fixed altitude over time, c) a 50 MHz radar at Vandenberg Air Force Base that senses at high temporal and spatial resolution to 20 km ASL, d) an instrumented aircraft system, and e) a suite of optical systems. The first four systems all provide estimates of C2 n , the eddy dissipation rate (\\Vegr), l ° and L °. Methods of calibration and problems of interpreting results from the measurement systems are discussed.
Isotropically polarized speckle patterns.
Schmidt, Mikolaj K; Aizpurua, Javier; Zambrana-Puyalto, Xavier; Vidal, Xavier; Molina-Terriza, Gabriel; Sáenz, Juan José
2015-03-20
The polarization of the light scattered by an optically dense and random solution of dielectric nanoparticles shows peculiar properties when the scatterers exhibit strong electric and magnetic polarizabilities. While the distribution of the scattering intensity in these systems shows the typical irregular speckle patterns, the helicity of the incident light can be fully conserved when the electric and magnetic polarizabilities of the scatterers are equal. We show that the multiple scattering of helical beams by a random dispersion of "dual" dipolar nanospheres leads to a speckle pattern exhibiting a perfect isotropic constant polarization, a situation that could be useful in coherent control of light as well as in lasing in random media.
Turbulence program for propulsion systems
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing
1995-01-01
Program goals at the Center for Modeling of Turbulence and Transition (CMOTT), NASA Lewis Research Center, are (1) to develop reliable turbulence (including bypass transition) and combustion models for complex flows in propulsion systems and (2) to integrate developed models into deliverable CFD tools for propulsion systems in collaboration with industry. This viewgraph presentation covers the following topics: development of turbulence and combustion models; collaboration with industry and technology transfer; isotropic eddy viscosity models; algebraic Reynolds stress models; scalar turbulence models; second order closure models; multiple scale k-epsilon models; and PDF modeling of turbulent reacting flows.
NASA Astrophysics Data System (ADS)
Variano, Evan; Cowen, Edwin
2009-11-01
Laboratory measurements in a stirred tank reveal the turbulent flux on the water side of an air--water interface. The tank is stirred from below by random jets, providing turbulence that is homogeneous and isotropic in the horizontal direction. This flow is an interesting counterpoint to cases where the turbulence at the surface is driven by shear there. The Taylor microscale Reynolds number Rλ 300, giving a wide range of scales. The contribution of these various scales to turbulent scalar flux is investigated by simultaneously measuring the velocity field and the concentration field of dissolved CO2. This is accomplished via quantitative imaging, and allows cospectra, structure functions, and coherent structures to be investigated. These are compared to theory for sheared interfaces, as well as to similar results obtained by other researchers at lower Schmidt and Reynolds numbers via CFD.
Direct numerical simulation of chemically reacting turbulence
NASA Astrophysics Data System (ADS)
Miyauchi, Toshio; Tanahashi, Mamoru
In this paper, we present two results of direct numerical simulation of chemically reacting flows. One is direct numerical simulation of chemically reacting two-dimensional mixing layer and the other is direct numerical simulation of chemically reacting compressible isotropic turbulence. As for the mixing layer, a low Mach number approximation was used to take into account the variable density effects on the flow fields and to clarify the effects of heat release and density difference of a mean flow. In the case of density difference, expansion and baroclinic torque has a negative contribution to the local vorticity transport in the high density side and a positive contribution in the low density side which results in an asymmetric vortical structure structure. Thes density difference suppresses the growth of mixing layer and causes the overshoot of mean velocity only in the high density side which coincides with an experimental result. Coupling effects of heat release and desnity difference are also investigated. As for the homogeneous turbulence, fully compressible Navier-Stokes equations are solved to clarify the interaction between turbulence and chemical reaction in turbulent diffusion flame. The chemical reaction is suppressed by the increase of heat release because of the decrease of density and local Reynolds number. However, the decay of enstrophy with heat release is slower than that without heat release because of strong baroclinic torque which is generated near the reaction zone. Also, large amount of heat release causes increase in turbulent energy through the pressure dilatation term. The pressure dilatation term shows the periodic fluctuation which has an acoustic time scale. The fluctuation is enhanced by the heat release and travels in the turbulent field as pressure and dilatation waves.
Fundamentals of pair diffusion in kinematic simulations of turbulence.
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.
Structure-function scaling of bounded two-dimensional turbulence.
Kramer, W; Keetels, G H; Clercx, H J H; van Heijst, G J F
2011-08-01
Statistical properties of forced two-dimensional turbulence generated in two different flow domains are investigated by numerical simulations. The considered geometries are the square domain and the periodic channel domain, both bounded by lateral no-slip sidewalls. The focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no-slip boundaries. The scaling exponents of the velocity and the vorticity structure functions are compared to the classical Kraichnan-Batchelor-Leith (KBL) theory, which assumes isotropy, homogeneity, and self-similarity for turbulence scales between the forcing and dissipation scale. Our investigation reveals that in the interior of the flow domain, turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range, but it is weakly intermittent. However, the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the KBL theory predicts. Near the walls the turbulence is strongly anisotropic at all flow scales.
