Anisotropic eddy viscosity models
NASA Technical Reports Server (NTRS)
Carati, D.; Cabot, W.
1996-01-01
A general discussion on the structure of the eddy viscosity tensor in anisotropic flows is presented. The systematic use of tensor symmetries and flow symmetries is shown to reduce drastically the number of independent parameters needed to describe the rank 4 eddy viscosity tensor. The possibility of using Onsager symmetries for simplifying further the eddy viscosity is discussed explicitly for the axisymmetric geometry.
Eddy viscosity measurements in a rectangular jet
NASA Technical Reports Server (NTRS)
Swan, David H.; Morrison, Gerald L.
1988-01-01
The flow field of a rectangular jet with a 2:1 aspect ratio was studied at a Reynolds number of 100,000 (Mach number 0.09) using three-dimensional laser Doppler velocimetry (LDV). Velocity gradients, Reynolds stress tensor components, and scalar eddy viscosities are presented for the major and minor axis planes of the jet. The eddy viscosity model was found to be applicable only in the direction of maximum mean velocity gradient.
A transport equation for eddy viscosity
NASA Technical Reports Server (NTRS)
Durbin, P. A.; Yang, Z.
1992-01-01
A transport equation for eddy viscosity is proposed for wall bounded turbulent flows. The proposed model reduces to a quasi-homogeneous form far from surfaces. Near to a surface, the nonhomogeneous effect of the wall is modeled by an elliptic relaxation model. All the model terms are expressed in local variables and are coordinate independent; the model is intended to be used in complex flows. Turbulent channel flow and turbulent boundary layer flows with/without pressure gradient are calculated using the present model. Comparisons between model calculations and direct numerical simulation or experimental data show good agreement.
Effects of Eddy Viscosity on Time Correlations in Large Eddy Simulation
NASA Technical Reports Server (NTRS)
He, Guowei; Rubinstein, R.; Wang, Lian-Ping; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
Subgrid-scale (SGS) models for large. eddy simulation (LES) have generally been evaluated by their ability to predict single-time statistics of turbulent flows such as kinetic energy and Reynolds stresses. Recent application- of large eddy simulation to the evaluation of sound sources in turbulent flows, a problem in which time, correlations determine the frequency distribution of acoustic radiation, suggest that subgrid models should also be evaluated by their ability to predict time correlations in turbulent flows. This paper compares the two-point, two-time Eulerian velocity correlation evaluated from direct numerical simulation (DNS) with that evaluated from LES, using a spectral eddy viscosity, for isotropic homogeneous turbulence. It is found that the LES fields are too coherent, in the sense that their time correlations decay more slowly than the corresponding time. correlations in the DNS fields. This observation is confirmed by theoretical estimates of time correlations using the Taylor expansion technique. Tile reason for the slower decay is that the eddy viscosity does not include the random backscatter, which decorrelates fluid motion at large scales. An effective eddy viscosity associated with time correlations is formulated, to which the eddy viscosity associated with energy transfer is a leading order approximation.
A local eddy viscosity model for turbulent shear flow
NASA Technical Reports Server (NTRS)
Ortwerth, P. J.; Rabe, D. C.; Mcerlean, D. P.
1973-01-01
In the model described, the eddy viscosity is assumed to be a fluid property dependent on the state of the fluid locally, namely the local density, turbulent kinetic energy, turbulence scale, and Mach number. An empirical law was found which related eddy viscosity to these properties satisfactorily for free jets. This law is used without modification for a set of test cases in free shear layers, free-jet decay, coaxial mixing, and wakes. The scale of turbulence is taken as a constant at any axial location equal to the width of the shear layer. By utilizing the boundary-layer order-of-magnitude analysis, a coupled set of fluid dynamic equations is formulated, which of necessity includes the equation for the production of turbulent kinetic energy.
Prediction of Transonic Vortex Flows Using Linear and Nonlinear Turbulent Eddy Viscosity Models
NASA Technical Reports Server (NTRS)
Bartels, Robert E.; Gatski, Thomas B.
2000-01-01
Three-dimensional transonic flow over a delta wing is investigated with a focus on the effect of transition and influence of turbulence stress anisotropies. The performance of linear eddy viscosity models and an explicit algebraic stress model is assessed at the start of vortex flow, and the results compared with experimental data. To assess the effect of transition location, computations that either fix transition or are fully turbulent are performed. To assess the effect of the turbulent stress anisotropy, comparisons are made between predictions from the algebraic stress model and the linear eddy viscosity models. Both transition location and turbulent stress anisotropy significantly affect the 3D flow field. The most significant effect is found to be the modeling of transition location. At a Mach number of 0.90, the computed solution changes character from steady to unsteady depending on transition onset. Accounting for the anisotropies in the turbulent stresses also considerably impacts the flow, most notably in the outboard region of flow separation.
RAS one-equation turbulence model with non-singular eddy-viscosity coefficient
NASA Astrophysics Data System (ADS)
Rahman, M. M.; Agarwal, R. K.; Siikonen, T.
2016-02-01
A simplified consistency formulation for Pk/ε (production to dissipation ratio) is devised to obtain a non-singular Cμ (coefficient of eddy-viscosity) in the explicit algebraic Reynolds stress model of Gatski and Speziale. The coefficient Cμ depends non-linearly on both rotational/irrotational strains and is used in the framework of an improved RAS (Rahman-Agarwal-Siikonen) one-equation turbulence model to calculate a few well-documented turbulent flows, yielding predictions in good agreement with the direct numerical simulation and experimental data. The strain-dependent Cμ assists the RAS model in constructing the coefficients and functions such as to benefit complex flows with non-equilibrium turbulence. Comparisons with the Spalart-Allmaras one-equation model and the shear stress transport k-ω model demonstrate that Cμ improves the response of RAS model to non-equilibrium effects.
Dependence of red edge on eddy viscosity model parameters
NASA Technical Reports Server (NTRS)
Deupree, R. G.; Cole, P. W.
1980-01-01
The dependence of the red edge location on the two fundamental free parameters in the eddy viscosity treatment was extensively studied. It is found that the convective flux is rather insensitive to any reasonable or allowed value of the two free parameters of the treatment. This must be due in part to the fact that the convective flux is determined more by the properties of the hydrogen ionization region than by differences in convective structure. The changes in the effective temperature of the red edge of the RR Lyrae gap resulting from these parameter variations is quite small (approximately 150 K). This is true both because the parameter variation causes only small changes and because large changes in the convective flux are required to produce any significant change in red edge location. The possible changes found are substantially less than the approximately 600 K required to change the predicted helium abundance mass fraction from 0.3 to 0.2.
A normal stress subgrid-scale eddy viscosity model in large eddy simulation
NASA Technical Reports Server (NTRS)
Horiuti, K.; Mansour, N. N.; Kim, John J.
1993-01-01
The Smagorinsky subgrid-scale eddy viscosity model (SGS-EVM) is commonly used in large eddy simulations (LES) to represent the effects of the unresolved scales on the resolved scales. This model is known to be limited because its constant must be optimized in different flows, and it must be modified with a damping function to account for near-wall effects. The recent dynamic model is designed to overcome these limitations but is compositionally intensive as compared to the traditional SGS-EVM. In a recent study using direct numerical simulation data, Horiuti has shown that these drawbacks are due mainly to the use of an improper velocity scale in the SGS-EVM. He also proposed the use of the subgrid-scale normal stress as a new velocity scale that was inspired by a high-order anisotropic representation model. The testing of Horiuti, however, was conducted using DNS data from a low Reynolds number channel flow simulation. It was felt that further testing at higher Reynolds numbers and also using different flows (other than wall-bounded shear flows) were necessary steps needed to establish the validity of the new model. This is the primary motivation of the present study. The objective is to test the new model using DNS databases of high Reynolds number channel and fully developed turbulent mixing layer flows. The use of both channel (wall-bounded) and mixing layer flows is important for the development of accurate LES models because these two flows encompass many characteristic features of complex turbulent flows.
An alternative eddy-viscosity representation and its implication to turbulence modeling
NASA Astrophysics Data System (ADS)
Jakirlic, Suad; Jovanovic, Jovan; Basara, Branislav
2013-11-01
Large majority of turbulence models in the RANS framework (it holds also in the case of the LES method) is based on the eddy-viscosity rationale. The principle task of modeling the Reynolds stress tensor reduces to modeling the eddy-viscosity, representing, according to Boussinesq (1877), the ``coefficient of proportionality'' between the Reynolds stress and mean rate of strain tensors. In the present contribution an extended formulation based on the least square approach applied to the Boussinesq's correlation is presented. Furthermore, a Taylor-microscale-based formulation is derived originating from the equilibrium assumption related to the equality between the production and dissipation rates of kinetic energy of turbulence. Finally, an expression is proposed reflecting the Reynolds stress anisotropy influence on the eddy-viscosity damping by approaching the solid wall as well as including an appropriate length-scale switch accounting for the viscosity effects through inclusion of the Kolmogorov scales blended with those of the energy-containing eddies. The latter formulation is successfully applied in the framework of an instability-sensitive Reynolds stress model of turbulence. The afore-mentioned eddy-viscosity definitions are comparatively assessed in a series of wall-bounded flow configurations (including separation) in a Reynolds number range.
A kinematic eddy viscosity model including the influence of density variations and preturbulence
NASA Technical Reports Server (NTRS)
Cohen, L. S.
1973-01-01
A model for the kinematic eddy viscosity was developed which accounts for the turbulence produced as a result of jet interactions between adjacent streams as well as the turbulence initially present in the streams. In order to describe the turbulence contribution from jet interaction, the eddy viscosity suggested by Prandtl was adopted, and a modification was introduced to account for the effect of density variation through the mixing layer. The form of the modification was ascertained from a study of the compressible turbulent boundary layer on a flat plate. A kinematic eddy viscosity relation which corresponds to the initial turbulence contribution was derived by employing arguments used by Prandtl in his mixing length hypothesis. The resulting expression for self-preserving flow is similar to that which describes the mixing of a submerged jet. Application of the model has led to analytical predictions which are in good agreement with available turbulent mixing experimental data.
Renormalization-group theory for the eddy viscosity in subgrid modeling
NASA Technical Reports Server (NTRS)
Zhou, YE; Vahala, George; Hossain, Murshed
1988-01-01
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.
A new non-eddy viscosity subgrid-scale model and its application to channel flow
NASA Technical Reports Server (NTRS)
Shah, K. B.; Ferziger, J. H.
1995-01-01
To date, most large-eddy simulations (LES) have been carried out with eddy viscosity subgrid scale (SGS) models, with only a few exceptions that used the mixed model. Even though the assumptions behind Smagorinsky's model are rather stringent, it has been applied successfully to a variety of turbulent flows. This success is attributed to the ability of eddy viscosity models to drain energy from large scales, thus simulating the dissipative nature of turbulence. Most SGS models are absolutely dissipative, i.e. they remove energy from the large scales at every instant. However, SGS stresses may transfer energy back to the large scales intermittently; this reverse transfer or backscatter is especially important in geophysical flows and in transition. In a fully developed channel flow, there is reverse flow of energy from small to large scales near the walls, but eddy viscosity models are unable to account for this important feature. The dynamic localization eddy viscosity model of Ghosal et al. (1995) allows backscatter by co-evolving an auxiliary equation for the SGS energy; however, the computational cost is considerably larger than for conventional SGS models (Cabot 1994). In this report, a new non-eddy viscosity model based on local approximation of total quantities in terms of filtered ones is introduced; the scale similarity model of Bardina (1983) is a special case of this model. This procedure does not require the assumption of homogeneity, permits backscatter of energy from small to large scales, and is readily implemented in finite difference codes. The results of applying the proposed model to second order finite volume simulation of plane channel flow at high Reynolds numbers (Re(sub b) = 38,000) is described in this report. Greater emphasis is placed on the high Reynolds number flow since it provides a more rigorous test of the SGS model and its potential application. The results are compared to ones produced by the conventional and dynamic Smagorinsky
Turbulent Eddy Viscosity and Large-Scale Convection in the Sun
NASA Technical Reports Server (NTRS)
Stothers, Richard B.
2000-01-01
It is suggested here that the laminar character of the large-scale deep convective flows appearing in numerical simulations of the Sun's convective envelope arises from the effect of turbulent eddy viscosity. Previously, M. Schwarzchild suggested the same idea to explain the observed surface granulation in the Sun.
NASA Astrophysics Data System (ADS)
Tian, Zhigang; Perlin, Marc; Choi, Wooyoung
2012-03-01
An eddy viscosity model to describe energy dissipation in two-dimensional breaking waves in deep water is implemented in a numerical model for the evolution of nonlinear surface waves and evaluated with experimental results. In the experiments, to develop a reliable eddy viscosity model, breaking waves are generated by both energy focusing and modulated wave groups. Local wave parameters prior to and following breaking are defined and then determined. Significant correlations between the pre-breaking and post-breaking parameters are identified and adopted in the eddy viscosity model. The numerical model detects automatically wave breaking onset based on local surface slope, determines pre-breaking local wave parameters, predicts post-breaking time and length scales, and estimates eddy viscosity to dissipate energy in wave breaking events. Numerical simulations with the model are performed and compared to the experiments. It is found that the model predicts well the total energy dissipation due to breaking waves. In addition, the computed surface elevations after wave breaking agree reasonably well with the measurements for the energy focusing (plunging) wave groups. However, for breaking wave groups due to modulational instability (plunging and spilling), a relatively large discrepancy between the surface elevation predictions and the experimental measurements is observed, in particular, at the downstream wave probe locations. This is possibly due to wave reflection and three-dimensionality in the experiments. To further validate the eddy viscosity model, the evolution of highly nonlinear irregular waves is studied numerically and the numerical solutions are compared with additional independent laboratory experiments for long-crested irregular waves. It is shown that the numerical model is capable of predicting the wave evolution subsequent to wave breaking.
NASA Astrophysics Data System (ADS)
Slepyshev, A. A.
2016-05-01
Free internal waves are considered in a Boussinesq approximation in the situation when horizontal eddy viscosity and diffusion in a vertically inhomogeneous flow are taken into account. The dispersion relation and wave damping factor are found in a linear approximation. The Stokes drift velocity is determined in the second order of smallness based on the wave amplitude. It has been indicated that the Stokes drift velocity, transverse with respect to the wave propagation direction, differs from zero if the flow-rate transverse component depends on the vertical coordinate. Vertical momentum fluxes differ from zero and can be comparable with or exceed the corresponding turbulent fluxes if eddy viscosity and diffusion are taken into account.
A dynamic subgrid-scale eddy viscosity model with a global model coefficient
NASA Astrophysics Data System (ADS)
Park, Noma; Lee, Sungwon; Lee, Jungil; Choi, Haecheon
2006-12-01
In the present study, a dynamic subgrid-scale eddy viscosity model is proposed for large eddy simulation of turbulent flows in complex geometry. A subgrid-scale eddy viscosity model recently proposed by Vreman [Phys. Fluids 16, 3670 (2004)] which guarantees theoretically zero subgrid-scale dissipation for various laminar shear flows, is considered as a base model. A priori tests with the original Vreman model show that it predicts the correct profile of subgrid-scale dissipation in turbulent channel flow but the optimal model coefficient is far from universal. A dynamic procedure of determining the model coefficient is proposed based on the "global equilibrium" between the subgrid-scale dissipation and the viscous dissipation. An important feature of the proposed procedure is that the model coefficient determined is globally constant in space but varies only in time. A posteriori tests of the proposed dynamic model are conducted through large eddy simulations of forced isotropic turbulence at Reλ=103, turbulent channel flows at Reτ=180 and 590, flow over a circular cylinder at Red=3900, and flows over a sphere at Red=3700 and 104. The proposed dynamic model produces excellent performance for all flows considered. As shown in the present paper, the proposed model is robust and it can be readily applied to complex flows without homogeneous direction.
NASA Astrophysics Data System (ADS)
Oberai, Assad A.; Hughes, Thomas J. R.
2016-04-01
We explore a general family of eddy viscosity models for the large-eddy simulation of turbulence within the framework of the Variational Multiscale Method. Our investigation encompasses various fine-scale eddy viscosities and coarse-scale residual-based constructs. We delineate the domain of parameter space in which physically and mathematically suitable models exist, and identify several sub-families of potentially useful models that are either entirely new or extend previously proposed ones. We also combine classical modeling ideas, that lead to turbulent kinetic energy evolution equations, with the residual-based approach to derive a new residual-driven, one-equation dynamic model.
Turbulent eddy viscosity modeling in transonic shock/boundary-layer interactions
NASA Technical Reports Server (NTRS)
Inger, G. R.
1989-01-01
The treatment of turbulence effects on transonic shock/turbulent boundary layer interaction is addressed within the context of a triple deck approach valid for arbitrary practical Reynolds numbers between 1000 and 10 billion. The modeling of the eddy viscosity and basic turbulent boundary profile effects in each deck is examined in detail using Law-of-the-Wall/Law-of-the-Wake concepts as the foundation. Results of parametric studies showing how each of these turbulence model aspects influences typical interaction zone property distributions (wall pressure, displacement thickness and local skin friction) are presented and discussed.
NASA Technical Reports Server (NTRS)
Shih, T.-H.; Liou, W. W.; Shabbir, A.; Yang, Z.; Zhu, J.
1994-01-01
A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.
NASA Astrophysics Data System (ADS)
Shih, T.-H.; Liou, W. W.; Shabbir, A.; Yang, Z.; Zhu, J.
1994-08-01
A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.