Behavior of local dissipation scales in turbulent pipe flow
NASA Astrophysics Data System (ADS)
Bailey, Sean; Hultmark, Marcus; Schumacher, Joerg; Yakhot, Victor; Smits, Alexander
2010-11-01
Classically, dissipation of turbulence has been thought to occur around the Kolmogorov scales. However, the Kolmogorov scales are prescribed using mean dissipation rate, whereas dissipation is spatially intermittent. It therefore seems natural to instead describe dissipation using a continuum of local length scales rather than a single scale. By connecting a local dissipation scale η to the velocity increment across this scale δuη, it is possible to derive a probability density function (PDF) of η which show how the dissipation is contained in scales larger and smaller than the Kolmogorov scale. Here we present a comparison between measured PDFs in turbulent pipe flow, the analytically derived PDF, and PDFs determined from direct numerical simulation of homogeneous isotropic turbulence. It was found that there is good general agreement between experiment, simulation and theory amongst both homogeneous and inhomogeneous turbulent flows, pointing to universality in the dissipation scales amongst different flows. It was also found that the PDFs are invariant with distance from the wall except for a region very near the wall (y^+<80), where dissipation was found to occur at increasingly larger length scales as the wall is approached.
Vacuum effects in a spatially homogeneous and isotropic cosmological background.
NASA Astrophysics Data System (ADS)
Villalba, V. M.; Percoco, U.
The authors obtain, by separation of variables, an exact solution to the Klein Gordon equation in a cosmological, spatially closed, Robertson-Walker space-time with a positive cosmological constant. The model is associated with a universe filled with radiation. The authors analyze the phenomenon of particle creation for different values of the dimensionless coupling constant. They discuss the relevance of the cosmological constant in this process.
Vacuum effects in a spatially homogeneous and isotropic cosmological background
NASA Astrophysics Data System (ADS)
Villalba, Victor M.; Percoco, Umberto
1992-03-01
We obtain, by separation of variables, an exact solution to the Klein-Gordon and Dirac equations in a cosmological, spatially-closed, Robertson-Walker space-time with a positive cosmological constant Lambda. The model is associated with a universe filled with radiation. We analyze the phenomenon of particle creation for different values of the dimensionless coupling constant xi.
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.
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
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
NASA Astrophysics Data System (ADS)
Kong, Bo; Feng, Heng; Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney
2015-11-01
In our previous works,the exact Reynolds-averaged equations for the particle phase were derived to develop a new mutilphase turbulence model with a rigorous conceptual foundation, and detailed Euler-Lagrange(EL) particle simulations of cluster-induced turbulence (CIT) were performed to aid its development. However, sophisticated filtering techniques have to be used to extract Eulerian particle-phase statistics from the EL simulations, which can be directly provided by Euler-Euler approaches. In this work, a novel Euler-Euler anisotropic Gaussian (AG) approach was used to perform mesoscale DNS of the CIT cases. A three-dimension Hermite Quadrature formulation is used to calculate finite-volume kinetic flux for ten velocity moments. Bhatnagar-Gross-Krook model is applied to account for the inelastic particle collisions. Detailed comparisons with EL simulations demonstrate that the AG particle velocity assumption is valid and this novel method can be used to perform mesoscale DNS for gas-particle flows with high fidelity.
Analysis of turbulence in the orthonormal wavelet representation
NASA Technical Reports Server (NTRS)
Meneveau, Charles
1991-01-01
The usefulness of the wavelet transform for the analysis of turbulent flow fields is explored by examining the wavelet transform properties of a decomposition of turbulent velocity fields into modes that exhibit the localization in a wavenumber and physical space. The calculations are performed on 3D fields from direct numerical simulations of isotropic flow and homogeneous shear flow, and from measurements in two laboratory wind-tunnel experimental velocity signals (boundary layer and wake behind a circular cylinder). The analysis confirmed that there is strong spatial intermittency in nonlinear quantities; their mean spectral behavior results from a delicate balance between large positive and negative excursions. The wavelet analysis is a way to quantify these observations in a standardized fashion by using 'flow-independent eddies' to decompose the velocity field.
Linearized holographic isotropization at finite coupling
NASA Astrophysics Data System (ADS)
Atashi, Mahdi; Fadafan, Kazem Bitaghsir; Jafari, Ghadir
2017-06-01
We study holographic isotropization of an anisotropic homogeneous non-Abelian strongly coupled plasma in the presence of Gauss-Bonnet corrections. It was verified before that one can linearize Einstein's equations around the final black hole background and simplify the complicated setup. Using this approach, we study the expectation value of the boundary stress tensor. Although we consider small values of the Gauss-Bonnet coupling constant, it is found that finite coupling leads to significant increasing of the thermalization time. By including higher order corrections in linearization, we extend the results to study the effect of the Gauss-Bonnet coupling on the entropy production on the event horizon.
On the preferential sampling of helicity by isotropic helicoids
NASA Astrophysics Data System (ADS)
Biferale, Luca; Gustavsson, Kristian; Scatamacchia, Riccardo
2016-11-01
We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows. These are particles whose motion is invariant under rotations but not under mirror reflections of the particle. This is the simplest, yet unexplored, extension of the much studied case of small spherical particles. We show that heavy isotropic helicoids, due to the coupling between translational and rotational degrees of freedom, preferentially sample different helical regions in laminar or chaotic advecting flows. This opens the way to control and engineer particles able to track complex flow structures with potential applications to microfluidics and turbulence. ERC AdG Grant NewTURB no. 339032.
NASA Astrophysics Data System (ADS)
Aliseda, Alberto; Bateson, Colin; Ayala, Orlando; Parishani, Hossein; Wang, Lian-Ping; Rosa, Bogdan
2011-11-01
We have conducted a multi-laboratory investigation of the dynamics of small inertial droplets (St ~ 0 . 1 - 1) immersed in homogeneous isotropic turbulence. We compare experimental results from a wind tunnel experiment with Direct Numerical Simulations of slowly decaying homogeneous isotropic turbulence laden with spherical droplets. The Reynolds number (Reλ) in both cases is of the order of 200 and the particle distribution is polydisperse with droplets in the 10 - 30 μm range. We compare the one-dimensional Radial Distribution Function from the experiments to the 1D, 2D and 3D RDFs from the simulations to validate the numerical treatment of the droplet dynamics in close proximity, and to develop methods to extrapolate the experimental measurements to 3D. We also compare the relative velocity of a pair of droplets, obtained along a line or in a plane from PDPA and PIV measurements, to the equivalent statistics obtained from the 3D velocity fields in the DNS. These are key components of the droplet collision kernel necessary to calculate turbulence-induced collision-coalescence and droplet growth.