Puleo, J.A.; Mouraenko, O.; Hanes, D.M.
2004-01-01
Six one-dimensional-vertical wave bottom boundary layer models are analyzed based on different methods for estimating the turbulent eddy viscosity: Laminar, linear, parabolic, k—one equation turbulence closure, k−ε—two equation turbulence closure, and k−ω—two equation turbulence closure. Resultant velocity profiles, bed shear stresses, and turbulent kinetic energy are compared to laboratory data of oscillatory flow over smooth and rough beds. Bed shear stress estimates for the smooth bed case were most closely predicted by the k−ω model. Normalized errors between model predictions and measurements of velocity profiles over the entire computational domain collected at 15° intervals for one-half a wave cycle show that overall the linear model was most accurate. The least accurate were the laminar and k−ε models. Normalized errors between model predictions and turbulence kinetic energy profiles showed that the k−ω model was most accurate. Based on these findings, when the smallest overall velocity profile prediction error is required, the processing requirements and error analysis suggest that the linear eddy viscosity model is adequate. However, if accurate estimates of bed shear stress and TKE are required then, of the models tested, the k−ω model should be used.
Convection without eddy viscosity: An attempt to model the interiors of giant planets
NASA Technical Reports Server (NTRS)
Ingersoll, A. P.
1986-01-01
In the theory of hydrostatic quasi-geostrophic flow in the Earth's atmosphere the principal results do not depend on the eddy viscosity. This contrasts with published theories of convection in deep rotating fluid spheres, where the wavelength of the fastest growing disturbance varies as E sup 1/3, where E, the Ekman number, is proportional to the eddy viscosity. A new theory of quasi-columnar motions in stably stratified fluid spheres attempts to capture the luck of the meteorologists. The theory allows one to investigate the stability of barotropic and baroclinic zonal flows that extend into the planetary interior. It is hypothesized that the internal heat Jupiter and Saturn comes out not radially but on sloping surfaces defined by the internal entropy distribution. To test the hypothesis one searches for basic states in which the wavelength of the fastest-growing disturbance remains finite as E tends to zero, and is which the heat flux vector is radially outward and poleward.
Predictions of axisymmetric free turbulent shear flows using a generalized eddy-viscosity approach
NASA Technical Reports Server (NTRS)
Morgenthaler, J. H.
1973-01-01
The generalized eddy viscosity approach is described and results are presented of test cases which show that predictions obtained by this approach are adequate for most engineering applications. Because of the importance of starting computations from the injection station where experimentally determined mean and turbulence parameters are rarely available, a very simple core model applicable to simple step-type (slug) profiles was developed. Agreement between predicted and experimental mean profiles was generally almost as good for calculations made by using this model throughout the core region and the transition model for all subsequent regions as predictions made by starting from experimental profiles in the transition region. The generalized eddy-viscosity model, which was developed in part through correlation of turbulence parameters, successfully predicted turbulent shear stress, turbulent intensity, and mean velocity profiles for a 0.040-inch-diameter microjet. Therefore, successful scaling by the model was demonstrated since data used in its development was for jet areas up to 90,000 times as large as the microjet and velocities only 1/20th as high.
NASA Astrophysics Data System (ADS)
Foreman, Richard J.; Emeis, Stefan; Canadillas, Beatriz
2015-02-01
A turbulence parametrization for wind speed in the stable boundary layer consisting of a single empirical parameter is proposed without the use of the eddy viscosity concept or turbulent kinetic energy equation. Instead, a drag-coefficient-type formulation as a function of the bulk Richardson number has been found to be able to reproduce observed stable boundary-layer wind speeds as effectively as a model based on the eddy viscosity approach. The advantage of this simpler approach is that the model can, in theory, be modified more easily for certain applications, such as the effects of large-scale wind parks on mesoscale meteorology.
NASA Astrophysics Data System (ADS)
Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.
2014-06-01
We have developed a three-fluid, three-dimensional magnetohydrodynamic solar wind model that incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a system of co-moving solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Numerical steady-state solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations for turbulence energy, cross helicity, and correlation length are obtained by the time relaxation method in the corotating with the Sun frame of reference in the region from 0.3 to 100 AU (but still inside the termination shock). The model equations include the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. The turbulence transport model is based on the Reynolds decomposition and turbulence phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. In addition to using separate energy equations for the solar wind protons and electrons, a significant improvement over our previous work is that the turbulence model now uses an eddy viscosity approximation for the Reynolds stress tensor and the mean turbulent electric field. The approximation allows the turbulence model to account for driving of turbulence by large-scale velocity gradients. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including embedded turbulence, heating, and acceleration throughout the heliosphere. The model results are
Usmanov, Arcadi V.; Matthaeus, William H.; Goldstein, Melvyn L.
2014-06-10
We have developed a three-fluid, three-dimensional magnetohydrodynamic solar wind model that incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a system of co-moving solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Numerical steady-state solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations for turbulence energy, cross helicity, and correlation length are obtained by the time relaxation method in the corotating with the Sun frame of reference in the region from 0.3 to 100 AU (but still inside the termination shock). The model equations include the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. The turbulence transport model is based on the Reynolds decomposition and turbulence phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. In addition to using separate energy equations for the solar wind protons and electrons, a significant improvement over our previous work is that the turbulence model now uses an eddy viscosity approximation for the Reynolds stress tensor and the mean turbulent electric field. The approximation allows the turbulence model to account for driving of turbulence by large-scale velocity gradients. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including embedded turbulence, heating, and acceleration throughout the heliosphere. The model results are
Building proper invariants for eddy-viscosity subgrid-scale models
NASA Astrophysics Data System (ADS)
Trias, F. X.; Folch, D.; Gorobets, A.; Oliva, A.
2015-06-01
Direct simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Hence, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for large-eddy simulation is probably the most popular example thereof: they rely on differential operators that should properly detect different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime, etc.). Most of them are based on the combination of invariants of a symmetric tensor that depends on the gradient of the resolved velocity field, G = ∇ u ¯ . In this work, models are presented within a framework consisting of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space. For instance, considering the three invariants PGGT, QGGT, and RGGT of the tensor G GT, and imposing the proper cubic near-wall behavior, i.e., ν e = O ( y 3 ) , we deduce that the eddy-viscosity is given by ν e = ( C s 3 p q r Δ ) 2 PG G T p QG G T - ( p + 1 ) RG G T ( p + 5 / 2 ) / 3 . Moreover, only RGGT-dependent models, i.e., p > - 5/2, switch off for 2D flows. Finally, the model constant may be related with the Vreman's model constant via C s 3 p q r = √{ 3 } C V r ≈ 0 . 458 ; this guarantees both numerical stability and that the models have less or equal dissipation than Vreman's model, i.e., 0 ≤ ν e ≤ νe V r . The performance of the proposed models is successfully tested for decaying isotropic turbulence and a turbulent channel flow. The former test-case has revealed that the model constant, Cs3pqr, should be higher than 0.458 to obtain the right amount of subgrid-scale dissipation, i.e., Cs3pq = 0.572 (p = - 5/2), Cs3pr = 0.709 (p = - 1), and Cs3qr = 0.762 (p = 0).
Three-fluid, 3D MHD solar wind modeling with turbulence transport and eddy viscosity
NASA Astrophysics Data System (ADS)
Usmanov, A. V.; Goldstein, M. L.; Matthaeus, W. H.
2014-12-01
We present results from a three-fluid, fully three-dimensional MHD solar wind model that includes turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a co-moving system of three species: the solar wind protons, electrons, and interstellar pickup protons. Separate energy equations are employed for each species. We obtain numerical solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations in the region from 0.3 to 100 AU. The integrated system of equations includes the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including turbulence parameters, throughout the heliosphere. The model results are compared with observations on WIND, Ulysses and Voyager 2 spacecraft. This work is partially supported by LWS and Heliophysics Grand Challenges programs.
Nonlinear eddy viscosity modeling and experimental study of jet spreading rates.
Heschl, C; Inthavong, K; Sanz, W; Tu, J
2014-02-01
Indoor airflow pattern is strongly influenced by turbulent shear and turbulent normal stresses that are responsible for entrainment effects and turbulence-driven secondary motion. Therefore, an accurate prediction of room airflows requires reliable modeling of these turbulent quantities. The most widely used turbulence models include RANS-based models that provide quick solutions but are known to fail in turbulent free shear and wall-affected flows. In order to cope with this deficiency, this study presents a nonlinear k-ε turbulence model and evaluates it along with linear k-ε models for an indoor isothermal linear diffuser jet flow measured in two model rooms using PIV. The results show that the flow contains a free jet near the inlet region and a wall-affected region downstream where the jet is pushed toward the ceiling by entrainment through the well-known Coanda effect. The CFD results show that an accurate prediction of the entrainment process is very important and that the nonlinear eddy viscosity model is able to predict the turbulence-driven secondary motions. Furthermore, turbulence models that are calibrated for high Reynolds free shear layer flows were not able to reproduce the measured velocity distributions, and it is suggested that the model constants of turbulence models should be adjusted before they are used for room airflow simulations. PMID:23668473
NASA Technical Reports Server (NTRS)
Omori, S.; Gross, K. W.
1973-01-01
The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall hydrogen reacts with the combustion products, liberating an extensive amount of heat.
Laskowski, Gregory Michael
2005-12-01
Flows with strong curvature present a challenge for turbulence models, specifically eddy viscosity type models which assume isotropy and a linear and instantaneous equilibrium relation between stress and strain. Results obtained from three different codes and two different linear eddy viscosity turbulence models are compared to a DNS simulation in order to gain some perspective on the turbulence modeling capability of SIERRA/Fuego. The Fuego v2f results are superior to the more common two-layer k-e model results obtained with both a commercial and research code in terms of the concave near wall behavior predictions. However, near the convex wall, including the separated region, little improvement is gained using the v2f model and in general the turbulent kinetic energy prediction is fair at best.
NASA Astrophysics Data System (ADS)
Knudsen, E.; Richardson, E. S.; Doran, E. M.; Pitsch, H.; Chen, J. H.
2012-05-01
Scalar dissipation rates and subfilter scalar variances are important modeling parameters in large eddy simulations (LES) of reacting flows. Currently available models capture the general behavior of these parameters, but these models do not always perform with the degree of accuracy that is needed for predictive LES. Here, two direct numerical simulations (DNS) are used to analyze LES dissipation rate and variance models, and to propose a new model for the dissipation rate that is based on a transport equation. The first DNS that is considered is a non-premixed auto-igniting C2H4 jet flame simulation originally performed by Yoo et al. [Proc. Combust. Inst. 33, 1619-1627 (2011)], 10.1016/j.proci.2010.06.147. A LES of this case is run using algebraic models for the dissipation rate and subfilter variance. It is shown that the algebraic models fail to adequately reproduce the DNS results. This motivates the introduction of a transport equation model for the LES dissipation rate. Closure of the equation is addressed by formulating a new adapted dynamic approach. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside on the smallest flow length scales. The adapted dynamic approach is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Data from this second DNS are used to confirm that the adapted dynamic approach successfully closes the dissipation rate equation over a wide range of LES filter widths. The first reacting jet case is then returned to and used to test the LES transport equation models. The transport equation model for the dissipation rate is shown to be more accurate than its algebraic counterpoint, and the dissipation rate is eliminated as a source of error in the transported variance model.
Borovsky, Joseph E.
2006-05-15
The coefficient of magnetohydrodynamic (MHD) eddy viscosity of the turbulent solar wind is calculated to be {nu}{sub eddy}{approx_equal}1.3x10{sup 17} cm{sup 2}/s: this coefficient is appropriate for velocity shears with scale thicknesses larger than the {approx}10{sup 6} km correlation length of the solar-wind turbulence. The coefficient of MHD eddy viscosity is calculated again accounting for the action of smaller-scale turbulent eddies on smaller scale velocity shears in the solar wind. This eddy viscosity is quantitatively tested with spacecraft observations of shear flows in co-rotating interaction regions (CIRs) and in coronal-mass-ejection (CME) sheaths and ejecta. It is found that the large-scale ({approx}10{sup 7} km) shear of the CIR fractures into intense narrow ({approx}10{sup 5} km) slip zones between slabs of differently magnetized plasma. Similarly, it is found that the large-scale shear of CME sheaths also fracture into intense narrow slip zones between parcels of differently magnetized plasma. Using the solar-wind eddy-viscosity coefficient to calculate vorticity-diffusion time scales and comparing those time scales with the {approx}100-h age of the solar-wind plasma at 1 AU, it is found that the slip zones are much narrower than eddy-viscosity theory says they should be. Thus, our concept of MHD eddy viscosity fails testing. For the freestream turbulence effect in solar-wind magnetosphere coupling, the eddy-viscous force of the solar wind on the Earth's magnetosphere is rederived accounting for the action of turbulent eddies smaller than the correlation length, along with other corrections. The improved derivation of the solar-wind driver function for the turbulence effect fails to yield higher correlation coefficients between measurements of the solar-wind driver and measurements of the response of the Earth's magnetosphere.
Solar tachocline dynamics: eddy viscosity, anti-friction, or something in between?
NASA Astrophysics Data System (ADS)
McIntyre, Michael E.
The tachocline has values of the stratification or buoyancy frequency N two or more orders of magnitude greater than the Coriolis frequency. In this and other respects it is very like the Earth's atmosphere, viewed globally, except that the Earth's solid surface is replaced by an abrupt, magnetically-constrained "tachopause" (Gough & McIntyre 1998). The tachocline is helium-poor through fast ventilation from above, down to the tachopause, on timescales of only a few million years. The corresponding sound-speed anomaly fits helioseismic data with a tachocline thickness (0.019±0.001) Rsolar, about 0.13×105km (Elliott & Gough 1999), implying large values of the gradient Richardson number such that stratification dominates vertical shear even more strongly than in the Earth's stratosphere, as earlier postulated by Spiegel & Zahn (1992). Therefore the tachocline ventilation circulation cannot be driven by vertically-transmitted frictional torques, any more than the ozone-transporting circulation and differential rotation of the Earth's stratosphere can thus be driven. Rather, the tachocline circulation must be driven mainly by the Reynolds and Maxwell stresses interior to the convection zone, through a gyroscopic pumping action and the downward-burrowing response to it. If layerwise-two-dimensional turbulence is important, then because of its potential-vorticity-transporting properties the effect will be anti-frictional rather than eddy-viscosity-like. In order to correctly predict the differential rotation of the Sun's convection zone, even qualitatively, a convection-zone model must be fully coupled to a tachocline model.
NASA Technical Reports Server (NTRS)
Omori, S.
1973-01-01
The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion; that is, combustion alters the velocity profile as if the mass injection rate is increased, reducing the skin-friction as a result of a smaller velocity gradient at the wall. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall, hydrogen reacts with the combustion products, liberating an extensive amount of heat. The resulting large increase in temperature reduces the eddy viscosity in this region.
NASA Technical Reports Server (NTRS)
Omori, S.
1973-01-01
As described in Vol. 1, the eddy viscosity is calculated through the turbulent kinetic energy, in order to include the history of the flow and the effect of chemical reaction on boundary layer characteristics. Calculations can be performed for two different cooling concepts; that is, transpiration and regeneratively cooled wall cases. For the regenerative cooling option, coolant and gas side wall temperature and coolant bulk temperature in a rocket engine can be computed along the nozzle axis. Thus, this computer program is useful in designing coolant flow rate and cooling tube geometry, including the tube wall thickness as well as in predicting the effects of boundary layers along the gas side wall on thrust performances.
NASA Astrophysics Data System (ADS)
Marras, Simone; Suckale, Jenny; Giraldo, Francis X.; Constantinescu, Emil
2016-04-01
We present the solution of the viscous shallow water equations where viscosity is built as a residual-based subgrid scale model originally designed for large eddy simulation of compressible [1] and stratified flows [2]. The necessity of viscosity for a shallow water model not only finds motivation from mathematical analysis [3], but is supported by physical reasoning as can be seen by an analysis of the energetics of the solution. We simulated the flow of an idealized wave as it hits a set of obstacles. The kinetic energy spectrum of this flow shows that, although the inviscid Galerkin solutions -by spectral elements and discontinuous Galerkin [4]- preserve numerical stability in spite of the spurious oscillations in the proximity of the wave fronts, the slope of the energy cascade deviates from the theoretically expected values. We show that only a sufficiently small amount of dynamically adaptive viscosity removes the unwanted high-frequency modes while preserving the overall sharpness of the solution. In addition, it yields a physically plausible energy decay. This work is motivated by a larger interest in the application of a shallow water model to the solution of tsunami triggered coastal flows. In particular, coastal flows in regions around the world where coastal parks made of mitigation hills of different sizes and configurations are considered as a means to deviate the power of the incoming wave. References [1] M. Nazarov and J. Hoffman (2013) "Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods" Int. J. Numer. Methods Fluids, 71:339-357 [2] S. Marras, M. Nazarov, F. X. Giraldo (2015) "Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES" J. Comput. Phys. 301:77-101 [3] J. F. Gerbeau and B. Perthame (2001) "Derivation of the viscous Saint-Venant system for laminar shallow water; numerical validation" Discrete Contin. Dyn. Syst. Ser. B, 1:89?102 [4] F
NASA Astrophysics Data System (ADS)
Lee, Jong Chan; Jung, Kyung Tae
1999-03-01
A three-dimensional mode-splitting, σ-coordinate barotropic finite-difference model, with subgrid scale diffusion represented using a range of eddy viscosity closure models, is used to examine M2 tidal elevation and currents in the Yellow Sea and the East China Sea. Four eddy viscosity formulations are considered: q2- q2l turbulence energy model (Blumberg and Mellor, 1987), Prandtl mixing length model, Davies and Furnes' (1980) simple flow-related model with mixing length which includes the bottom boundary layer thickness, and a time and space invariant eddy viscosity with 650 cm 2/s. The bottom friction at the sea bed is given in a quadratic form using a constant bottom friction coefficient, cf and near-bottom velocities. A series of M2 tide model runs were carried out and optimal values of cf were determined through the comparison with tidal elevation amplitudes and phases at 203 stations. From these comparisons it is shown that the M2 tidal charts computed with a range of eddy viscosity formulations are in good agreement with each other when optimal values of cf are chosen; comparing with M2 tidal current amplitudes and phases at 15 stations, it is shown that tidal current distributions and its profiles are in reasonably good agreement with winter-time observations in the central part of the Yellow Sea; relatively poor results are obtained near the Chinese coast where non-tidal effects such as abrupt changes in tidal current phase in the vertical due to large freshwater discharge are pronounced. It is noted that the bottom friction coefficient has a major influence on tidal elevation and tidal currents and optimal values of bottom friction coefficient are closely related to the near-bottom eddy viscosity. The considered eddy viscosity closure models appear to work well for tidal problem when the bottom friction parameter is optimized. Results indicate that for a barotropic tide the Prandtl mixing length model which can account of the boundary layer thickness
NASA Technical Reports Server (NTRS)
Hickey, M. P.