Emergence of a turbulent cascade in a quantum gas
NASA Astrophysics Data System (ADS)
Navon, Nir; Gaunt, Alexander L.; Smith, Robert P.; Hadzibabic, Zoran
2016-11-01
A central concept in the modern understanding of turbulence is the existence of cascades of excitations from large to small length scales, or vice versa. This concept was introduced in 1941 by Kolmogorov and Obukhov, and such cascades have since been observed in various systems, including interplanetary plasmas, supernovae, ocean waves and financial markets. Despite much progress, a quantitative understanding of turbulence remains a challenge, owing to the interplay between many length scales that makes theoretical simulations of realistic experimental conditions difficult. Here we observe the emergence of a turbulent cascade in a weakly interacting homogeneous Bose gas—a quantum fluid that can be theoretically described on all relevant length scales. We prepare a Bose-Einstein condensate in an optical box, drive it out of equilibrium with an oscillating force that pumps energy into the system at the largest length scale, study its nonlinear response to the periodic drive, and observe a gradual development of a cascade characterized by an isotropic power-law distribution in momentum space. We numerically model our experiments using the Gross-Pitaevskii equation and find excellent agreement with the measurements. Our experiments establish the uniform Bose gas as a promising new medium for investigating many aspects of turbulence, including the interplay between vortex and wave turbulence, and the relative importance of quantum and classical effects.
Wall-resolved spectral cascade-transport turbulence model
Brown, C. S.; Shaver, D. R.; Lahey, R. T.; ...
2017-07-08
A spectral cascade-transport model has been developed and applied to turbulent channel flows (Reτ= 550, 950, and 2000 based on friction velocity, uτ ; or ReδΜ= 8,500; 14,800 and 31,000, based on the mean velocity and channel half-width). This model is an extension of a spectral model previously developed for homogeneous single and two-phase decay of isotropic turbulence and uniform shear flows; and a spectral turbulence model for wall-bounded flows without resolving the boundary layer. Data from direct numerical simulation (DNS) of turbulent channel flow was used to help develop this model and to assess its performance in the 1Dmore » direction across the channel width. The resultant spectral model is capable of predicting the mean velocity, turbulent kinetic energy and energy spectrum distributions for single-phase wall-bounded flows all the way to the wall, where the model source terms have been developed to account for the wall influence. We implemented the model into the 3D multiphase CFD code NPHASE-CMFD and the latest results are within reasonable error of the 1D predictions.« less
Turbulence modeling of sediment-laden, open channel flows
NASA Astrophysics Data System (ADS)
Jha, Sanjeev; Bombardelli, Fabian
2007-11-01
In spite of the knowledge already gained of multi-phase flows by employing the multi-component flow theory in fluid mechanics, there is still no consensus among researchers on the most appropriate models to use in a given case. The issue complicates even further with the modeling of turbulence in those flows. In the special case of sediment transport in natural open channels (i.e., rivers), the understanding of the interaction between the different phases (water and sediment) presents diverse challenges. First, the bottom of the channel interchanges material with the water column, creating a constant source of disperse phase; second, the turbulence is non-homogeneous and non-isotropic. Most studies in the past have focused on the mean flow characteristics and on the distribution of sediment in the vertical, but they have not dealt with the turbulence statistics. In this work, we test diverse theoretical and numerical models for one-dimensional, open-channel flow with the dataset of Muste et al. (2005), one of the few datasets reporting detailed distributions of turbulence statistics in the vertical direction in the open channel. We analyze the performance of models of different complexity, ranging from simple ``mixture'' models to complete two-fluid models. For turbulence closure, we test the standard k-ɛ, k-φ and Reynolds stress (RSM) models, and also their extended versions proposed by different authors.
Adaptive entropy-constrained discontinuous Galerkin method for simulation of turbulent flows
NASA Astrophysics Data System (ADS)
Lv, Yu; Ihme, Matthias
2015-11-01
A robust and adaptive computational framework will be presented for high-fidelity simulations of turbulent flows based on the discontinuous Galerkin (DG) scheme. For this, an entropy-residual based adaptation indicator is proposed to enable adaptation in polynomial and physical space. The performance and generality of this entropy-residual indicator is evaluated through direct comparisons with classical indicators. In addition, a dynamic load balancing procedure is developed to improve computational efficiency. The adaptive framework is tested by considering a series of turbulent test cases, which include homogeneous isotropic turbulence, channel flow and flow-over-a-cylinder. The accuracy, performance and scalability are assessed, and the benefit of this adaptive high-order method is discussed. The funding from NSF CAREER award is greatly acknowledged.