1988-01-01
The chemical-dynamical model of Walterscheid et al. (1987), which describes wave-driven fluctuations in OH nightglow, was modified to include the effects of both eddy thermal conduction and viscosity, as well as the Coriolis force (with the shallow atmosphere approximation). Using the new model, calculations were performed for the same nominal case as used by Walterscheid et al. but with only wave periods considered. For this case, the Coriolis force was found to be unimportant at any wave period. For wave periods greater than 2 or 3 hours, the inclusion of thermal conduction alone greatly modified the results (in terms of a complex ratio 'eta' which expresses the relationship between the intensity oscillation about the time-averaged intensity and the temperature oscillation about the time-averaged temperature); this effect was reduced with the further inclusion of the eddy viscosity.
NASA Astrophysics Data System (ADS)
Chen, Wei; de Swart, Huib E.
2016-03-01
Several field studies in bays and estuaries have revealed pronounced subsurface maxima in the vertical profiles of the current amplitude of the principal tidal harmonic, or of its vertical shear, over the water column. To gain fundamental understanding about these phenomena, a semi-analytical model is designed and analysed, with focus on the sensitivity of the vertical structure of the tidal current amplitude to formulations of the vertical shape of the eddy viscosity. The new analytical solutions for the tidal current amplitude are used to explore their dependence on the degree of surface mixing, the vertical shape of eddy viscosity in the upper part of the water column and the density stratification. Sources of surface mixing are wind and whitecapping. Results show three types of current amplitude profiles of tidal harmonics, characterised by monotonically decreasing shear towards the surface, "surface jumps" (vertical shear of tidal current amplitude has a subsurface maximum) and "subsurface jets" (maximum tidal current amplitude below the surface), respectively. The "surface jumps" and "subsurface jets" both occur for low turbulence near the surface, whilst additionally the surface jumps only occur if the eddy viscosity in the upper part of the water column decreases faster than linearly to the surface. Furthermore, "surface jumps" take place for low density stratification, while and "subsurface jets" occur for high density stratification. The physics causing the presence of surface jumps and subsurface jets is also discussed.
NASA Astrophysics Data System (ADS)
Elmekawy, Ahmed M. Nagib M.
When turbulent flow generates unsteady differential pressure over an aircraft's structure, this may generate buffeting, a random oscillation of the structure. The buffet phenomenon is observed on a wide range of fighter aircraft, especially fighters with twin-tail. More research is needed to better understand the physics behind the vortical flow over a delta wing and the subsequent tail buffet. This dissertation reports the modeling and simulation of a steady-state one-way fluid-structure interaction for the tail buffet problem observed on a F/A-18 fighter. The time-averaged computational results are compared to available experimental data. Next, computations are extended to simulate an unsteady two-way fluid-structure interaction problem of the tail buffet of a F/A-18 fighter. For the modeling herein, a commercial software ANSYS version 14.0, is employed. For the fluid domain, the unsteady Reynolds-averaged Navier Stokes (URANS) equations with different turbulent models are utilized. The first turbulence model selected is the modified Spalart-Allmaras model (SARRC) with a strain-vorticity based production and curvature treatment. The second turbulence model selected is the Non-linear Eddy Viscosity Model (NLEVM) based on the Wilcox k--o model. This model uses the formulation of an explicit algebraic Reynolds stress model. The structural simulation is conducted by a finite element analysis model with shell elements. Both SARRC and NLEVM turbulence models are in ANSYS software. The experimental data used for validation were conducted on a simplified geometry: a 0.3 Mach number flow past a 76-deg delta wing pitched to 30-deg. Two vertical tails were placed downstream of the delta wing. The present work is the first ever study of the tail buffet problem of the F/A-18 fighter with two-way fluid-structure interaction using the two advanced turbulence models. The steady-state, time-averaged, one-way fluid-structure interaction case of the present investigation indicates
Turbulent Damping without Eddy Viscosity
NASA Astrophysics Data System (ADS)
Thalabard, Simon
2015-11-01
The intrinsic Non-Gaussianity of turbulence may explain why the standard Quasi-Normal cumulant discard closures can fail dramatically, an example being the development of negative energy spectra in Millionshtchikov's 1941 Quasi-Normal (QN) theory. While Orszag's 1977 EDQNM provides an ingenious patch to the issue, the reason why QN fails so badly is not so clear. Is it because of the Gaussian Ansatz itself? Or rather its inconsistent use? The purpose of the talk is to argue in favor of the latter option, using the lights of a new ``optimal closure'' recently exposed by [Turkington,2013], which allows Gaussians to be used consistently with an intrinsic damping. The key to this apparent paradox lies in a clear distinction between the ensemble averages and their proxies, most easily grasped provided one uses the Liouville equation rather than the cumulant hierarchy as a starting point. Schematically said, closure is achieved by minimizing a lack-of-fit residual, that retains the intrinsic features of the dynamics. For the sake of clarity, I will discuss the optimal closure on a problem where it can be entirely implemented and compared to DNS: the relaxation of an arbitrarily far from equilibrium energy shell towards the Gibbs equilibrium for truncated Euler dynamics.
NASA Technical Reports Server (NTRS)
Ahn, Kyung H.
1994-01-01
The RNG-based algebraic turbulence model, with a new method of solving the cubic equation and applying new length scales, is introduced. An analysis is made of the RNG length scale which was previously reported and the resulting eddy viscosity is compared with those from other algebraic turbulence models. Subsequently, a new length scale is introduced which actually uses the two previous RNG length scales in a systematic way to improve the model performance. The performance of the present RNG model is demonstrated by simulating the boundary layer flow over a flat plate and the flow over an airfoil.
Computation of turbulent rotating channel flow with an algebraic Reynolds stress model
NASA Technical Reports Server (NTRS)
Warfield, M. J.; Lakshminarayana, B.
1986-01-01
An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.
Algebraic turbulence modeling for unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1990-01-01
An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.
Constrained Large Eddy Simulation of Separated Turbulent Flows
NASA Astrophysics Data System (ADS)
Xia, Zhenhua; Shi, Yipeng; Wang, Jianchun; Xiao, Zuoli; Yang, Yantao; Chen, Shiyi
2011-11-01
Constrained Large-eddy Simulation (CLES) has been recently proposed to simulate turbulent flows with massive separation. Different from traditional large eddy simulation (LES) and hybrid RANS/LES approaches, the CLES simulates the whole flow domain by large eddy simulation while enforcing a RANS Reynolds stress constraint on the subgrid-scale (SGS) stress models in the near-wall region. Algebraic eddy-viscosity models and one-equation Spalart-Allmaras (S-A) model have been used to constrain the Reynolds stress. The CLES approach is validated a posteriori through simulation of flow past a circular cylinder and periodic hill flow at high Reynolds numbers. The simulation results are compared with those from RANS, DES, DDES and other available hybrid RANS/LES methods. It is shown that the capability of the CLES method in predicting separated flows is comparable to that of DES. Detailed discussions are also presented about the effects of the RANS models as constraint in the near-wall layers. Our results demonstrate that the CLES method is a promising alternative towards engineering applications.
Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models
NASA Technical Reports Server (NTRS)
Girimaji, Sharath S.
1995-01-01
A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.
A stochastic extension of the explicit algebraic subgrid-scale models
Rasam, A. Brethouwer, G.; Johansson, A. V.
2014-05-15
The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data.
NASA Technical Reports Server (NTRS)
Baurle, R. A.
2015-01-01
Steady-state and scale-resolving simulations have been performed for flow in and around a model scramjet combustor flameholder. The cases simulated corresponded to those used to examine this flowfield experimentally using particle image velocimetry. A variety of turbulence models were used for the steady-state Reynolds-averaged simulations which included both linear and non-linear eddy viscosity models. The scale-resolving simulations used a hybrid Reynolds-averaged / large eddy simulation strategy that is designed to be a large eddy simulation everywhere except in the inner portion (log layer and below) of the boundary layer. Hence, this formulation can be regarded as a wall-modeled large eddy simulation. This effort was undertaken to formally assess the performance of the hybrid Reynolds-averaged / large eddy simulation modeling approach in a flowfield of interest to the scramjet research community. The numerical errors were quantified for both the steady-state and scale-resolving simulations prior to making any claims of predictive accuracy relative to the measurements. The steady-state Reynolds-averaged results showed a high degree of variability when comparing the predictions obtained from each turbulence model, with the non-linear eddy viscosity model (an explicit algebraic stress model) providing the most accurate prediction of the measured values. The hybrid Reynolds-averaged/large eddy simulation results were carefully scrutinized to ensure that even the coarsest grid had an acceptable level of resolution for large eddy simulation, and that the time-averaged statistics were acceptably accurate. The autocorrelation and its Fourier transform were the primary tools used for this assessment. The statistics extracted from the hybrid simulation strategy proved to be more accurate than the Reynolds-averaged results obtained using the linear eddy viscosity models. However, there was no predictive improvement noted over the results obtained from the explicit
NASA Technical Reports Server (NTRS)
Baldwin, B. S.; Maccormack, R. W.
1976-01-01
Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
Production and destruction of eddy kinetic energy in forced submesoscale eddy-resolving simulations
NASA Astrophysics Data System (ADS)
Mukherjee, Sonaljit; Ramachandran, Sanjiv; Tandon, Amit; Mahadevan, Amala
2016-09-01
We study the production and dissipation of the eddy kinetic energy (EKE) in a submesoscale eddy field forced with downfront winds using the Process Study Ocean Model (PSOM) with a horizontal grid resolution of 0.5 km. We simulate an idealized 100 m deep mixed-layer front initially in geostrophic balance with a jet in a domain that permits eddies within a range of O(1 km-100 km). The vertical eddy viscosities and the dissipation are parameterized using four different subgrid vertical mixing parameterizations: the k - ɛ , the KPP, and two different constant eddy viscosity and diffusivity profiles with a magnitude of O(10-2m2s-1) in the mixed layer. Our study shows that strong vertical eddy viscosities near the surface reduce the parameterized dissipation, whereas strong vertical eddy diffusivities reduce the lateral buoyancy gradients and consequently the rate of restratification by mixed-layer instabilities (MLI). Our simulations show that near the surface, the spatial variability of the dissipation along the periphery of the eddies depends on the relative alignment of the ageostrophic and geostrophic shear. Analysis of the resolved EKE budgets in the frontal region from the simulations show important similarities between the vertical structure of the EKE budget produced by the k - ɛ and KPP parameterizations, and earlier LES studies. Such an agreement is absent in the simulations using constant eddy-viscosity parameterizations.
NASA Astrophysics Data System (ADS)
Read, Nicholas
2015-03-01
Viscosity is a transport coefficient relating to transport of momentum, and usually thought of as the analog of friction that occurs in fluids and solids. More formally, it is the response of the stress to the gradients of the fluid velocity field, or to the rate of change of strain (derivatives of displacement from a reference state). In general, viscosity is described by a fourth-rank tensor. Invoking rotation invariance, it reduces to familiar shear and bulk viscosity parts, which describe dissipation, but it can also contain an antisymmetric part, analogous to the Hall conductivity part of the conductivity tensor. In two dimensions this part is a single number, the Hall viscosity. Symmetry of the system under time reversal (or, in two dimensions, reflections) forces it to vanish. In quantum fluids with a gap in the bulk energy spectrum and which lack both time reversal and reflection symmetries the Hall viscosity can be nonzero even at zero temperature. For integer quantum Hall states, it was first calculated by Avron, Seiler, and Zograf, using a Berry curvature approach, analogous to the Chern number for Hall conductivity. In 2008 this was extended by the present author to fractional quantum Hall states and to BCS states in two dimensions. I found that the general result is given by a simple formula ns / 2 , where n is the particle number density, and s is the ``orbital spin'' per particle. The spin s is also related to the shift S, which enters the relation between particle number and magnetic flux needed to put the ground state on a surface of non-trivial topology with introducing defect excitations, by S = 2 s ; the connection was made by Wen and Zee. The values of s and S are rational numbers, and are robust--unchanged under perturbations that do not cause the bulk energy gap to collapse--provided rotation as well as translation symmetry are maintained. Hall viscosity can be measured in principle, though a simple way to do so is lacking. It enters various
Computation of turbulent boundary layer flows with an algebraic stress turbulence model
NASA Technical Reports Server (NTRS)
Kim, Sang-Wook; Chen, Yen-Sen
1986-01-01
An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.
ERIC Educational Resources Information Center
Schaufele, Christopher; Zumoff, Nancy
Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…
ERIC Educational Resources Information Center
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
NASA Technical Reports Server (NTRS)
Jongen, T.; Machiels, L.; Gatski, T. B.
1997-01-01
Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.
Eddies and vortices in ocean basin dynamics
NASA Astrophysics Data System (ADS)
Siegel, A.; Weiss, Jeffrey B.; Toomre, Juri; McWilliams, James C.; Berloff, Pavel S.; Yavneh, Irad
A wind-driven, closed-basin quasi-geostrophic ocean model is computed at very high horizontal resolution to study the effect of increasing Reynolds number (Re) on eddy variability. Five numerical simulations are performed with identical configurations, varying only in horizontal resolution and viscosity coefficient (and therefore Re). Qualitative changes in the structure of eddy variability are evident in the dramatic increase of isolated vortex structures at the highest Re. While the time-mean kinetic energy is relatively independent of Re, the vortex emergence contributes to a continual increase with Re of eddy kinetic energy and meridional vorticity flux. The rate of increase slows somewhat at the highest Re, indicating the possibility of a regime where eddy variability becomes insensitive to further increases in Re.
Large Eddy Simulations using Lattice Boltzmann algorithms. Final report
Serling, J.D.
1993-09-28
This report contains the results of a study performed to implement eddy-viscosity models for Large-Eddy-Simulations (LES) into Lattice Boltzmann (LB) algorithms for simulating fluid flows. This implementation requires modification of the LB method of simulating the incompressible Navier-Stokes equations to allow simulation of the filtered Navier-Stokes equations with some subgrid model for the Reynolds stress term. We demonstrate that the LB method can indeed be used for LES by simply locally adjusting the value of the BGK relaxation time to obtain the desired eddy-viscosity. Thus, many forms of eddy-viscosity models including the standard Smagorinsky model or the Dynamic model may be implemented using LB algorithms. Since underresolved LB simulations often lead to instability, the LES model actually serves to stabilize the method. An alternative method of ensuring stability is presented which requires that entropy increase during the collision step of the LB method. Thus, an alternative collision operator is locally applied if the entropy becomes too low. This stable LB method then acts as an LES scheme that effectively introduces its own eddy viscosity to damp short wavelength oscillations.
Large Eddy Simulation of Transitional Boundary Layer
NASA Astrophysics Data System (ADS)
Sayadi, Taraneh; Moin, Parviz
2009-11-01
A sixth order compact finite difference code is employed to investigate compressible Large Eddy Simulation (LES) of subharmonic transition of a spatially developing zero pressure gradient boundary layer, at Ma = 0.2. The computational domain extends from Rex= 10^5, where laminar blowing and suction excites the most unstable fundamental and sub-harmonic modes, to fully turbulent stage at Rex= 10.1x10^5. Numerical sponges are used in the neighborhood of external boundaries to provide non-reflective conditions. Our interest lies in the performance of the dynamic subgrid scale (SGS) model [1] in the transition process. It is observed that in early stages of transition the eddy viscosity is much smaller than the physical viscosity. As a result the amplitudes of selected harmonics are in very good agreement with the experimental data [2]. The model's contribution gradually increases during the last stages of transition process and the dynamic eddy viscosity becomes fully active and dominant in the turbulent region. Consistent with this trend the skin friction coefficient versus Rex diverges from its laminar profile and converges to the turbulent profile after an overshoot. 1. Moin P. et. al. Phys Fluids A, 3(11), 2746-2757, 1991. 2. Kachanov Yu. S. et. al. JFM, 138, 209-247, 1983.
Southern Ocean eddy phenomenology
NASA Astrophysics Data System (ADS)
Frenger, I.; Münnich, M.; Gruber, N.; Knutti, R.
2015-11-01
Mesoscale eddies are ubiquitous features in the Southern Ocean, yet their phenomenology is not well quantified. To tackle this task, we use satellite observations of sea level anomalies and sea surface temperature (SST) as well as in situ temperature and salinity measurements from profiling floats. Over the period 1997-2010, we identified over a million mesoscale eddy instances and were able to track about 105 of them over 1 month or more. The Antarctic Circumpolar Current (ACC), the boundary current systems, and the regions where they interact are hot spots of eddy presence, representing also the birth places and graveyards of most eddies. These hot spots contrast strongly to areas shallower than about 2000 m, where mesoscale eddies are essentially absent, likely due to topographical steering. Anticyclones tend to dominate the southern subtropical gyres, and cyclones the northern flank of the ACC. Major causes of regional polarity dominance are larger formation numbers and lifespans, with a contribution of differential propagation pathways of long-lived eddies. Areas of dominance of one polarity are generally congruent with the same polarity being longer-lived, bigger, of larger amplitude, and more intense. Eddies extend down to at least 2000 m. In the ACC, eddies show near surface temperature and salinity maxima, whereas eddies in the subtropical areas generally have deeper anomaly maxima, presumably inherited from their origin in the boundary currents. The temperature and salinity signatures of the average eddy suggest that their tracer anomalies are a result of both trapping in the eddy core and stirring.
NASA Astrophysics Data System (ADS)
Anderson, Laurence A.; McGillicuddy, Dennis J.; Maltrud, Mathew E.; Lima, Ivan D.; Doney, Scott C.
2011-09-01
Two eddy-resolving (0.1°) physical-biological simulations of the North Atlantic Ocean are compared, one with the surface momentum flux computed only from wind velocities and the other using the difference between air and ocean velocity vectors. This difference in forcing has a significant impact on the intensities and relative number of different types of mesoscale eddies in the Sargasso Sea. Eddy/wind interaction significantly reduces eddy intensities and increases the number of mode-water eddies and "thinnies" relative to regular cyclones and anticyclones; it also modifies upward isopycnal displacements at the base of the euphotic zone, increasing them in the centers of mode water eddies and at the edges of cyclones, and decreasing them in the centers of cyclones. These physical changes increase phytoplankton growth rates and biomass in mode-water eddies, bringing the biological simulation into better agreement with field data. These results indicate the importance of including the eddy/wind interaction in simulations of the physics and biology of eddies in the subtropical North Atlantic. However, eddy intensities in the simulation with eddy/wind interaction are lower than observed, which suggests a decrease in horizontal viscosity or an increase in horizontal grid resolution will be necessary to regain the observed level of eddy activity.
Twisted Quantum Toroidal Algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Liu, Rongjia
2014-09-01
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
Algebraic vs physical N = 6 3-algebras
Cantarini, Nicoletta; Kac, Victor G.
2014-01-15
In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.
Transport by negative eddy viscosity in soliton turbulence
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
The forced Schrodinger equation is used to describe the microhydrodynamical state of strong soliton turbulence. The Schrodinger equation is transformed into a master equation and is decomposed into a macrogroup, a microgroup, and a submicrogroup, representative of the three transport processes of spectral evolution, transport property, and relaxation. The kinetic equation for the macrodistribution is derived and reverted to the continuum by the method of moments in order to find the equation of spectral evolution. The spectral flow is found to be governed by three types of transport, which are discussed.
Hall Viscosity II: Extracting Viscosity from Conductivity
NASA Astrophysics Data System (ADS)
Goldstein, Moshe; Bradlyn, Barry; Read, Nicholas
2012-02-01
When time reversal symmetry is broken, the viscosity tensor of a fluid can have non-dissipative components, similarly to the non-dissipative off-diagonal Hall conductivity. This ``Hall viscosity'' was recently shown to be half the particle density times the orbital angular momentum per particle. Its observation can thus help elucidate the nature of the more exotic quantum Hall states and related systems (e.g., p+ip superconductors). However, no concrete measurement scheme has hitherto been proposed. Motivated by this question we use linear response theory to derive a general relation between the viscosity tensor and the wave-vector dependent conductivity tensor for a Galilean-invariant quantum fluid. This relation enables one to extract the Hall viscosity, as well as other viscosity coefficients (shear and bulk) when relevant, from electromagnetic response measurements. We also discuss the connection between this result and a similar one recently derived by C. Hoyos and D. T. Son [arXiv:1109.2651].
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, Inc., Reston, VA.
This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…
Nonequilibrium viscosity of glass
NASA Astrophysics Data System (ADS)
Mauro, John C.; Allan, Douglas C.; Potuzak, Marcel
2009-09-01
Since glass is a nonequilibrium material, its properties depend on both composition and thermal history. While most prior studies have focused on equilibrium liquid viscosity, an accurate description of nonequilibrium viscosity is essential for understanding the low temperature dynamics of glass. Departure from equilibrium occurs as a glass-forming system is cooled through the glass transition range. The glass transition involves a continuous breakdown of ergodicity as the system gradually becomes trapped in a subset of the available configurational phase space. At very low temperatures a glass is perfectly nonergodic (or “isostructural”), and the viscosity is described well by an Arrhenius form. However, the behavior of viscosity during the glass transition range itself is not yet understood. In this paper, we address the problem of glass viscosity using the enthalpy landscape model of Mauro and Loucks [Phys. Rev. B 76, 174202 (2007)] for selenium, an elemental glass former. To study a wide range of thermal histories, we compute nonequilibrium viscosity with cooling rates from 10-12 to 1012K/s . Based on these detailed landscape calculations, we propose a simplified phenomenological model capturing the essential physics of glass viscosity. The phenomenological model incorporates an ergodicity parameter that accounts for the continuous breakdown of ergodicity at the glass transition. We show a direct relationship between the nonequilibrium viscosity parameters and the fragility of the supercooled liquid. The nonequilibrium viscosity model is validated against experimental measurements of Corning EAGLE XG™ glass. The measurements are performed using a specially designed beam-bending apparatus capable of accurate nonequilibrium viscosity measurements up to 1016Pas . Using a common set of parameters, the phenomenological model provides an accurate description of EAGLE XG™ viscosity over the full range of measured temperatures and fictive temperatures.
Figueroa-O'Farrill, Jose Miguel
2009-11-15
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.
Pal, Abhro; Anupindi, Kameswararao; Delorme, Yann; Ghaisas, Niranjan; Shetty, Dinesh A; Frankel, Steven H
2014-07-01
In the present study, we performed large eddy simulation (LES) of axisymmetric, and 75% stenosed, eccentric arterial models with steady inflow conditions at a Reynolds number of 1000. The results obtained are compared with the direct numerical simulation (DNS) data (Varghese et al., 2007, "Direct Numerical Simulation of Stenotic Flows. Part 1. Steady Flow," J. Fluid Mech., 582, pp. 253-280). An inhouse code (WenoHemo) employing high-order numerical methods for spatial and temporal terms, along with a 2nd order accurate ghost point immersed boundary method (IBM) (Mark, and Vanwachem, 2008, "Derivation and Validation of a Novel Implicit Second-Order Accurate Immersed Boundary Method," J. Comput. Phys., 227(13), pp. 6660-6680) for enforcing boundary conditions on curved geometries is used for simulations. Three subgrid scale (SGS) models, namely, the classical Smagorinsky model (Smagorinsky, 1963, "General Circulation Experiments With the Primitive Equations," Mon. Weather Rev., 91(10), pp. 99-164), recently developed Vreman model (Vreman, 2004, "An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications," Phys. Fluids, 16(10), pp. 3670-3681), and the Sigma model (Nicoud et al., 2011, "Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations," Phys. Fluids, 23(8), 085106) are evaluated in the present study. Evaluation of SGS models suggests that the classical constant coefficient Smagorinsky model gives best agreement with the DNS data, whereas the Vreman and Sigma models predict an early transition to turbulence in the poststenotic region. Supplementary simulations are performed using Open source field operation and manipulation (OpenFOAM) ("OpenFOAM," http://www.openfoam.org/) solver and the results are inline with those obtained with WenoHemo. PMID:24801556
Dynamics of gelling liquids: algebraic relaxation.
Srivastava, Sunita; Kumar, C N; Tankeshwar, K
2009-08-19
The sol-gel system which is known, experimentally, to exhibit a power law decay of stress autocorrelation function has been studied theoretically. A second-order nonlinear differential equation obtained from Mori's integro-differential equation is derived which provides the algebraic decay of a time correlation function. Involved parameters in the expression obtained are related to exact properties of the corresponding correlation function. The algebraic model has been applied to Lennard-Jones and sol-gel systems. The model shows the behaviour of viscosity as has been observed in computer simulation and theoretical studies. The expression obtained for the viscosity predicts a logarithmic divergence at a critical value of the parameter in agreement with the prediction of other theories. PMID:21828600
Viscosity of paraproteinemic sera.
Tichý, M
1996-01-01
Viscosity was determined in a series of 1402 paraproteinemic sera. Viscosity was measured on an ultrasonic viscosimeter of domestic design and was expressed in relative units(ru). Increased viscosity over 2.1 ru was found in 288 sera, i.e. 20.5%. Clinical symptoms of the hyperviscosity syndrome were found in 44 cases (3%) with viscosity over 4.0 ru. Malignant monoclonal gammopathy as proved in all 44 cases. In 17 determinations with the presence of paraprotein IgM, the mean viscosity was 6.35% +/- 2.6 ru, and the mean paraprotein concentration was 41.12 +/- 11.26g/l. In 17 cases we found paraprotein IgG with a mean viscosity of 6.38 +/- 2.4 ru and a mean concentration of paraprotein was 63.66 +/- 14.52g/l. In 9 determinations with the presence of paraprotein IgA, the mean viscosity as 5.22 +/- 1.02 ru and the mean paraprotein concentration was 49.77 +/- 13.89g/1. In one case we found a double paraproteinemia of IgG-lambda + IgA-kappa (31.9 + 24.2g/l), with a viscosity of 10.5 ru. PMID:9106390
Viscosity measuring using microcantilevers
Oden, Patrick Ian
2001-01-01
A method for the measurement of the viscosity of a fluid uses a micromachined cantilever mounted on a moveable base. As the base is rastered while in contact with the fluid, the deflection of the cantilever is measured and the viscosity determined by comparison with standards.
ERIC Educational Resources Information Center
Robertson, C. T.
1973-01-01
Discusses theories underlying the phenomena of solution viscosities, involving the Jones and Dole equation, B-coefficient determination, and flickering cluster model. Indicates that viscosity measurements provide a basis for the study of the structural effects of ions in aqueous solutions and are applicable in teaching high school chemistry. (CC)
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
NASA Astrophysics Data System (ADS)
Kuzmin, Dmitri; Möller, Matthias; Gurris, Marcel
Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, and the transformation of antidiffusive fluxes. An a posteriori control mechanism is implemented to make the limiter failsafe. The numerical treatment of initial and boundary conditions is discussed in some detail. The initialization is performed using an FCT-constrained L 2 projection. The characteristic boundary conditions are imposed in a weak sense, and an approximate Riemann solver is used to evaluate the fluxes on the boundary. We also present an unconditionally stable semi-implicit time-stepping scheme and an iterative solver for the fully discrete problem. The results of a numerical study indicate that the nonlinearity and non-differentiability of the flux limiter do not inhibit steady state convergence even in the case of strongly varying Mach numbers. Moreover, the convergence rates improve as the pseudo-time step is increased.
Time Filtering in Large Eddy Simulations
NASA Technical Reports Server (NTRS)
Carati, Daniele; Wray, Alan A.
2000-01-01
An explicit time filter is applied to the Navier-Stokes equation prior to a space filter. The time filter is supposed to be smooth, and an exact expansion depending on the time derivatives of the velocity is derived for the associated stress tensor. On the contrary, the effect of the space filter is treated as usual and an eddy viscosity model is introduced in the LES equation. The total stress is thus represented using a new class of mixed models combining time and space derivatives of the LES field.
NASA Astrophysics Data System (ADS)
Workman, G. L.
1980-10-01
Since a large number of the procedures used for inspecting the external tank are concerned with determining flaws in welds, there is a need to develop an inspection technique, which can be automated, to determine flaws in welds and structures with complex geometries. Techniques whereby an eddy current is generated in a metallic material and the changes in the circuit parameters due to material differences are observed, were chosen as one possible approach. Pulsed eddy current and its relationship to multifrequency techniques is discussed as well as some preliminary results obtained from observing pulsed waveforms with apparatus and algorithms currently in use for ultrasonic testing of welds. It can be shown the pulsed eddy current techniques can provide similar results, can eliminate some of the noncritical parameters affecting the eddy current signals, and can facilitate in the detection of critical parameter such as flaws, subsurface voids, and corrosion.
NASA Technical Reports Server (NTRS)
Pasley, R. L.; Birdwell, J. A.
1973-01-01
Eddy-current inspection is discussed as a method for locating subsurface flaws in electrically conductive materials. The physical principles and electrical circuitry are described along with the test equipment.
NASA Astrophysics Data System (ADS)
Pichevin, Thierry; Nof, Doron
1996-09-01
A new nonlinear mechanism for the generation of "Meddies" by a cape is proposed. The essence of the new process is that the flow-force associated with any steady current that curves back on itself around a cape cannot be balanced without generating and shedding eddies. The process is modeled as follows. A westward flowing density current advances along a zonal wall and turns eastward after reaching the edge of the wall (i.e. the Cape of St Vincent). Integration of the steady (and inviscid) momentum equation along the wall gives the long-shore flow-force and shows that, no matter what the details of the turning process are, such a scenario is impossible. It corresponds to an unbalanced flow-force and, therefore, cannot exist. Namely, in an analogy to a rocket, the zonal longshore current forces the entire system to the west. A flow field that can compensate for such a force is westward drifting eddies that push the system to the east. In a similar fashion to the backward push associated with a firing cannon, the westward moving eddies (bullets) balance the integrated momentum of the flow around the cape. Nonlinear solutions are constructed analytically using an approach that enables one to compute the eddies' size and generation frequency without solving for the incredibly complicated details of the generation process itself. The method takes advantage of the fact that, after each eddy is generated, the system returns to its original structure. It is based on the integration of the momentum equation (for periodic flows) over a control volume and a perturbation expansion in ɛ, the ratio between the eddies' westward drift and the parent current speed. It is found that, because of the relatively small size of the Mediterranean eddies, β is not a sufficiently strong mechanism to remove the eddies (from the Cape of St Vincent) at the observed frequency. It is, therefore, concluded that westward advection must also take place. Specifically, it is found that an advection
Learning Algebra in a Computer Algebra Environment
ERIC Educational Resources Information Center
Drijvers, Paul
2004-01-01
This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…
Realizations of Galilei algebras
NASA Astrophysics Data System (ADS)
Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena
2016-03-01
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.
NASA Technical Reports Server (NTRS)
Iachello, Franco
1995-01-01
An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.
Orientation in operator algebras
Alfsen, Erik M.; Shultz, Frederic W.
1998-01-01
A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457
Developing Thinking in Algebra
ERIC Educational Resources Information Center
Mason, John; Graham, Alan; Johnson-Wilder, Sue
2005-01-01
This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…
Connecting Arithmetic to Algebra
ERIC Educational Resources Information Center
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Applied Algebra Curriculum Modules.
ERIC Educational Resources Information Center
Texas State Technical Coll., Marshall.
This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…
Profiles of Algebraic Competence
ERIC Educational Resources Information Center
Humberstone, J.; Reeve, R.A.
2008-01-01
The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…
Ternary Virasoro - Witt algebra.
Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham
2008-01-01
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.
On explicit algebraic stress models for complex turbulent flows
NASA Technical Reports Server (NTRS)
Gatski, T. B.; Speziale, C. G.
1992-01-01
Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.
Turbulent viscosity in natural surf zones
NASA Astrophysics Data System (ADS)
Grasso, F.; Ruessink, B. G.
2012-12-01
Waves breaking in the shallow surf zone near the shoreline inject turbulence into the water column that may reach the bed to suspend sediment. Breaking-wave turbulence in the surf zone is, however, poorly understood, which is one of the reasons why many process-based coastal-evolution models predict coastal change during severe storms inadequately. Here, we use data collected in two natural surf zones to derive a new parameterization for the stability function Cμ that determines the magnitude of the eddy viscosity νt in two-equation turbulent-viscosity models, νt = Cμk2/ε, where k is turbulent kinetic energy and ε is the turbulence dissipation rate. In both data sets, the ratio of turbulence production to dissipation is small (≈0.15), while vertical turbulence diffusion is significant. This differs from assumptions underlying existing Cμ parameterizations, which we show to severely overpredict observed Cμ for most conditions. Additionally, we rewrite our new Cμ parameterization into a formulation that accurately reproduces our Reynolds-stress based estimates of turbulence production. This formulation is linear with strain, consistent with earlier theoritical work for large strain rates. Also, it does not depend on ε and can, therefore, also be applied in one-equation turbulent-viscosity models. We anticipate our work to improve turbulence modeling in natural surf zones and to eventually lead to more reliable predictions of coastal evolution in response to severe storms.
Computer algebra and operators
NASA Technical Reports Server (NTRS)
Fateman, Richard; Grossman, Robert
1989-01-01
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.
Groove dimensioning using remote field eddy current inspection
NASA Astrophysics Data System (ADS)
Davoust, M.-E.; Fleury, G.