Wavelet multi-resolution analysis of energy transfer in turbulent premixed flames
NASA Astrophysics Data System (ADS)
Kim, Jeonglae; Bassenne, Maxime; Towery, Colin; Poludnenko, Alexei; Hamlington, Peter; Ihme, Matthias; Urzay, Javier
2016-11-01
Direct numerical simulations of turbulent premixed flames are examined using wavelet multi-resolution analyses (WMRA) as a diagnostics tool to evaluate the spatially localized inter-scale energy transfer in reacting flows. In non-reacting homogeneous-isotropic turbulence, the net energy transfer occurs from large to small scales on average, thus following the classical Kolmogorov energy cascade. However, in turbulent flames, our prior work suggests that thermal expansion leads to a small-scale pressure-work contribution that transfers energy in an inverse cascade on average, which has important consequences for LES modeling of reacting flows. The current study employs WMRA to investigate, simultaneously in physical and spectral spaces, the characteristics of this combustion-induced backscatter effect. The WMRA diagnostics provide spatial statistics of the spectra, scale-conditioned intermittency of velocity and vorticity, along with energy-transfer fluxes conditioned on the local progress variable.
Development and anisotropy of three-dimensional turbulence in a current sheet
Onofri, M.; Veltri, P.; Malara, F.
2007-06-15
The nonlinear evolution of three-dimensional reconnection instabilities are studied in a current sheet where many resonant surfaces are simultaneously present at different locations of the simulation domain. The nonlinear evolution produces the development of anisotropic magnetohydrodynamic turbulence. The development of the energy spectrum is followed until the energy is transported to the dissipative length scale and the anisotropy of the spectrum is analyzed. The energy cascade is affected by the Alfven effect and it takes place mainly in the direction perpendicular to the local average magnetic field. Anisotropy is also affected by propagation of perturbations across the main magnetic field, due to the growth of a transverse component related to reconnection. The direction of anisotropy varies with the position in space. The spectral index is different both from what is found in homogeneous isotropic turbulence and from the values predicted for magnetohydrodynamic turbulence with a uniform large-scale magnetic field.
Equation of State and Sound Velocities from Isotropic Continuum Mechanics.
1986-10-01
of state and the shear and longitudinal velocity to fifth order elastic constants. The resulting expressions are implicit in terms of the pressure...The methods of finite elasticity in continuum mechanics of homogeneous isotropic materials are used to obtain the pressure dependence of the equation
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.
The Boundary Layer Late Afternoon and Sunset Turbulence Project
NASA Astrophysics Data System (ADS)
Lothon, Marie; Lohou, Fabienne; Darbieu, Clara; Couvreux, Fleur; Pino, David; Blay, Estel; Vila-Guerau de Arellano, Jordi; Pietersen, Henk; Hartogensis, Oscar; Pardyjak, Eric; Alexander, Daniel; Reuder, Joachim; Baaserud, Line; Nilsson, Erik; Jimenez, Maria Antonia; Faloona, Ian; Sastre-Marugan, Mariano; Angevine, Wayne M.; Canut, Guylaine; Bazile, Eric
2014-05-01
The BLLAST (Boundary Layer Late Afternoon and Sunset Turbulence) project aims at better understanding the turbulence processes which occur during the transition from a well-mixed convective boundary layer to a residual layer overlying a stabilized nocturnal layer. This phase of the diurnal cycle is challenging from both modeling and observational perspectives: it is transitory, most of the forcings are small or null during the transition and the turbulence regime changes from the fully convective regime of turbulence, close to homogeneous and isotropic, toward more heterogeneous and intermittent turbulence during its decay. Those issues motivated a field campaign that was conducted from 14 June to 8 July 2011 in southern France in complex terrain and consisted of a range of integrated instrument platforms including: full-size aircraft, Remotely Piloted Airplane Systems (RPAS), remote sensing instruments, radiosoundings, tethered balloons, surface flux stations, and various meteorological towers deployed over different surface covers. The boundary layer, from the earth's surface to free troposphere was densely probed during the entire day, with a focus and intense observations from midday until sunset. The field dataset now forms the base of a set of studies utilizing the observations and several types of models including: Large Eddy Simulation, Mesoscale models, forecast models. The presentation will expose an overview of this experiment and of the current observational and modeling studies, with the focus on: the turbulence decay process within the entire boundary layer from surface to the top, the mesoscale forcings of importance during BLLAST, the ability of the forecast models to represent the diurnal cycle, the relevance of the Monin Obukhov similarity theory, and shallow drainage flows. Reference: Lothon M. et al., 2012. The Boundary-Layer Late Afternoon and Sunset Turbulence field experiment, Proc. of the 20th Symposium on Boundary-Layers and Turbulence, 7
NASA Astrophysics Data System (ADS)
Yu, R.; Lipatnikov, A. N.; Bai, X. S.
2014-08-01
In order to gain further insight into (i) the use of conditioned quantities for characterizing turbulence within a premixed flame brush and (ii) the influence of front propagation on turbulent scalar transport, a 3D Direct Numerical Simulation (DNS) study of an infinitely thin front that self-propagates in statistically stationary, homogeneous, isotropic, forced turbulence was performed by numerically integrating Navier-Stokes and level set equations. While this study was motivated by issues relevant to premixed combustion, the density was assumed to be constant in order (i) to avoid the influence of the front on the flow and, therefore, to know the true turbulence characteristics as reference quantities for assessment of conditioned moments and (ii) to separate the influence of front propagation on turbulent transport from the influence of pressure gradient induced by heat release. Numerical simulations were performed for two turbulence Reynolds numbers (50 and 100) and four ratios (1, 2, 5, and 10) of the rms turbulent velocity to the front speed. Obtained results show that, first, the mean front thickness is decreased when a ratio of the rms turbulent velocity to the front speed is decreased. Second, although the gradient diffusion closure yields the right direction of turbulent scalar flux obtained in the DNS, the diffusion coefficient Dt determined using the DNS data depends on the mean progress variable. Moreover, Dt is decreased when the front speed is increased, thus, indicating that the front propagation affects turbulent scalar transport even in a constant-density case. Third, conditioned moments of the velocity field differ from counterpart mean moments, thus, disputing the use of conditioned velocity moments for characterizing turbulence when modeling premixed turbulent combustion. Fourth, computed conditioned enstrophies are close to the mean enstrophy in all studied cases, thus, suggesting the use of conditioned enstrophy for characterizing turbulence
Effect of ambient turbulence on the evolution of a counter-rotating vortex pair.
NASA Astrophysics Data System (ADS)
Ahmed, Madiha; Hussain, Fazle
2007-11-01
In an attempt to explain and develop strategy for control of aircraft wake vortex in a turbulent atmosphere, the evolution of a vortex column dipole (a pair of counter-rotating vortices) in the presence of fine-scale (homogeneous and isotropic) freestream turbulence is studied via DNS of the Navier-Stokes equations. The freestream turbulence is found to significantly accelerate the vortex decay via a complex vortex-turbulence coupling scenario, which we study. External fine-scale turbulence is first stretched into azimuthal filaments (see also Melander & Hussain, PRE, vol 48 (1993)) which merge into threads through successive pairings and advect along the column dipole by self-induction. Oppositely-directed advection of opposite-signed threads forms thread dipoles which then move outward by mutual-induction and also eject column fluid (see also J. S. Marshall, JFM, vol 345 (1997)). This has the effect of enhancing both mixing with the ambient fluid and the nominally planar reconnection (cross-diffusion) between the column vortex pair. We then further explore the column vortex dipole-turbulence interaction scenario and vortex decay dependence on parameters like the column vortex Reynolds number, separation of the vortices, and the intensity and scale of freestream turbulence.
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
Turbulent scales of dilute particle-laden flows in microgravity
NASA Astrophysics Data System (ADS)
Groszmann, Daniel E.; Rogers, Chris B.
2004-12-01
The work described in this paper attempts to characterize the effects of inertia, isolated from gravity, on the dispersion of solid particles in a turbulent air flow. The experiment consisted of releasing particles of various sizes in an enclosed box of fan-generated, near-homogeneous, isotropic, and stationary turbulent airflow and examining the particle behavior in a microgravity environment. The turbulence box was characterized in ground-based experiments using laser Doppler velocimetry techniques. Microgravity was established by free floating the experiment apparatus during the parabolic trajectory of NASA's KC-135 reduced-gravity aircraft. The microgravity generally lasted about 20 s, with about 50 parabolas per flight and one flight per day over a testing period of four days. To cover a broad range of flow regimes of interest, particles with Stokes numbers St of about 1-100 were released in the turbulence box. The three-dimensional measurements of particle motion were made with a particle-tracking algorithm using a three-camera stereo imaging system. Digital photogrammetric techniques were used to determine the particle locations from the calibrated camera images. The epipolar geometry constraint identified matching particles from the three different camera views and a direct spatial intersection scheme determined the coordinates of particles in three-dimensional space. Since particle loadings were light, velocity and acceleration constraints allowed particles in a sequence of frames to be matched, resulting in particle tracks and dispersion measurements. The goal was to compare the dispersion of different Stokes number particles in zero gravity and thereby decouple the effects of gravity from inertia on the dispersion. Results show that higher inertia particles disperse less in isotropic, nondecaying turbulent flows under zero gravity, in agreement with current models. Measurements show that particles with St≈1 dispersed about ten times more than the St
Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations
NASA Astrophysics Data System (ADS)
Mihai, L. Angela; Neff, Patrizio
2017-03-01
We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit, through detailed calculations, an example with inhomogeneous continuous deformation but constant Cauchy stress. The example is derived from a non rank-one convex elastic energy.
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.
NASA Astrophysics Data System (ADS)
Pinsky, M.; Khain, A.; Rosenfeld, D.; Pokrovsky, A.
The motion of water drops and graupel particles within a turbulent medium is analyzed. The turbulence is assumed to be homogeneous and isotropic. It is demonstrated that the inertia of drops and graupel particles falling within a turbulent flow leads to the formation of significant velocity deviations from the surrounding air, as well as to the formation of substantial relative velocity between drops and graupel particles. The results of calculations of the continuous growth of raindrops and graupel particles moving within a cloud of small droplets are presented both in a non-turbulent medium and within turbulent flows of different turbulence intensity. Continuous growth of a drop-collector was calculated with the coalescence efficiency E ɛ=1, as well as using E ɛ values provided by Beard and Ochs [Beard, K.V., Ochs, H.T., 1984. Collection and coalescence efficiencies for accretion. J. Geophys. Res., 89: 7165-7169.] ranging from 0.5 to about 0.75 for different droplet sizes. In the case of graupel-droplet interaction E ɛ was assumed equal to 1. It is shown that in the case E ɛ=1 in a non-turbulent medium, the growth rates of graupel and raindrops are close. Under turbulent conditions typical of mature convective clouds, graupel grows much faster than a raindrop. In the case E ɛ<1 the growth rate of a water drop slows down significantly, so that graupel grows faster than raindrops even under non-turbulent conditions. Turbulence greatly increases the difference between the growth rates of graupel and drop-collectors. Possible consequences of the faster growth of graupel in terms of cloud microphysics are discussed.
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
Isotropic Monte Carlo Grain Growth
Mason, J.
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.