2000-09-01
The remote field eddy current technique is used for dimensioning the grooves that may occur in the ferromagnetic pipes. We propose a method to estimate the depth and the length of corrosion grooves from measurement of a pick-up coil signal phase at different positions close to the defect. Groove dimensioning requires the knowledge of the physical relation between measurements and defect dimensions; therefore finite-element calculations are performed to design parametric algebraic functions for modeling the physical phenomena. Different models are possible; the choice of this algebraic function is discussed from identification criteria. By means of new measurement formalism and two previously defined measurement relations, estimates of groove sizes may be given. In the first approach, algebraic function parameters and groove dimensions are linked through a polynomial function; this approach is proved to be better than a second one which tries to take advantage of more physical considerations.
Homogeneous and inhomogeneous eddies
Pavia, E.G.
1994-12-31
This work deals with mesoscale warm oceanic eddies; i.e., self-contained bodies of water which transport heat, among other things, for several months and for several hundreds of kilometers. This heat transport is believed to play an important role in the atmospheric and oceanic conditions of the region where it is being transported. Here the author examines the difference in evolution between eddies modeled as blobs of homogeneous water and eddies in which density varies in the horizontal. Preliminary results suggest that instability is enhanced by inhomogeneities, which would imply that traditional modeling studies, based on homogeneous vortices have underestimated the rate of heat-release from oceanic eddies to the surroundings. The approach is modeling in the simplest form; i.e., one single active layer. Although previous studies have shown the drastic effect on stability brought by two or more dynamically-relevant homogeneous layers, the author believes the single-layer eddy-model has not been investigated thoroughly.
Micromagnetics with eddy currents
NASA Astrophysics Data System (ADS)
Iyer, R.; Millhollon, J.; Long, K.
2011-01-01
In this paper, we study the modified Landau-Lifshitz-Gilbert (LLG) equation for of a conducting, magnetic body. The modified LLG equations include the magnetic field due to eddy currents in the total effective magnetic field. We derive an expression for the magnetic field due to eddy current losses and show that it is well defined. We then show that the work done by the eddy currents in opposing the change of magnetization is a Rayleigh type dissipation function, and derive the modified LLG equations using the calculus of variations. Finally, we show that the modified LLG equations lead to a decrease in the Gibbs energy. This implies that the LLG equations describes a dynamic process proceeding spontaneously forward in time.
NASA Technical Reports Server (NTRS)
Lissauer, J. J.; Shu, F. H.; Cuzzi, J. N.
1982-01-01
The technique of estimating the viscosity in Saturn's rings from the damping rate of waves observed to be propagating within the rings is discussed. The wavetrains of attempts using spiral density waves as a diagnostic suffer significant complications that compromise the interpretations. A method that considers the damping of spiral bending waves was used to deduce a kinematic viscosity of 260 (+150, -100) sqcm/sec for the middle of the A ring where bending waves are excited by the 5:3 vertical resonance with Mimas. This value implies upper limits on the particle velocity dispersion and local ring thickness of 0.4 cm/sec and 30 m, respectively.
NASA Technical Reports Server (NTRS)
Ellis, R. C.; Fink, R. A.; Rich, R. W.
1989-01-01
A high torque capacity eddy current damper used as a rate limiting device for a large solar array deployment mechanism is discussed. The eddy current damper eliminates the problems associated with the outgassing or leaking of damping fluids. It also provides performance advantages such as damping torque rates, which are truly linear with respect to input speed, continuous 360 degree operation in both directions of rotation, wide operating temperature range, and the capability of convenient adjustment of damping rates by the user without disassembly or special tools.
Viscosity of colloidal suspensions
Cohen, E.G.D.; Schepper, I.M. de
1995-12-31
Simple expressions are given for the effective Newtonian viscosity as a function of concentration as well as for the effective visco-elastic response as a function of concentration and imposed frequency, of monodisperse neutral colloidal suspensions over the entire fluid range. The basic physical mechanisms underlying these formulae are discussed. The agreement with existing experiments is very good.
A Richer Understanding of Algebra
ERIC Educational Resources Information Center
Foy, Michelle
2008-01-01
Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…
Estimation of turbulence dissipation rate by Large eddy PIV method in an agitated vessel
NASA Astrophysics Data System (ADS)
Kysela, Bohuš; Jašíková, Darina; Konfršt, Jiří; Šulc, Radek; Ditl, Pavel
2015-05-01
The distribution of turbulent kinetic energy dissipation rate is important for design of mixing apparatuses in chemical industry. Generally used experimental methods of velocity measurements for measurement in complex geometries of an agitated vessel disallow measurement in resolution of small scales close to turbulence dissipation ones. Therefore, Particle image velocity (PIV) measurement method improved by large eddy Ply approach was used. Large eddy PIV method is based on modeling of smallest eddies by a sub grid scale (SGS) model. This method is similar to numerical calculations using Large Eddy Simulation (LES) and the same SGS models are used. In this work the basic Smagorinsky model was employed and compared with power law approximation. Time resolved PIV data were processed by Large Eddy PIV approach and the obtained results of turbulent kinetic dissipation rate were compared in selected points for several operating conditions (impeller speed, operating liquid viscosity).
ERIC Educational Resources Information Center
Owen, Hazel
2013-01-01
Eddie Reisch is currently working as a policy advisor for Te Reo Maori Operational Policy within the Student Achievement group with the Ministry of Education in New Zealand, where he has implemented and led a range of e-learning initiatives and developments, particularly the Virtual Learning Network (VLN). He is regarded as one of the leading…
NASA Technical Reports Server (NTRS)
2002-01-01
This true-color satellite image shows a large phytoplankton bloom, several hundred square kilometers in size, in the Indian Ocean off the west coast of Tasmania. In this scene, the rich concentration of microscopic marine plants gives the water a lighter, more turquoise appearance which helps to highlight the current patterns there. Notice the eddies, or vortices in the water, that can be seen in several places. It is possible that these eddies were formed by converging ocean currents flowing around Tasmania, or by fresh river runoff from the island, or both. Often, eddies in the sea serve as a means for stirring the water, thus providing nutrients that help support phytoplankton blooms, which in turn provide nutrition for other organisms. Effectively, these eddies help feed the sea (click to read an article on this topic). This image was acquired November 7, 2000, by the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) flying aboard the Orbview-2 satellite. Tasmania is located off Australia's southeastern coast. Image courtesy SeaWiFS Project, NASA/Goddard Space Flight Center, and ORBIMAGE
Connecting Algebra and Chemistry.
ERIC Educational Resources Information Center
O'Connor, Sean
2003-01-01
Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)
Turbulence Modeling: A NASA Perspective
NASA Technical Reports Server (NTRS)
Gatski, T. B.
2001-01-01
This paper presents turbulence modeling from NASA's perspective. The topics include: 1) Hierarchy of Solution Methods; 2) Turbulence Modeling Focus; 3) Linear Eddy Viscosity Models; and 4) Nonlinear Eddy Viscosity Algebraic Stress Models.
VERTICAL STRUCTURE OF TIME-DEPENDENT FLOW FOR VISCOSITY THAT DEPENDS ON BOTH DEPTH AND TIME
A previously developed eigenfunction expansion, that describes horizontal current as a function of depth and time, is extended to include any eddy viscosity given as a product of a function of depth and a function of time. (Copyright (c) 1982 American Meteorological Society.)
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Shear thirning will cause a normally viscous fluid -- such as pie filling or whipped cream -- to deform and flow more readily under high shear conditions. In shear thinning, a pocket of fluid will deform and move one edge forward, as depicted here.
Ballato, Arthur
2010-03-01
Quartz shear resonators are employed widely as sensors to measure Newtonian viscosities of liquids. Perturbation of the electrical equivalent circuit parameters of the plate resonator by the fluid loading permits calculation of the mass density-shear viscosity product. Use of doubly rotated resonators does permit additional information to be obtained, but in no case can the viscosity and mass density values be separated. In these measurements, the resonator surface is exposed to a measurand bath whose extent greatly exceeds the penetration depth of the evanescent shear mode excited by the active element. Here we briefly review past techniques and current art, and sketch a proposal involving the interesting situation in which the separation between the resonator and a confining wall is less than the penetration depth of the fluid occupying the intervening region. To highlight the salient features of this novel case, the discussion is limited to the very idealized circumstance of a strictly 1-D problem, unencumbered by the vicissitudes inevitably encountered in practice. An appendix mentions some of these functional impedimenta and indicates how deviations from ideality might be approached in engineering embodiments. When the fluid confinement is of the order of the penetration depth, the resonator perturbation becomes a sensitive function of the separation, and it is found that viscosity and density may be separately and uniquely determined. Moreover, extreme miniaturization is a natural consequence because the penetration depth generally is on the order of micrometers for frequencies around 1 MHz at temperatures and pressures ordinarily encountered with gases and liquids. Micro-electro-mechanical (MEMS) versions of viscometers and associated types of fluid sensors are thereby enabled. PMID:20211786
ERIC Educational Resources Information Center
Merlin, Ethan M.
2013-01-01
This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…
ERIC Educational Resources Information Center
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…
NASA Technical Reports Server (NTRS)
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…
A Realizable Reynolds Stress Algebraic Equation Model
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.
1993-01-01
The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.
Large eddy simulation of longitudinal stationary vortices
NASA Astrophysics Data System (ADS)
Sreedhar, Madhu; Ragab, Saad
1994-07-01
The response of longitudinal stationary vortices when subjected to random perturbations is investigated using temporal large-eddy simulation. Simulations are obtained for high Reynolds numbers and at a low subsonic Mach number. The subgrid-scale stress tensor is modeled using the dynamic eddy-viscosity model. The generation of large-scale structures due to centrifugal instability and their subsequent breakdown to turbulence is studied. The following events are observed. Initially, ring-shaped structures appear around the vortex core. These structures are counter-rotating vortices similar to the donut-shaped structures observed in a Taylor-Couette flow between rotating cylinders. These structures subsequently interact with the vortex core resulting in a rapid decay of the vortex. The turbulent kinetic energy increases rapidly until saturation, and then a period of slow decay prevails. During the period of maximum turbulent kinetic energy, the normalized mean circulation profile exhibits a logarithmic region, in agreement with the universal inner profile of Hoffman and Joubert [J. Fluid Mech. 16, 395 (1963)].
Semigroups and computer algebra in algebraic structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2012-11-01
Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.
Lie algebra extensions of current algebras on S3
NASA Astrophysics Data System (ADS)
Kori, Tosiaki; Imai, Yuto
2015-06-01
An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The sample cell at the heart of CVX-2 will sit inside a thermostat providing three layers of insulation. The cell itself comprises a copper body that conducts heat efficiently and smoothes out thermal variations that that would destroy the xenon's uniformity. Inside the cell, the oscillating screen viscometer element is supported between two pairs of electrodes that deflect the screen and then measure screen motion.
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2001 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The thermostat for CVX sits inside the white cylinder on a support structure that is placed inside a pressure canister. A similar canister holds the electronics and control systems. The CVX-2 arrangement is identical. The principal investigator is Dr. Robert F. Berg (not shown) of the National Institutes of Standards and Technology, Gaithersburg, MD. This is a detail view of MSFC 0100143.
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Because xenon near the critical point will collapse under its own weight, experiments on Earth (green line) are limited as they get closer (toward the left) to the critical point. CVX in the microgravity of space (red line) moved into unmeasured territory that scientists had not been able to reach.
Critical exponent for viscosity
NASA Technical Reports Server (NTRS)
Berg, Robert F.; Moldover, Michael R.
1990-01-01
The critical exponent y characterizing the divergence of the viscosity for carbon dioxide and xenon has been measured. The values of y for both fluids fall within the range y = 0.041 + or - 0.001 and are consistent with the range y = 0.042 + or - 0.002 spanned by earlier data for four binary liquid mixtures. This agreement is the strongest evidence that pure fluids and binary liquids are in the same dynamic universality class; however, the results for y are inconsistent with the recent theoretical value of 0.032.
Leibniz algebras associated with representations of filiform Lie algebras
NASA Astrophysics Data System (ADS)
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
Eddy Flow during Magma Emplacement: The Basemelt Sill, Antarctica
NASA Astrophysics Data System (ADS)
Petford, N.; Mirhadizadeh, S.
2014-12-01
The McMurdo Dry Valleys magmatic system, Antarctica, forms part of the Ferrar dolerite Large Igneous Province. Comprising a vertical stack of interconnected sills, the complex provides a world-class example of pervasive lateral magma flow on a continental scale. The lowermost intrusion (Basement Sill) offers detailed sections through the now frozen particle macrostructure of a congested magma slurry1. Image-based numerical modelling where the intrusion geometry defines its own unique finite element mesh allows simulations of the flow regime to be made that incorporate realistic magma particle size and flow geometries obtained directly from field measurements. One testable outcome relates to the origin of rhythmic layering where analytical results imply the sheared suspension intersects the phase space for particle Reynolds and Peclet number flow characteristic of macroscopic structures formation2. Another relates to potentially novel crystal-liquid segregation due to the formation of eddies locally at undulating contacts at the floor and roof of the intrusion. The eddies are transient and mechanical in origin, unrelated to well-known fluid dynamical effects around obstacles where flow is turbulent. Numerical particle tracing reveals that these low Re number eddies can both trap (remove) and eject particles back into the magma at a later time according to their mass density. This trapping mechanism has potential to develop local variations in structure (layering) and magma chemistry that may otherwise not occur where the contact between magma and country rock is linear. Simulations indicate that eddy formation is best developed where magma viscosity is in the range 1-102 Pa s. Higher viscosities (> 103 Pa s) tend to dampen the effect implying eddy development is most likely a transient feature. However, it is nice to think that something as simple as a bumpy contact could impart physical and by implication chemical diversity in igneous rocks. 1Marsh, D.B. (2004), A
Viscosity of Hydrous Rhyolitic Melts
NASA Astrophysics Data System (ADS)
Zhang, Y.; Xu, Z.; Liu, Y.
2002-12-01
It is critical to understand and to be able to predict viscosity of hydrous silicate melts for understanding magma transport, bubble growth, volcanic eruptions, and magma fragmentation. We report new viscosity data for hydrous rhyolitic melt in the viscosity range of 109 to 1015 Pa s based on the kinetics of hydrous species reaction in the melt upon cooling (i.e., based on the equivalence between the glass transition temperature and the apparent equilibrium temperature). We also report viscosity data obtained from bubble growth experiments. Our data show that the viscosity model of Hess and Dingwell (1996) systematically overestimates the viscosity of hydrous rhyolitic melt at the high viscosity range by a factor of 2 to 4 (still within their stated 2σ uncertainty). Another problem with the model of Hess and Dingwell is that the functional dependence of viscosity on total H2O content cannot be extended to dry melt: as total H2O content decreases to zero, the viscosity would first increase, and then decrease to zero. A zero viscosity for a dry melt makes no sense. Hence we need a mixing law for hydrous melt viscosity that is extendible to dry melts. By examining the viscosity of rhyolitic melts containing 6 ppm to about 8.0 wt% total H2O (both our own data and literature data), we propose the following relation for the dependence of viscosity on total H2O content: 1/η = 1/η 1+(1/η 2-1/η 1)xn ≈ 1/η 1+xn/η 2 where η is viscosity and 1/η is fluidity, η 1 is the viscosity of the dry melt, x is the mole fraction of total dissolved H2O, n and η 2 are two fitting parameters, and η 2 can be identified to be the viscosity of the hypothetical melt consisting of pure H2O (η 2 cannot be directly measured since such a melt does not exist). The above equation appears to work well for the viscosity of hydrous rhyolitic melts. By fitting hydrous rhyolitic melt viscosity with the above equation, we find that rhyolitic melt viscosity vary by 1.2 orders of magnitude
A subfilter-scale stress model for large eddy simulations
NASA Astrophysics Data System (ADS)
Rouhi, Amirreza; Piomelli, Ugo
2013-11-01
In most large eddy simulations, the filter width is related to the grid. This method of specification, however, causes problems in complex flows where local refinement results in grid discontinuities. Following the work of Piomelli and Geurts (Proce. 8th Workshop on DLES, 2010) we propose an eddy-viscosity approach in which the filter width is based on the flow parameters only, with no explicit relationship to the grid size. This model can achieve grid-independent LES solutions, vanishing dynamically in the regions of low turbulence activity and a computational cost less than the dynamic models. The Successive Inverse Polynomial Interpolation (Geurts & Meyers Phys. Fluids 18, 2006) was used to calculate the model parameter. Calculating implicitly the eddy-viscosity at each time-step removes the numerical instabilities found in previous studies, while maintaining the local character of the model. Results of simulations of channel flow at Reτ up to 2,000, and forced homogeneous isotropic turbulence will be presented.
Coreflections in Algebraic Quantum Logic
NASA Astrophysics Data System (ADS)
Jacobs, Bart; Mandemaker, Jorik
2012-07-01
Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
Gyrokinetic large eddy simulations
Morel, P.; Navarro, A. Banon; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.
2011-07-15
The large eddy simulation approach is adapted to the study of plasma microturbulence in a fully three-dimensional gyrokinetic system. Ion temperature gradient driven turbulence is studied with the GENE code for both a standard resolution and a reduced resolution with a model for the sub-grid scale turbulence. A simple dissipative model for representing the effect of the sub-grid scales on the resolved scales is proposed and tested. Once calibrated, the model appears to be able to reproduce most of the features of the free energy spectra for various values of the ion temperature gradient.
Developing Algebraic Thinking.