Lagrangian analysis of premixed turbulent combustion in hydrogen-air flames
NASA Astrophysics Data System (ADS)
Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter
2016-11-01
Lagrangian analysis has long been a tool used to analyze non-reacting turbulent flows, and has recently gained attention in the reacting flow and combustion communities. The approach itself allows one to separate local molecular effects, such as those due to reactions or diffusion, from turbulent advective effects along fluid pathlines, or trajectories. Accurate calculation of these trajectories can, however, be rather difficult due to the chaotic nature of turbulent flows and the added complexity of reactions. In order to determine resolution requirements and verify the numerical algorithm, extensive tests are described in this talk for prescribed steady, unsteady, and chaotic flows, as well as for direct numerical simulations (DNS) of non-reacting homogeneous isotropic turbulence. The Lagrangian analysis is then applied to DNS of premixed hydrogen-air flames at two different turbulence intensities for both single- and multi-step chemical mechanisms. Non-monotonic temperature and fuel-mass fraction evolutions are found to exist along trajectories passing through the flame brush. Such non-monotonicity is shown to be due to molecular diffusion resulting from large spatial gradients created by turbulent advection. This work was supported by the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-14-1-0273, and the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) under a Frontier project award.
Spatial-temporal spectra of velocity fluctuations in turbulent shear flows
NASA Astrophysics Data System (ADS)
He, Guowei; Wu, Ting; Zhao, Xin
2015-11-01
Space-time correlation or its Fourier form, spatial-temporal spectrum, is a minimal quantity to statistically characterize the temporal evolutions of spatial structures in turbulent flows. The Kraichnan-Tennekes random-sweeping model is well-known for spatial-temporal spectra in isotropic and homogeneous turbulence. Recently, Wilczek, Stevens and Meneveau (J. Fluid Mech. 2015 vol. 769, R1) have developed a simple model for spatial-temporal spectra in the Logarithmic layer of wall turbulence. In this study, we propose a model equation for turbulent shear flows. This model equation includes both sweeping and stretching effects and its solution gives an analytical expression for spatial-temporal spectra of stream-wise velocities. The results obtained are compared with the data from direct numerical simulation (DNS) of turbulent channel flows. It is found that this model is reasonably consistent with the DNS results for either small or large shear rates. This model is also discussed in comparison with the EA (elliptic approximation) model for space-time correlations in turbulent shear flows (Phys. Rev. E 79 046316 2009).
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.
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.
Indentation of Transversely Isotropic Materials
NASA Astrophysics Data System (ADS)
Bhat, Talapady Srivatsa
Instrumented indentation, as a tool for characterization of mechanical properties, has well been established in the past decades. Studies have been conducted to understand the behavior of isotropic materials under indentation and techniques to accurately predict isotropic material properties have also been reported. Further, within the isotropic regime, work has been done to predict the indentation hardness without having to investigate the area of contact during indentation. Studies have also reported the prospect of utilizing indentation to predict the fatigue behavior of isotropic materials. This dissertation is made with the intent of extending the use of indentation, as a characterization tool, to the anisotropic regime. The effect of transverse isotropy on the indentation response of materials is systematically studied here. Extensive computational analysis is performed to elucidate the underlying deformation mechanics of indentation of transversely isotropic materials. Owing to the anisotropy, indentation may be performed parallel or perpendicular to the plane of isotropy of the specimen. It is observed that the indentation response varies significantly for each of these cases. The two cases are treated as unique and an identical systematic analysis is carried for both. The indentation orientations shall henceforth be referred to as transverse and longitudinal indentation for indentation parallel and perpendicular to the plane of isotropy respectively. A technique is developed capable of extracting the elastic-plastic properties of transversely isotropic materials from interpretation of indentation response in either direction. The technique is rigorously tested for its robustness, accuracy and uniqueness of results. A sensitivity analysis is performed to determine how sensitive the technique is to errors in experimental results. Rigorous studies are performed to understand the variation in pile-up or sink-in during indentation with varying anisotropy in the
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.
Charged Particle Diffusion in Isotropic Random Magnetic Fields
NASA Astrophysics Data System (ADS)
Subedi, P.; Sonsrettee, W.; Blasi, P.; Ruffolo, D.; Matthaeus, W. H.; Montgomery, D.; Chuychai, P.; Dmitruk, P.; Wan, M.; Parashar, T. N.; Chhiber, R.
2017-03-01
The investigation of the diffusive transport 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 the diffusion of charged particles in fully three-dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. We identify different ranges of particle energy depending upon the ratio of Larmor radius to the characteristic outer length scale of turbulence. Two different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical results are compared to those from computer simulations, showing good 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.
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.
Transversely isotropic elasticity and poroelasticity arising from thin isotropic layers
Berryman, J.G.
1997-07-01
Since the classic work of Postma [1955] and Backus [1962], much has been learned about elastic constants in vertical transversely isotropic (VTI) media when the anisotropy is due to fine layering of isotropic elastic materials. However, new results are still being discovered. For example, the P-wave anisotropy parameter c{sub 11}/c{sub 33} lies in the range 1/4 {<=} c{sub 11}/c{sub 33} {<=} <{lambda}+2{mu}><1/({lambda}+2{mu})>, when the layers are themselves composed of isotropic elastic materials with Lame constants {lambda} and {mu} and the vertical average of the layers is symbolized by <{center_dot}>. The lower bound corrects a result of Postma. For porous layers, 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. For isotropic and anisotropic poroelastic media, we establish 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 [1951] formulas that must be satisfied by any anisotropic poroelastic medium and found to be in complete agreement. Such results are important for applications to oil exploration using AVO (amplitude versus offset) since the presence or absence of a fluid component, as well as the nature of the fluid, is the critical issue and the ways in which the fluid influences seismic reflection data still need to be better understood.
Transformation to zero offset in transversely isotropic media
Alkhalifah, T.
1995-02-01
Nearly all dip moveout correction (DMO) implementations to date assume isotropic homogeneous media. Usually, this has been acceptable considering the tremendous cost savings of homogeneous isotropic DMO and considering the difficulty of obtaining the anisotropy parameters required for effective implementation. In the presence of typical anisotropy, however, ignoring the anisotropy can yield inadequate results. Since anisotropy may introduce large deviations from hyperbolic moveout, accurate transformation to zero-offset in anisotropic media should address such nonhyperbolic moveout behavior of reflections. Artley and Hale`s (1994) v(z) ray tracing-based DMO, developed for isotropic media, provides an attractive approach to treating such problems. By using a ray-tracing procedure crafted for anisotropic media, the author modifies some aspects of Artley and Hale`s DMO so that it can work for v(z) anisotropic media. Application of this anisotropic DMO to data from offshore Africa resulted in a considerably better alignment of reflections from horizontal and dipping reflectors in common-midpoint gather than that obtained using an isotropic DMO. Even the presence of vertical inhomogeneity in this medium could not eliminate the importance of considering the shale induced anisotropy.
Du, Xinyue; Zhao, Daomu; Korotkova, Olga
2007-12-10
We report analytic formulas for the elements of the e 2 X2 cross-spectral density matrix of a stochastic electromagnetic anisotropic beam propagating through the turbulent atmosphere with the help of vector integration. From these formulas the changes in the spectral density (spectrum), in the spectral degree of polarization, and in the spectral degree of coherence of such a beam on propagation are determined. As an example, these quantities are calculated for a so-called anisotropic electromagnetic Gaussian Schell-model beam propagating in the isotropic and homogeneous atmosphere. In particular, it is shown numerically that for a beam of this class, unlike for an isotropic electromagnetic Gaussian Schell-model beam, its spectral degree of polarization does not return to its value in the source plane after propagating at sufficiently large distances in the atmosphere. It is also shown that the spectral degree of coherence of such a beam tends to zero with increasing distance of propagation through the turbulent atmosphere, in agreement with results previously reported for isotropic beams.
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.
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.
Plane Waves in a Transparent Isotropic Chiral Medium
NASA Astrophysics Data System (ADS)
Fisanov, V. V.
2015-04-01
A homogeneous isotropic transparent chiral medium supports two normal plane waves with left and right circular polarization and differently valued positive wave numbers. The presence or absence of forward and backward Beltrami waves and their helicity are regulated by the signs of the permittivity and permeability and the strength of the chirality. The ray refractive index is a universal parameter whose sign differentiates the forward and backward waves.
NASA Astrophysics Data System (ADS)
Schulreich, M. M.; Breitschwerdt, D.; Feige, J.; Dettbarn, C.
2017-08-01
Context. The discovery of radionuclides like 60Fe with half-lives of million years in deep-sea crusts and sediments offers the unique possibility to date and locate nearby supernovae. Aims: We want to quantitatively establish that the 60Fe enhancement is the result of several supernovae which are also responsible for the formation of the Local Bubble, our Galactic habitat. Methods: We performed three-dimensional hydrodynamic adaptive mesh refinement simulations (with resolutions down to subparsec scale) of the Local Bubble and the neighbouring Loop I superbubble in different homogeneous, self-gravitating environments. For setting up the Local and Loop I superbubble, we took into account the time sequence and locations of the generating core-collapse supernova explosions, which were derived from the mass spectrum of the perished members of certain stellar moving groups. The release of 60Fe and its subsequent turbulent mixing process inside the superbubble cavities was followed via passive scalars, where the yields of the decaying radioisotope were adjusted according to recent stellar evolution calculations. Results: The models are able to reproduce both the timing and the intensity of the 60Fe excess observed with rather high precision, provided that the external density does not exceed 0.3 cm-3 on average. Thus the two best-fit models presented here were obtained with background media mimicking the classical warm ionised and warm neutral medium. We also found that 60Fe (which is condensed onto dust grains) can be delivered to Earth via two physical mechanisms: either through individual fast-paced supernova blast waves, which cross the Earth's orbit sometimes even twice as a result of reflection from the Local Bubble's outer shell, or, alternatively, through the supershell of the Local Bubble itself, injecting the 60Fe content of all previous supernovae at once, but over a longer time range.
How long do particles spend in vortical regions in turbulent flows?
NASA Astrophysics Data System (ADS)
Bhatnagar, Akshay; Gupta, Anupam; Mitra, Dhrubaditya; Pandit, Rahul; Perlekar, Prasad
2016-11-01
We consider passive, heavy, inertial, particles (HIP) in three-dimensional, homogeneous, and isotropic turbulence. Whether a particle is in a vortical regions or not is determined by the two invariants of the (flow) velocity gradient matrix , Q and R, at the position of the parti cle. Using direct numerical simulations, we calculate the probability distribution functions (PDFs) of the first-passage-time of a tracer or a HIP in a vortical region. The corresponding PDF in two dimensions is known to show power-law tail. In three dimensions we find that the PDF possesses exponential tail with a characteristic time of the order of large-eddy-turnover-time of the flow. partially supported by the Knut and Alice Wallenberg Foundation (DM and AB) under project "Bottlenecks for particle growth in turbulent aerosols" (Dnr. KAW 2014.0048).