ERIC Educational Resources Information Center
Alejandre, Suzanne
2002-01-01
Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)
Algebraic integrability: a survey.
Vanhaecke, Pol
2008-03-28
We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863
Algebraic Semantics for Narrative
ERIC Educational Resources Information Center
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
Aprepro - Algebraic Preprocessor
Energy Science and Technology Software Center (ESTSC)
2005-08-01
Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
1995-01-01
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
Viscosity of the earth's core.
NASA Technical Reports Server (NTRS)
Gans, R. F.
1972-01-01
Calculation of the viscosity of the core at the boundary of the inner and outer core. It is assumed that this boundary is a melting transition and the viscosity limits of the Andrade (1934,1952) hypothesis (3.7 to 18.5 cp) are adopted. The corresponding kinematic viscosities are such that the precessional system explored by Malkus (1968) would be unstable. Whether it would be sufficiently unstable to overcome a severely subadiabatic temperature gradient cannot be determined.
High-Frequency Shear Viscosity of Low-Viscosity Liquids
NASA Astrophysics Data System (ADS)
Kaatze, U.; Behrends, R.
2014-11-01
A thickness shear quartz resonator technique is described to measure the shear viscosity of low-viscosity liquids in the frequency range from 6 MHz to 130 MHz. Examples of shear-viscosity spectra in that frequency range are presented to show that various molecular processes are accompanied by shear-viscosity relaxation. Among these processes are conformational variations of alkyl chains, with relaxation times of about 0.3 ns for -pentadecane and -hexadecane at 25 C. These variations can be well represented in terms of a torsional oscillator model. Also featured briefly are shear-viscosity relaxations associated with fluctuations of hydrogen-bonded clusters in alcohols, for which values between 0.3 ns (-hexanol) and 1.5 ns (-dodecanol) have been found at 25 C. In addition, the special suitability of high-frequency shear-viscosity spectroscopy to the study of critically demixing mixtures is demonstrated by some illustrative examples. Due to slowing, critical fluctuations do not contribute to the shear viscosity at sufficiently high frequencies of measurements so that the non-critical background viscosity of critical systems can be directly determined from high-frequency shear-viscosity spectroscopy. Relaxations in appear also in the shear-viscosity spectra with, for example, 2 ns for the critical triethylamine-water binary mixture at temperatures between 10 C and 18 C. Such relaxations noticeably influence the relaxation rate of order parameter fluctuations. They may be also the reason for the need of a special mesoscopic viscosity when mutual diffusion coefficients of critical polymer solutions are discussed in terms of mode-coupling theory.
NASA Astrophysics Data System (ADS)
Hiley, B. J.
In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.
DG Poisson algebra and its universal enveloping algebra
NASA Astrophysics Data System (ADS)
Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin
2016-05-01
In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of liquid xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Resembling a tiny bit of window screen, the oscillator at the heart of CVX-2 will vibrate between two pairs of paddle-like electrodes. The slight bend in the shape of the mesh has no effect on the data. What counts are the mesh's displacement in the xenon fluid and the rate at which the displacement dampens. The unit shown here is encased in a small test cell and capped with a sapphire windown to contain the xenon at high pressure.
Viscosity measuring instrument
NASA Technical Reports Server (NTRS)
Feinstein, S. P. (Inventor)
1980-01-01
A method and apparatus are provided for enabling the measurement of the viscosity of substances, especially those containing volatiles at elevated temperatures, with greater accuracy and at less cost than before. The apparatus includes a cylinder with a narrow exit opening at one end and a piston which closely slides within the cylinder to apply force against a sample in the cylinder to force the sample through the exit opening. In order to more rapidly heat a sample the ends of the cylinder and piston are tapered and the sample is correspondingly tapered, to provide a large surface to volume ratio. A corresponding coal sample is formed by compressing particles of coal under high pressure in a mold of appropriate shape.
Are Eddy Covariance series stationary?
Technology Transfer Automated Retrieval System (TEKTRAN)
Spectral analysis via a discrete Fourier transform is used often to examine eddy covariance series for cycles (eddies) of interest. Generally the analysis is performed on hourly or half-hourly data sets collected at 10 or 20 Hz. Each original series is often assumed to be stationary. Also automated ...
NASA Technical Reports Server (NTRS)
Workman, Gary L.; Wang, Morgan
1992-01-01
The recognition of materials properties still presents a number of problems for nondestructive testing in aerospace systems. This project attempts to utilize current capabilities in eddy current instrumentation, artificial intelligence, and robotics in order to provide insight into defining geometrical aspects of flaws in composite materials which are capable of being evaluated using eddy current inspection techniques.
Volatiles Which Increase Magma Viscosity
NASA Astrophysics Data System (ADS)
Webb, S.
2015-12-01
The standard model of an erupting volcano is one in which the viscosity of a decompressing magma increases as the volatiles leave the melt structure to form bubbles. It has now been observed that the addition of the "volatiles" P, Cl and F result in an increase in silicate melt viscosity. This observation would mean that the viscosity of selected degassing magmas would decrease rather than increase. Here we look at P, Cl and F as three volatiles which increase viscosity through different structural mechanisms. In all three cases the volatiles increase the viscosity of peralkaline composition melts, but appear to always decrease the viscosity of peraluminous melts. Phosphorus causes the melt to unmix into a Na-P rich phase and a Na-poor silicate phase. Thus as the network modifying Na (or Ca) are removed to the phosphorus-rich melt, the matrix melt viscosity increases. With increasing amounts of added phosphorus (at network modifying Na ~ P) the addition of further phosphorus causes a decrease in viscosity. The addition of chlorine to Fe-free aluminosilicate melts results in an increase in viscosity. NMR data on these glass indicates that the chlorine sits in salt-like structures surrounded by Na and/or Ca. Such structures would remove network-modifying atoms from the melt structure and thus result in an increase in viscosity. The NMR spectra of fluorine-bearing glasses shows that F takes up at least 5 different structural positions in peralkaline composition melts. Three of these positions should result in a decrease in viscosity due to the removal of bridging oxygens. Two of the structural positons of F, however, should result in an increase in viscosity as they require the removal of network-modifying atoms from the melt structure (with one of the structures being that observed for Cl). This would imply that increasing amounts of F might result in an increase in viscosity. This proposed increase in viscosity with increasing F has now been experimentally confirmed.
Conservative smoothing versus artificial viscosity
Guenther, C.; Hicks, D.L.; Swegle, J.W.
1994-08-01
This report was stimulated by some recent investigations of S.P.H. (Smoothed Particle Hydrodynamics method). Solid dynamics computations with S.P.H. show symptoms of instabilities which are not eliminated by artificial viscosities. Both analysis and experiment indicate that conservative smoothing eliminates the instabilities in S.P.H. computations which artificial viscosities cannot. Questions were raised as to whether conservative smoothing might smear solutions more than artificial viscosity. Conservative smoothing, properly used, can produce more accurate solutions than the von Neumann-Richtmyer-Landshoff artificial viscosity which has been the standard for many years. The authors illustrate this using the vNR scheme on a test problem with known exact solution involving a shock collision in an ideal gas. They show that the norms of the errors with conservative smoothing are significantly smaller than the norms of the errors with artificial viscosity.
Anomalous - viscosity current drive
Stix, Thomas H.; Ono, Masayuki
1988-01-01
An apparatus and method for maintaining a steady-state current in a toroidal magnetically confined plasma. An electric current is generated in an edge region at or near the outermost good magnetic surface of the toroidal plasma. The edge current is generated in a direction parallel to the flow of current in the main plasma and such that its current density is greater than the average density of the main plasma current. The current flow in the edge region is maintained in a direction parallel to the main current for a period of one or two of its characteristic decay times. Current from the edge region will penetrate radially into the plasma and augment the main plasma current through the mechanism of anomalous viscosity. In another aspect of the invention, current flow driven between a cathode and an anode is used to establish a start-up plasma current. The plasma-current channel is magnetically detached from the electrodes, leaving a plasma magnetically insulated from contact with any material obstructions including the cathode and anode.
NASA Astrophysics Data System (ADS)
Roitman, Michael
2008-08-01
In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V0 Å V2 Å V3 Å ¼, such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
Computer Program For Linear Algebra
NASA Technical Reports Server (NTRS)
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1991-01-01
The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.
NASA Astrophysics Data System (ADS)
Bouwknegt, Peter
1988-06-01
We investigate extensions of the Virasoro algebra by a single primary field of integer or halfinteger conformal dimension Δ. We argue that for vanishing structure constant CΔΔΔ, the extended conformal algebra can only be associative for a generic c-value if Δ=1/2, 1, 3/2, 2 or 3. For the other Δ<=5 we compute the finite set of allowed c-values and identify the rational solutions. The case CΔΔΔ≠0 is also briefly discussed. I would like to thank Kareljan Schoutens for discussions and Sander Bais for a careful reading of the manuscript.
ZBLAN Viscosity Instrumentation
NASA Technical Reports Server (NTRS)
Kaukler, William
2001-01-01
The past year's contribution from Dr. Kaukler's experimental effort consists of these 5 parts: a) Construction and proof-of-concept testing of a novel shearing plate viscometer designed to produce small shear rates and operate at elevated temperatures; b) Preparing nonlinear polymeric materials to serve as standards of nonlinear Theological behavior; c) Measurements and evaluation of above materials for nonlinear rheometric behavior at room temperature using commercial spinning cone and plate viscometers available in the lab; d) Preparing specimens from various forms of pitch for quantitative comparative testing in a Dynamic Mechanical Analyzer, Thermal Mechanical Analyzer; and Archeological Analyzer; e) Arranging to have sets of pitch specimens tested using the various instruments listed above, from different manufacturers, to form a baseline of the viscosity variation with temperature using the different test modes offered by these instruments by compiling the data collected from the various test results. Our focus in this project is the shear thinning behavior of ZBLAN glass over a wide range of temperature. Experimentally, there are no standard techniques to perform such measurements on glasses, particularly at elevated temperatures. Literature reviews to date have shown that shear thinning in certain glasses appears to occur, but no data is available for ZBLAN glass. The best techniques to find shear thinning behavior require the application of very low rates of shear. In addition, because the onset of the thinning behavior occurs at an unknown elevated temperature, the instruments used in this study must provide controlled low rates of shear and do so for temperatures approaching 600 C. In this regard, a novel shearing parallel plate viscometer was designed and a prototype built and tested.
An eddy closure for potential vorticity
Ringler, Todd D
2009-01-01
The Gent-McWilliams (GM) parameterization is extended to include a direct influence in the momentum equation. The extension is carried out in two stages; an analysis of the inviscid system is followed by an analysis of the viscous system. In the inviscid analysis the momentum equation is modified such that potential vorticity is conserved along particle trajectories following a transport velocity that includes the Bolus velocity in a manner exactly analogous to the continuity and tracer equations. In addition (and in contrast to traditional GM closures), the new formulation of the inviscid momentum equation results in a conservative exchange between potential and kinetic forms of energy. The inviscid form of the eddy closure conserves total energy to within an error proportional to the time derivative of the Bolus velocity. The hypothesis that the viscous term in the momentum equation should give rise to potential vorticity being diffused along isopycnals in a manner analogous to other tracers is examined in detail. While the form of the momentum closure that follows from a strict adherence to this hypothesis is not immediately interpretable within the constructs of traditional momentum closures, three approximations to this hypothesis results in a form of dissipation that is consistent with traditional Laplacian diffusion. The first two approximations are that relative vorticity, not potential vorticity, is diffused along isopyncals and that the flow is in approximate geostrophic balance. An additional approximation to the Jacobian term is required when the dissipation coefficient varies in space. More importantly, the critique of this hypothesis results in the conclusion that the viscosity parameter in the momentum equation should be identical to the tradition GM closure parameter {Kappa}. Overall, we deem the viscous form of the eddy closure for potential vorticity as a viable closure for use in ocean circulation models.
Viscosity Measurement for Tellurium Melt
NASA Technical Reports Server (NTRS)
Lin, Bochuan; Li, Chao; Ban, Heng; Scripa, Rosalia N.; Su, Ching-Hua; Lehoczky, Sandor L.
2006-01-01
The viscosity of high temperature Te melt was measured using a new technique in which a rotating magnetic field was applied to the melt sealed in a suspended ampoule, and the torque exerted by rotating melt flow on the ampoule wall was measured. Governing equations for the coupled melt flow and ampoule torsional oscillation were solved, and the viscosity was extracted from the experimental data by numerical fitting. The computational result showed good agreement with experimental data. The melt velocity transient initiated by the rotating magnetic field reached a stable condition quickly, allowing the viscosity and electrical conductivity of the melt to be determined in a short period.
Fluid Merging Viscosity Measurement (FMVM)
NASA Technical Reports Server (NTRS)
2004-01-01
Astronaut Mike Fincke places droplets of honey onto the strings for the Fluid Merging Viscosity Measurement (FMVM) investigation onboard the International Space Station (ISS). The FMVM experiment measures the time it takes for two individual highly viscous fluid droplets to coalesce or merge into one droplet. Different fluids and droplet size combinations were tested in the series of experiments. By using the microgravity environment, researchers can measure the viscosity or 'thickness' of fluids without the influence of containers and gravity using this new technique. Understanding viscosity could help scientists understand industrially important materials such as paints, emulsions, polymer melts and even foams used to produce pharmaceutical, food, and cosmetic products.
Critical Viscosity of Xenon investigators
NASA Technical Reports Server (NTRS)
2001-01-01
Dr. Dr. Robert F. Berg (right), principal investigator and Dr. Micheal R. Moldover (left), co-investigator, for the Critical Viscosity of Xenon (CVX/CVX-2) experiment. They are with the National Institutes of Standards and Technology, Gaithersburg, MD. The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Although it does not easily combine with other chemicals, its viscosity at the critical point can be used as a model for a range of chemicals.
Latitude dependence of eddy variances
NASA Technical Reports Server (NTRS)
Bowman, Kenneth P.; Bell, Thomas L.
1987-01-01
The eddy variance of a meteorological field must tend to zero at high latitudes due solely to the nature of spherical polar coordinates. The zonal averaging operator defines a length scale: the circumference of the latitude circle. When the circumference of the latitude circle is greater than the correlation length of the field, the eddy variance from transient eddies is the result of differences between statistically independent regions. When the circumference is less than the correlation length, the eddy variance is computed from points that are well correlated with each other, and so is reduced. The expansion of a field into zonal Fourier components is also influenced by the use of spherical coordinates. As is well known, a phenomenon of fixed wavelength will have different zonal wavenumbers at different latitudes. Simple analytical examples of these effects are presented along with an observational example from satellite ozone data. It is found that geometrical effects can be important even in middle latitudes.
Teaching Arithmetic and Algebraic Expressions
ERIC Educational Resources Information Center
Subramaniam, K.; Banerjee, Rakhi
2004-01-01
A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…
Assessing Elementary Algebra with STACK
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2007-01-01
This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…
Spinors in the hyperbolic algebra
NASA Astrophysics Data System (ADS)
Ulrych, S.
2006-01-01
The three-dimensional universal complex Clifford algebra Cbar3,0 is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.
ERIC Educational Resources Information Center
Glick, David
1995-01-01
Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)
ERIC Educational Resources Information Center
Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott
2007-01-01
Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…
Computer Algebra versus Manipulation
ERIC Educational Resources Information Center
Zand, Hossein; Crowe, David
2004-01-01
In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…
ERIC Educational Resources Information Center
Boiteau, Denise; Stansfield, David
This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative Numbers"; and (5) "Using Positive…
Thinking Visually about Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
ERIC Educational Resources Information Center
Kennedy, John
This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…
ERIC Educational Resources Information Center
Nwabueze, Kenneth K.
2004-01-01
The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…
NASA Astrophysics Data System (ADS)
Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Grundestam, O.; Johansson, A. V.
2016-02-01
A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper
Viscosity Depressants for Coal Liquefaction
NASA Technical Reports Server (NTRS)
Kalfayan, S. H.
1983-01-01
Proposed process modification incorporates viscosity depressants to prevent coal from solidifying during liquefaction. Depressants reduce amount of heat needed to liquefy coal. Possible depressants are metallic soaps, such as stearate, and amides, such as stearamide and dimer acid amides.
NONDESTRUCTIVE EDDY CURRENT TESTING
Renken, C.J. Jr.
1961-05-23
An eddy current testing device is described for measuring metal continuity independent of probe-to-sample spacing. An inductance would test probe is made a leg of a variable impedance bridge and the bridge is balanced with the probe away from the sample. An a-c signal is applied across the input terminals of the bridge circuit. As the probe is brought into proximity with the metal sample, the resulting impedance change in the probe gives an output signal from the bridge whose phase angle is proportional to the sample continuity and amplitude is proportional to the probe-tosample spacing. The output signal from the bridge is applied to a compensating network where, responsive to amplitude changes from the bridge output signal, a constant phased voltage output is maintained when the sample is continuous regardless of probe-to-sample spacing. A phase meter calibrated to read changes in resistivity of the metal sample measures the phase shift between the output of the compensating network and the original a-c signal applied to the bridge.
NASA Astrophysics Data System (ADS)
Zhang, Ming; Yao, JingTao
2004-04-01
The XML is a new standard for data representation and exchange on the Internet. There are studies on XML query languages as well as XML algebras in literature. However, attention has not been paid to research on XML algebras for data mining due to partially the fact that there is no widely accepted definition of XML mining tasks. This paper tries to examine the XML mining tasks and provide guidelines to design XML algebras for data mining. Some summarization and comparison have been done to existing XML algebras. We argue that by adding additional operators for mining tasks, XML algebras may work well for data mining with XML documents.