3D DNS of Turbulent Premixed Flame with over 50 Species and 300 Elementary Reactions
NASA Astrophysics Data System (ADS)
Shimura, Masayasu; Yenerdag, Basmil; Naka, Yoshitsugu; Nada, Yuzuru; Tanahashi, Mamoru
2014-11-01
Three-dimensional direct numerical simulation of methane-air premixed planar flame propagating in homogenous isotropic turbulence is conducted to investigate local flame structure in thin reaction zones. Detailed kinetic mechanism, GRI-Mech 3.0 which includes 53 species and 325 elementary reactions, is used to represent methane-air reaction, and temperature dependences of transport and thermal properties are considered. For a better understanding of the local flame structure in thin reaction zones regime, distributions of mass fractions of major species, heat release rate, temperature and turbulent structures are investigated. Characteristic flame structures, such as radical fingering and multi-layered-like flame structures, are observed. The most expected maximum heat release rate in flame elements is lower than that of laminar flame with same mixture. To clarify mechanism of the decrease in local heat release rate, effects of strain rates tangential to flame front on local heat release rate are investigated.
Numerical study of small-scale intermittency in three-dimensional turbulence
NASA Astrophysics Data System (ADS)
Siggia, E. D.
1981-06-01
A study is presented of the intermittency effects (comparable to the 1949 Batchelor and Townsend experiments) which are studied for stationary, homogeneous, isotropic turbulence by means of a direct spectral simulation on a 64 x 64 x 64 lattice. The turbulence is kept stationary, and the rate of energy input and viscosity are free parameters. The interrelations of intermittency and parameterizations of the large scales are discussed. The equations for energy and vorticity balance are checked as a function of wavenumber, and the locality of the energy cascade in wavenumber is also examined. First- and second-derivative flatness factors of order 4.5, 5.0 and 9.0 respectively are found under stationary conditions with bursts to higher values. Three-dimensional plots of the vorticity reveal persistent and extended tubes, sheets, and blobs.
NASA Astrophysics Data System (ADS)
Lian, Huan; Soulopoulos, Nikolaos; Hardalupas, Yannis
2017-09-01
The experimental evaluation of the topological characteristics of the turbulent flow in a `box' of homogeneous and isotropic turbulence (HIT) with zero mean velocity is presented. This requires an initial evaluation of the effect of signal noise on measurement of velocity invariants. The joint probability distribution functions (pdfs) of experimentally evaluated, noise contaminated, velocity invariants have a different shape than the corresponding noise-free joint pdfs obtained from the DNS data of the Johns Hopkins University (JHU) open resource HIT database. A noise model, based on Gaussian and impulsive Salt and Pepper noise, is established and added artificially to the DNS velocity vector field of the JHU database. Digital filtering methods, based on Median and Wiener Filters, are chosen to eliminate the modeled noise source and their capacity to restore the joint pdfs of velocity invariants to that of the noise-free DNS data is examined. The remaining errors after filtering are quantified by evaluating the global mean velocity, turbulent kinetic energy and global turbulent homogeneity, assessed through the behavior of the ratio of the standard deviation of the velocity fluctuations in two directions, the energy spectrum of the velocity fluctuations and the eigenvalues of the rate-of-strain tensor. A method of data filtering, based on median filtered velocity using different median filter window size, is used to quantify the clustering of zero velocity points of the turbulent field using the radial distribution function (RDF) and Voronoï analysis to analyze the 2D time-resolved particle image velocimetry (TR-PIV) velocity measurements. It was found that a median filter with window size 3 × 3 vector spacing is the effective and efficient approach to eliminate the experimental noise from PIV measured velocity images to a satisfactory level and extract the statistical two-dimensional topological turbulent flow patterns.
Bi-isotropic constitutive relations
NASA Astrophysics Data System (ADS)
Sihvola, A. H.; Lindell, I. V.
1991-03-01
The constitutive relations of general bi-isotropic media, requiring four material parameters, can be written in different ways to describe their electromagnetic behavior. This communication contains a two-way 'dictionary' between a proposed formulation of the constitutive relations with three other sets of relations, generalized from relations used for chiral materials.
Subgrid-scale models for large-eddy simulation of rotating turbulent flows
NASA Astrophysics Data System (ADS)
Silvis, Maurits; Trias, Xavier; Abkar, Mahdi; Bae, Hyunji Jane; Lozano-Duran, Adrian; Verstappen, Roel
2016-11-01
This paper discusses subgrid models for large-eddy simulation of anisotropic flows using anisotropic grids. In particular, we are looking into ways to model not only the subgrid dissipation, but also transport processes, since these are expected to play an important role in rotating turbulent flows. We therefore consider subgrid-scale models of the form τ = - 2νt S +μt (SΩ - ΩS) , where the eddy-viscosity νt is given by the minimum-dissipation model, μt represents a transport coefficient; S is the symmetric part of the velocity gradient and Ω the skew-symmetric part. To incorporate the effect of mesh anisotropy the filter length is taken in such a way that it minimizes the difference between the turbulent stress in physical and computational space, where the physical space is covered by an anisotropic mesh and the computational space is isotropic. The resulting model is successfully tested for rotating homogeneous isotropic turbulence and rotating plane-channel flows. The research was largely carried out during the CTR SP 2016. M.S, and R.V. acknowledge the financial support to attend this Summer Program.
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.
Statistics of particle pair relative velocity in the homogeneous shear flow
NASA Astrophysics Data System (ADS)
Gualtieri, P.; Picano, F.; Sardina, G.; Casciola, C. M.
2012-02-01
Small scale clustering of inertial particles and relative velocity of particle pairs have been fully characterized for statistically steady homogeneous isotropic flows. Depending on the particle Stokes relaxation time, the spatial distribution of the disperse phase results in a multi-scale manifold characterized by local particle concentration and voids and, because of finite inertia, the two nearby particles have high probability to exhibit large relative velocities. Both effects might explain the speed-up of particle collision rate in turbulent flows. Recently it has been shown that the large scale geometry of the flow plays a crucial role in organizing small scale particle clusters. For instance, a mean shear preferentially orients particl