Scale-Similar Models for Large-Eddy Simulations
NASA Technical Reports Server (NTRS)
Sarghini, F.
1999-01-01
Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide an improvement of the results: the adjustment of the coefficient results in more accurate prediction of the perturbation from equilibrium. The Lagrangian-ensemble approach [Meneveau et al., J. Fluid Mech. 319, 353 (1996)] is found to be very beneficial. Models that included a scale-similar term and a dissipative one, as well as the Lagrangian ensemble averaging, gave results in the best agreement with the direct simulation and experimental data.
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
Algebraic connectivity and graph robustness.
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
Applied large eddy simulation.
Tucker, Paul G; Lardeau, Sylvain
2009-07-28
Large eddy simulation (LES) is now seen more and more as a viable alternative to current industrial practice, usually based on problem-specific Reynolds-averaged Navier-Stokes (RANS) methods. Access to detailed flow physics is attractive to industry, especially in an environment in which computer modelling is bound to play an ever increasing role. However, the improvement in accuracy and flow detail has substantial cost. This has so far prevented wider industrial use of LES. The purpose of the applied LES discussion meeting was to address questions regarding what is achievable and what is not, given the current technology and knowledge, for an industrial practitioner who is interested in using LES. The use of LES was explored in an application-centred context between diverse fields. The general flow-governing equation form was explored along with various LES models. The errors occurring in LES were analysed. Also, the hybridization of RANS and LES was considered. The importance of modelling relative to boundary conditions, problem definition and other more mundane aspects were examined. It was to an extent concluded that for LES to make most rapid industrial impact, pragmatic hybrid use of LES, implicit LES and RANS elements will probably be needed. Added to this further, highly industrial sector model parametrizations will be required with clear thought on the key target design parameter(s). The combination of good numerical modelling expertise, a sound understanding of turbulence, along with artistry, pragmatism and the use of recent developments in computer science should dramatically add impetus to the industrial uptake of LES. In the light of the numerous technical challenges that remain it appears that for some time to come LES will have echoes of the high levels of technical knowledge required for safe use of RANS but with much greater fidelity. PMID:19531503
Marquette, Ian
2013-07-15
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.
Might eddies dominate carbon export ?
NASA Astrophysics Data System (ADS)
Allen, J.; Rixen, M.; Fielding, S.; Mustard, A.; Brown, L.; Sanders, R.
2003-04-01
Yes - from a review of recent data sets we present a scale analysis of the potential for globally integrated carbon export, from the surface ocean, due to the vertical transports of mesoscale eddies. Mesoscale eddies are the oceanic equivalent of atmospheric storms, most are a fundamental result of horizontally unstable density gradients on the surface of a rotating sphere (baroclinic instability) and ~ 90% of the oceans energy exchanges take place at this scale. Recent studies from satellite remote sensing and high resolution models show that mesoscale eddies are a ubiquitous feature of the open ocean in both time and space; they are even present in sub-tropical oligotrophic gyres. Individual atmospheric weather systems generally have little ecological impact on terrestrial or marine biological systems. Grass grows and herbivores munch through many cyclone and anticyclone periods. In the open ocean we have a very different picture. The primary producers and herbivores have shorter time scales; time scales that coincide with those of mesoscale eddies. Plankton can have either good or bad weather lifetimes associated with just a single cyclone or anticyclone period. Furthermore, although the spring bloom may be the single largest source of material for the export of carbon from the upper ocean, it is short lived and may not be dominant everywhere in the annual export budget. The magnitude of vertical motion associated with mesoscale eddies is significant on biological timescales both for phytoplankton growth and the development of zooplankton grazing pressure. Critically this motion does not form a closed vertical circulation; baroclinic instability releases potential energy and thus water masses are exchanged both vertically and horizontally across water mass boundaries. Thus mesoscale eddies have been shown to provide a mechanism for export both in the direct transport of biomass downwards out of the surface mixed layer and the fertilisation of an exhausted
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
ERIC Educational Resources Information Center
Beigie, Darin
2014-01-01
Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
Vertex Algebras, Kac-Moody Algebras, and the Monster
NASA Astrophysics Data System (ADS)
Borcherds, Richard E.
1986-05-01
It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The ``Moonshine'' representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation.
Viscosities of aqueous blended amines
Hsu, C.H.; Li, M.H.
1997-07-01
Solutions of alkanolamines are an industrially important class of compounds used in the natural gas, oil refineries, petroleum chemical plants, and synthetic ammonia industries for the removal of acidic components like CO{sub 2} and H{sub 2}S from gas streams. The viscosities of aqueous mixtures of diethanolamine (DEA) + N-methyldiethanolamine (MDEA), DEA + 2-amino-2-methyl-1-propanol (AMP), and monoethanolamine (MEA) + 2-piperidineethanol (2-PE) were measured from 30 C to 80 C. A Redlich-Kister equation for the viscosity deviation was applied to represent the viscosity. On the basis of the available viscosity data for five ternary systems, MEA + MDEA + H{sub 2}O, MEA + AMP + H{sub 2}O, DEA + MDEA + H{sub 2}O, DEA + AMP + H{sub 2}O, and MEA + 2-PE + H{sub 2}O, a generalized set of binary parameters were determined. For the viscosity calculation of the systems tested, the overall average absolute percent deviation is about 1.0% for a total of 499 data points.
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2014-01-01
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
NASA Technical Reports Server (NTRS)
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
Palmkvist, Jakob
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
Eddy current scanning at Fermilab
Boffo, C.; Bauer, P.; Foley, M.; Brinkmann, A.; Ozelis, J.; /Jefferson Lab
2005-07-01
In the framework of SRF cavity development, Fermilab is creating the infrastructure needed for the characterization of the material used in the cavity fabrication. An important step in the characterization of ''as received'' niobium sheets is the eddy current scanning. Eddy current scanning is a non-destructive technique first adopted and further developed by DESY with the purpose of checking the cavity material for sub-surface defects and inclusions. Fermilab has received and further upgraded a commercial eddy current scanner previously used for the SNS project. The upgrading process included developing new filtering software. This scanner is now used daily to scan the niobium sheets for the Fermilab third harmonic and transverse deflecting cavities. This paper gives a status report on the scanning results obtained so far, including a discussion of the typology of signals being detected. We also report on the efforts to calibrate this scanner, a work conducted in collaboration with DESY.
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
Minimum-dissipation models for large-eddy simulation
NASA Astrophysics Data System (ADS)
Rozema, Wybe; Bae, Hyun J.; Moin, Parviz; Verstappen, Roel
2015-08-01
Minimum-dissipation eddy-viscosity models are a class of sub-filter models for large-eddy simulation that give the minimum eddy dissipation required to dissipate the energy of sub-filter scales. A previously derived minimum-dissipation model is the QR model. This model is based on the invariants of the resolved rate-of-strain tensor and has many desirable properties. It appropriately switches off for laminar and transitional flows, has low computational complexity, and is consistent with the exact sub-filter tensor on isotropic grids. However, the QR model proposed in the literature gives insufficient eddy dissipation. It is demonstrated that this can be corrected by increasing the model constant. The corrected QR model gives good results in simulations of decaying grid turbulence on an isotropic grid. On anisotropic grids the QR model is not consistent with the exact sub-filter tensor and requires an approximation of the filter width. It is demonstrated that the results of the QR model on anisotropic grids are primarily determined by the used filter width approximation, and that no approximation gives satisfactory results in simulations of both a temporal mixing layer and turbulent channel flow. A new minimum-dissipation model for anisotropic grids is proposed. This anisotropic minimum-dissipation (AMD) model generalizes the desirable practical and theoretical properties of the QR model to anisotropic grids and does not require an approximation of the filter width. The AMD model is successfully applied in simulations of decaying grid turbulence on an isotropic grid and in simulations of a temporal mixing layer and turbulent channel flow on anisotropic grids.
Locally finite dimensional Lie algebras
NASA Astrophysics Data System (ADS)
Hennig, Johanna
We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, *), K( R, *)] / (Z(R) ∩ [ K(R, *), K(R, *)]) for a simple, locally finite dimensional associative algebra R with involution *. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(ninfinity), o( ninfinity), and sp(n infinity).
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075
On the cohomology of Leibniz conformal algebras
NASA Astrophysics Data System (ADS)
Zhang, Jiao
2015-04-01
We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.
Assessing Algebraic Solving Ability: A Theoretical Framework
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam
2012-01-01
Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…
Eddy diffusion at Saturn's homopause
NASA Technical Reports Server (NTRS)
Sandel, B. R.; Mcconnell, J. C.; Strobel, D. F.
1982-01-01
Measurements of Saturn's He 584 A dayglow and the CH4 density profile deduced from stellar occultation data near the homopause have been combined to infer an eddy diffusion coefficient of 8 + or - 4 x 10 to the 7th sq cm/s and a temperature of 125 + 40 or - 25 K near the homopause at Voyager 2 encounter. It appears that the eddy diffusion coefficient may have increased between the Voyager encounters. Saturn's H Ly-alpha dayglow is qualitatively compatible with this increase and the interpretation of the He 584 A dayglow and CH4 absorption measurement.
NASA Astrophysics Data System (ADS)
Carper, Matthew A.; Porté-Agel, Fernando
2008-04-01
The ability of subfilter-scale (SFS) models to reproduce the statistical properties of SFS stresses and energy transfers over heterogeneous surface roughness is key to improving the accuracy of large-eddy simulations of the atmospheric boundary layer. In this study, several SFS models are evaluated a priori using experimental data acquired downwind of a rough-to-smooth transition in a wind tunnel. The SFS models studied include the eddy-viscosity, similarity, non-linear and a mixed model consisting of a combination of the eddy-viscosity and non-linear models. The dynamic eddy-viscosity model is also evaluated. The experimental data consist of vertical and horizontal planes of high-spatial-resolution velocity fields measured using particle image velocimetry. These velocity fields are spatially filtered and used to calculate SFS stresses and SFS transfer rates of resolved kinetic energy. Coefficients for each SFS model are calculated by matching the measured and modelled SFS energy transfer rates. For the eddy-viscosity model, the Smagorinsky coefficient is also evaluated using a dynamic procedure. The model coefficients are found to be scale dependent when the filter scales are larger than the vertical measurement height and fall into the production subrange of the turbulence where the flow scales are anisotropic. Near the surface, the Smagorinsky coefficient is also found to decrease with distance downwind from the transition, in response to the increase in mean shear as the flow adjusts to the smooth surface. In a priori tests, the ability of each model to reproduce statistical properties of the SFS stress is assessed. While the eddy-viscosity model has low spatial correlation with the measured stress, it predicts mean stresses with the same accuracy as the other models. However, the deficiency of the eddy-viscosity model is apparent in the underestimation of the standard deviation of the SFS stresses and the inability to predict transfers of kinetic energy from
ERIC Educational Resources Information Center
Novotna, Jarmila; Hoch, Maureen
2008-01-01
Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…
Higher level twisted Zhu algebras
Ekeren, Jethro van
2011-05-15
The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by {Gamma}/Z for some subgroup {Gamma} of R containing Z, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras Zhu{sub p,{Gamma}}(V), and we prove the following theorems: For each p, there is a bijection between the irreducible Zhu{sub p,{Gamma}}(V)-modules and the irreducible {Gamma}-twisted positive energy V-modules, and V is ({Gamma}, H)-rational if and only if all its Zhu algebras Zhu{sub p,{Gamma}}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra Vir{sup c} and the universal affine Kac-Moody vertex algebra V{sup k}(g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.
Expert system for analyzing eddy current measurements
Levy, Arthur J.; Oppenlander, Jane E.; Brudnoy, David M.; Englund, James M.; Loomis, Kent C.
1994-01-01
A method and apparatus (called DODGER) analyzes eddy current data for heat exchanger tubes or any other metallic object. DODGER uses an expert system to analyze eddy current data by reasoning with uncertainty and pattern recognition. The expert system permits DODGER to analyze eddy current data intelligently, and obviate operator uncertainty by analyzing the data in a uniform and consistent manner.
Expert system for analyzing eddy current measurements
Levy, A.J.; Oppenlander, J.E.; Brudnoy, D.M.; Englund, J.M.; Loomis, K.C.
1994-08-16
A method and apparatus (called DODGER) analyzes eddy current data for heat exchanger tubes or any other metallic object. DODGER uses an expert system to analyze eddy current data by reasoning with uncertainty and pattern recognition. The expert system permits DODGER to analyze eddy current data intelligently, and obviate operator uncertainty by analyzing the data in a uniform and consistent manner. 21 figs.
Plasma viscosity in spherical ICF implosion simulations
NASA Astrophysics Data System (ADS)
Vold, E.; Joglekar, A.; Ortega, M.; Moll, R.; Fenn, D.; Molvig, K.
2016-05-01
Inertial confinement fusion (ICF) hydrodynamic codes often ignore the effects of viscosity though recent research indicates plasma viscosity and mixing by classical transport processes may have a substantial impact on implosion dynamics. A Lagrangian hydrodynamic code in one-dimensional spherical geometry with plasma viscosity and mass transport, and including a three temperature model for ions, electrons, and radiation treated in a gray radiation diffusion approximation, is used to study differences between ICF implosions with and without plasma viscosity and to examine the role of artificial viscosity in a Lagrangian implosion simulation. It was found that plasma viscosity has substantial impacts on ICF shock dynamics characterized by shock burn timing, maximum burn temperatures, fuel compression, and time history of neutron production rates. Plasma viscosity reduces the need for artificial viscosity to maintain numerical stability in the Lagrangian formulation and this study suggests that artificial viscosity may provide an unphysical stability in implosion simulations.
Viscosity in spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Ray, Arnab K.
2003-10-01
The influence of viscosity on the flow behaviour in spherically symmetric accretion has been studied here. The governing equation chosen has been the Navier-Stokes equation. It has been found that at least for the transonic solution, viscosity acts as a mechanism that detracts from the effectiveness of gravity. This has been conjectured to set up a limiting scale of length for gravity to bring about accretion, and the physical interpretation of such a length scale has been compared with the conventional understanding of the so-called `accretion radius' for spherically symmetric accretion. For a perturbative presence of viscosity, it has also been pointed out that the critical points for inflows and outflows are not identical, which is a consequence of the fact that under the Navier-Stokes prescription, there is a breakdown of the invariance of the stationary inflow and outflow solutions - an invariance that holds good under inviscid conditions. For inflows, the critical point gets shifted deeper within the gravitational potential well. Finally, a linear stability analysis of the stationary inflow solutions, under the influence of a perturbation that is in the nature of a standing wave, has indicated that the presence of viscosity induces greater stability in the system than has been seen for the case of inviscid spherically symmetric inflows.
Anomalous-viscosity current drive
Stix, T.H.; Ono, M.
1986-04-25
The present invention relates to a method and apparatus for maintaining a steady-state current for magnetically confining the plasma in a toroidal magnetic confinement device using anomalous viscosity current drive. A second aspect of this invention relates to an apparatus and method for the start-up of a magnetically confined toroidal plasma.
Eddy current thickness measurement apparatus
Rosen, Gary J.; Sinclair, Frank; Soskov, Alexander; Buff, James S.
2015-06-16
A sheet of a material is disposed in a melt of the material. The sheet is formed using a cooling plate in one instance. An exciting coil and sensing coil are positioned downstream of the cooling plate. The exciting coil and sensing coil use eddy currents to determine a thickness of the solid sheet on top of the melt.
Inexpensive Eddy-Current Standard
NASA Technical Reports Server (NTRS)
Berry, Robert F., Jr.
1985-01-01
Radial crack replicas serve as evaluation standards. Technique entails intimately joining two pieces of appropriate aluminum alloy stock and centering drilled hole through and along interface. Bore surface of hole presents two vertical stock interface lines 180 degrees apart. These lines serve as radial crack defect replicas during eddy-current technique setup and verification.
Handheld Computer Algebra Systems in the Pre-Algebra Classroom
ERIC Educational Resources Information Center
Gantz, Linda Ann Galofaro
2010-01-01
This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…
Abstract Algebra to Secondary School Algebra: Building Bridges
ERIC Educational Resources Information Center
Christy, Donna; Sparks, Rebecca
2015-01-01
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…
Algebra and Algebraic Thinking in School Math: 70th YB
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, 2008
2008-01-01
Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…
Philip, Bobby; Chartier, Dr Timothy
2012-01-01
methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.
Statecharts Via Process Algebra
NASA Technical Reports Server (NTRS)
Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance
1999-01-01
Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics
Energy Science and Technology Software Center (ESTSC)
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less
Eddy fluxes in baroclinic turbulence
NASA Astrophysics Data System (ADS)
Thompson, Andrew F.
The eddy heat flux generated by the statistically equilibrated baroclinic instability of a uniform, horizontal temperature gradient is studied using a two-mode quasigeostrophic model. An overview of the dependence of the eddy diffusivity of heat Dtau on the planetary potential vorticity gradient beta, the bottom friction kappa, the deformation radius lambda, the vertical shear of the large-scale flow 2U and the domain size L is provided at 70 numerical simulations with beta = 0 (f-plane) and 110 simulations with beta ≠ 0 (beta-plane). Strong, axisymmetric, well-separated baroclinic vortices dominate the equilibrated barotropic vorticity and temperature fields of f-plane turbulence. The heat flux arises from a systematic northward (southward) migration of anti-cyclonic (cyclonic) eddies with warm (cold) fluid trapped in the cores. Zonal jets form spontaneously on the beta-plane, and stationary, isotropic, jet-scale eddies align within the strong eastward-flowing regions of the jets. In both studies, the vortices and jets give rise to a strong anti-correlation between the barotropic vorticity zeta and the temperature field tau. The baroclinic mode is also an important contributor to dissipation by bottom friction and energizes the barotropic mode at scales larger than lambda. This in part explains why previous parameterizations for the eddy heat flux based on Kolmogorovian cascade theories are found to be unreliable. In a separate study, temperature and salinity profiles obtained with expendable conductivity, temperature and depth (XCTD) probes within Drake Passage, Southern Ocean are used to analyze the turbulent diapycnal eddy diffusivity kappa rho to a depth of 1000 meters. The Polar Front separates two dynamically different regions with strong, surface-intensified mixing north of the Front. South of the Polar Front mixing is weaker and peaks at a depth of approximately 500 m, near the local temperature maximum. Peak values of kapparho are found to exceed 10-3 m
Large eddy simulations of laminar separation bubble
NASA Astrophysics Data System (ADS)
Cadieux, Francois
The flow over blades and airfoils at moderate angles of attack and Reynolds numbers ranging from ten thousand to a few hundred thousands undergoes separation due to the adverse pressure gradient generated by surface curvature. In many cases, the separated shear layer then transitions to turbulence and reattaches, closing off a recirculation region -- the laminar separation bubble. To avoid body-fitted mesh generation problems and numerical issues, an equivalent problem for flow over a flat plate is formulated by imposing boundary conditions that lead to a pressure distribution and Reynolds number that are similar to those on airfoils. Spalart & Strelet (2000) tested a number of Reynolds-averaged Navier-Stokes (RANS) turbulence models for a laminar separation bubble flow over a flat plate. Although results with the Spalart-Allmaras turbulence model were encouraging, none of the turbulence models tested reliably recovered time-averaged direct numerical simulation (DNS) results. The purpose of this work is to assess whether large eddy simulation (LES) can more accurately and reliably recover DNS results using drastically reduced resolution -- on the order of 1% of DNS resolution which is commonly achievable for LES of turbulent channel flows. LES of a laminar separation bubble flow over a flat plate are performed using a compressible sixth-order finite-difference code and two incompressible pseudo-spectral Navier-Stokes solvers at resolutions corresponding to approximately 3% and 1% of the chosen DNS benchmark by Spalart & Strelet (2000). The finite-difference solver is found to be dissipative due to the use of a stability-enhancing filter. Its numerical dissipation is quantified and found to be comparable to the average eddy viscosity of the dynamic Smagorinsky model, making it difficult to separate the effects of filtering versus those of explicit subgrid-scale modeling. The negligible numerical dissipation of the pseudo-spectral solvers allows an unambiguous
A new climatological oceanic eddy census
NASA Astrophysics Data System (ADS)
Mason, Evan; Pascual, Ananda; Pujol, Isabel; Faugère, Yannice; Delepoulle, Antoine; Briol, Frederic
2015-04-01
We present a new climatological oceanic eddy census dataset based on gridded sea level anomalies from satellite altimeter observations that is due for release by Archiving, Validation and Interpretation of Satellite Oceanographic data (AVISO). The identification and automated tracking of oceanic eddies is carried out using the py-eddy-tracker of Mason et al. (2014). Daily outputs of eddy properties (including position, radius, amplitude and nonlinearity) covering the period 1993-2013 over the global domain are presented and discussed. Validation and comparison is made with the published global eddy track database of Chelton et al. (2011).
The Algebra of Complex Numbers.
ERIC Educational Resources Information Center
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
Algebraic Squares: Complete and Incomplete.
ERIC Educational Resources Information Center
Gardella, Francis J.
2000-01-01
Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)
ERIC Educational Resources Information Center
Buerman, Margaret
2007-01-01
Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…
Online Algebraic Tools for Teaching
ERIC Educational Resources Information Center
Kurz, Terri L.
2011-01-01
Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)
Condensing Algebra for Technical Mathematics.
ERIC Educational Resources Information Center
Greenfield, Donald R.
Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…
Algebraic Thinking in Adult Education
ERIC Educational Resources Information Center
Manly, Myrna; Ginsburg, Lynda
2010-01-01
In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…
Linear Algebra and Image Processing
ERIC Educational Resources Information Center
Allali, Mohamed
2010-01-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)
ERIC Educational Resources Information Center
Instructional Objectives Exchange, Los Angeles, CA.
A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…
Exploring Algebraic Patterns through Literature.
ERIC Educational Resources Information Center
Austin, Richard A.; Thompson, Denisse R.
1997-01-01
Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as writing about…
Learning Algebra from Worked Examples
ERIC Educational Resources Information Center
Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.
2014-01-01
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is…
Thermodynamics. [algebraic structure
NASA Technical Reports Server (NTRS)
Zeleznik, F. J.
1976-01-01
The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.
Transient eddies in the MACDA Mars reanalysis
NASA Astrophysics Data System (ADS)
Mooring, Todd A.; Wilson, R. John
2015-10-01
We present a survey of the transient eddy activity in the Mars Analysis Correction Data Assimilation (MACDA) reanalysis. The spatial structure and propagation characteristics of the eddies are emphasized. Band-pass-filtered variance and covariance fields are found to be zonally modulated, indicating a longitude dependence of the typical amplitudes of Martian transient eddies. Considerable repeatability of the eddy field spatial structures is found across Mars years, including a roughly wave number 3 pattern of low-level eddy meridional temperature transport (v'T'
Invariants of triangular Lie algebras
NASA Astrophysics Data System (ADS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-07-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.
NASA Technical Reports Server (NTRS)
Hide, R.
1972-01-01
Estimates of the coefficient of kinematical viscosity nu of the earth's liquid metallic core that are given in the geophysical literature range from approximately 0.001 sq cm/s, the viscosity of molten iron at ordinary pressures, to approximately less than 10 to the 8th power sq cm/s, based on the observation that compressional waves traverse the core without suffering serious attenuation. Bumps on the core-mantle boundary with typical horizontal dimensions up to a few thousand km and vertical dimensions h of a few km would produce the topographic coupling between the core and mantle that is evidently implied by the observed decade variations in the length of the day (unless the coupling is due to the presence of rapidly fluctuating magnetic fields in the core).
Viscosity-stabilized aqueous solutions
Wier, D. R.
1981-01-27
Thiourea functions as a solution viscosity stabilizer in aqueous compositions comprising thiourea, nonionic polymers such as polyalkylene oxides and anionic surfactants such as petroleum sulfonates. The aqueous compositions are useful in connection with fluid-drive oil recovery processes, processes for drilling, completing, or working over wells, or the like processes in which a thickened fluid is injected into or brought into contact with a subterranean earth formation.
NASA Astrophysics Data System (ADS)
Wang, W. Q.; Hao, D. W.; Zhang, L. X.; Guo, Y. K.
2012-11-01
In the present study, the subgrid-scale (SGS) eddy-viscosity model developed by Vreman [Phys. Fluids 16 (2004) 3670] and its dynamic version [Phys. Fluids 19 (2007) 065110] are tested in large-eddy simulations (LES) of the inhomogeneous turbulent flow in a full passage of Francis turbine. Distributions of pressure, velocity and vortices as well as some flow structure are gained, which is helpful to examine the performance of SGS model for complex turbulent flow and understand the flow characters in full passage of Francis turbine.
Viscosity Index Improvers and Thickeners
NASA Astrophysics Data System (ADS)
Stambaugh, R. L.; Kinker, B. G.
The viscosity index of an oil or an oil formulation is an important physical parameter. Viscosity index improvers, VIIs, are comprised of five main classes of polymers: polymethylmethacrylates (PMAs), olefin copolymers (OCPs), hydrogenated poly(styrene-co-butadiene or isoprene) (HSD/SIP/HRIs), esterified polystyrene-co-maleic anhydride (SPEs) and a combination of PMA/OCP systems. The chemistry, manufacture, dispersancy and utility of each class are described. The comparative functions, properties, thickening ability, dispersancy and degradation of VIIs are discussed. Permanent and temporary shear thinning of VII-thickened formulations are described and compared. The end-use performance and choice of VI improvers is discussed in terms of low- and high-temperature viscosities, journal bearing oil film thickness, fuel economy, oil consumption, high-temperature pumping efficiency and deposit control. Discussion of future developments concludes that VI improvers will evolve to meet new challenges of increased thermal-oxidative degradation from increased engine operating temperatures, different base stocks of either synthetic base oils or vegetable oil-based, together with alcohol- or vegetable oil-based fuels. VI improvers must also evolve to deal with higher levels of fuel dilution and new types of sludge and also enhanced low-temperature requirements.
Liquid Viscosities of Fluorinated Dialkylethers
NASA Astrophysics Data System (ADS)
Nakazawa, Noriaki; Kawamura, Mitsutaka; Sekiya, Akira; Ootake, Katsuto; Tamai, Ryoichi; Kurokawa, Yuji; Murata, Junji
The liquid viscosities of thirteen fluorinated dialkylethers which are expected as promising candidates of CFC alternatives were measured at temperatures from 276 K to 328 K and atmospheric pressure. The fluorinated dialkylethers used in this study are 1-methoxy-1, 1, 2, 2- tetrafluoroethane; 1-difluoromethoxy- 1, 1 , 2 -trifluoroethane; 1-methoxy-1, 1 , 2 , 2 , 3 , 3 -hexafluoropropane; 1-methoxy-1-trifluoro-methyl-2, 2 , 2-trifluoroethane; 1-difluoro-methoxy-2, 2, 3, 3-tetrafluoropropane; 1-(2, 2, 2-trifruoroethoxy)-1, 1, 2, 2-tetrafluoroethane 1-difluoromethoxy-2, 2, 3, 3, 3-pentafluoropropane 1-methoxy-2, 2, 3, 3 -tetrafluoropropane; 1-methoxy-1, 1, 2, 2, 3, 3, 3-heptafluoropropane; 1-pentafluoroethoxy-1, 1, 2, 2-tetrafluoroethane; 2-trifluoromethoxy-1, 1, 1, 2-tetrafluorobutane; 1-proxy-nonafluorobutane; and 1-ethoxyundeca-fluoropentane. The liquid viscosities have been measured by the torsionally vibrating viscometer (YAMAICHI DENKI, F VM-80A) within an uncertainty of ±3%.The liquid viscosities of those compounds decrease exponentially with increase of temperature.
Density and viscosity of lipids under pressure
Technology Transfer Automated Retrieval System (TEKTRAN)
There is a lack of data for the viscosity of lipids under pressure. The current report is a part of the effort to fill this gap. The viscosity, density, and elastohydrodynamic film thicknesses of vegetable oil (HOSuO) were investigated. Pressure–viscosity coefficients (PVC) of HOSuO at different tem...
Eddy transport of reacting substances
NASA Astrophysics Data System (ADS)
Flierl, Glenn
2015-11-01
We examine an exact formulation of eddy fluxes but extended to tracers which react with each other. The resulting formula is evaluated using the lattice model approach, allowing not only control (including elimination) of sub-grid-scale diffusion and efficient enough computation to generate an adequate ensemble. The theory predicts that the flux is a non-local average of the mean gradients, even for passive scalars, and we can calculate the averaging kernel. The reaction terms alter the effective transport for a single scalar depending on decay time scale compared to that of the Lagrangian covariance. But, in addition, the eddies produce ``cross-fluxes'' whereby the transport of each tracer depends on the gradients of all of them.
Remote field eddy current inspection
Atherton, D.L.
1995-11-01
The Remote Field Eddy Current (RFEC) technique uses an internal probe to inspect conducting tubes nondestructively. A coaxial solenoidal exciter, energized with low frequency AC, and detector coils near the inside of the pipe wall are separated by about two pipe diameters to obtain through wall transmission and equal sensitivity to defects on the outside or inside of the pipe wall. Calculation methods are outlined and the voltage plane polar plot signal representation for defect measurement is described. Slit defect interactions in ferromagnetic and non-ferromagnetic tubes are discussed. Defect-induced anomalous fields are interpreted in terms of anomalous source eddy current and missing magnetization defect models. The use of computer animations to represent the time variations of high resolution field measurements and calculations is described.
Large eddy simulation of turbulent channel flow: ILLIAC 4 calculation
NASA Technical Reports Server (NTRS)
Kim, J.; Moin, P.
1979-01-01
The three-dimensional time dependent equations of motion were numerically integrated for fully-developed turbulent channel flow. A large scale flow field was obtained directly from the solution of these equations, and small scale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC 4 computer. The computed flow patterns show that the wall layer consists of coherent structures of low speed and high speed streaks alternating in the spanwise direction. These structures were absent in the regions away from the wall. Hot spots, small localized regions of very large turbulent shear stress, were frequently observed. The profiles of the pressure velocity-gradient correlations show a significant transfer of energy from the normal to the spanwise component of turbulent kinetic energy in the immediate neighborhood of the wall ('the splatting effect').
ERIC Educational Resources Information Center
Gonzalez-Vega, Laureano
1999-01-01
Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)
Chen, J.; Safro, I.
2011-01-01
Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.
Constraint algebra in bigravity
Soloviev, V. O.
2015-07-15
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
electromagnetics, eddy current, computer codes
Energy Science and Technology Software Center (ESTSC)
2002-03-12
TORO Version 4 is designed for finite element analysis of steady, transient and time-harmonic, multi-dimensional, quasi-static problems in electromagnetics. The code allows simulation of electrostatic fields, steady current flows, magnetostatics and eddy current problems in plane or axisymmetric, two-dimensional geometries. TORO is easily coupled to heat conduction and solid mechanics codes to allow multi-physics simulations to be performed.
Quantum algebra of N superspace
Hatcher, Nicolas; Restuccia, A.; Stephany, J.
2007-08-15
We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.
Localized dynamic kinetic-energy-based models for stochastic coherent adaptive large eddy simulation
NASA Astrophysics Data System (ADS)
De Stefano, Giuliano; Vasilyev, Oleg V.; Goldstein, Daniel E.
2008-04-01
Stochastic coherent adaptive large eddy simulation (SCALES) is an extension of the large eddy simulation approach in which a wavelet filter-based dynamic grid adaptation strategy is employed to solve for the most "energetic" coherent structures in a turbulent field while modeling the effect of the less energetic background flow. In order to take full advantage of the ability of the method in simulating complex flows, the use of localized subgrid-scale models is required. In this paper, new local dynamic one-equation subgrid-scale models based on both eddy-viscosity and non-eddy-viscosity assumptions are proposed for SCALES. The models involve the definition of an additional field variable that represents the kinetic energy associated with the unresolved motions. This way, the energy transfer between resolved and residual flow structures is explicitly taken into account by the modeling procedure without an equilibrium assumption, as in the classical Smagorinsky approach. The wavelet-filtered incompressible Navier-Stokes equations for the velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy variable, are numerically solved by means of the dynamically adaptive wavelet collocation solver. The proposed models are tested for freely decaying homogeneous turbulence at Reλ=72. It is shown that the SCALES results, obtained with less than 0.5% of the total nonadaptive computational nodes, closely match reference data from direct numerical simulation. In contrast to classical large eddy simulation, where the energetic small scales are poorly simulated, the agreement holds not only in terms of global statistical quantities but also in terms of spectral distribution of energy and, more importantly, enstrophy all the way down to the dissipative scales.
NASA Astrophysics Data System (ADS)
Hunt, Julian C. R.; Moustaoui, Mohamed; Mahalov, Alex
2015-09-01
High resolution three-dimensional simulations are presented of the interactions between turbulent shear flows moving with mean relative velocity ΔU below a stably stratified region with buoyancy frequency (N+). An artificial forcing in the simulation, with a similar effect as a small negative eddy viscosity, leads to a steady state flow which models thin interfaces. Characteristic eddies of the turbulence have length scale L. If the bulk Richardson number Rib=(LN+/ΔU)2 lies between lower and upper critical values denoted as Ri∗(<1/5) and R~i(˜ 1), a "detached" layer is formed in the stable region with thickness L+ greater than L, in which rotational fluctuations and inhomogeneous turbulence are induced above an interface with large gradients of density/temperature. Comparisons are made with shear turbulent interfaces with no stratification. When Rib>R~i, vertical propagating waves are generated, with shear stresses carrying significant momentum flux and progressively less as Rib increases. Simulations for a jet and a turbulent mixing layer show similar results. A perturbation analysis, using inhomogeneous Rapid Distortion Theory, models the transition zone between shear eddies below the interface and the fluctuations in the stratified region, consistent with the simulations. It demonstrates how the wave-momentum-flux has a maximum when Rib˜2 and then decreases as Rib increases. This coupling mechanism between eddies and waves, which is neglected in eddy viscosity models for shear layers, can drive flows in the stratosphere and the deeper ocean, with significant consequences for short- and long-term flow phenomena. The "detached layer" is a mechanism that contributes to the formation of stratus clouds and polluted layers above the atmospheric boundary layer.
The morphology of shelfbreak eddies
NASA Astrophysics Data System (ADS)
Garvine, R. W.; Wong, K.-C.; Gawarkiewicz, G. G.; McCarthy, R. K.; Houghton, R. W.; Aikman, F.
1988-12-01
We used a combination of buoy tracking, intensive hydrography, satellite thermal imagery, and moored current meters to resolve the structure of eddies at the shelfbreak front in the Middle Atlantic Bight south of New England. Eddylike features were always present at the front in our study area throughout the 15-day period of observations in June 1984. We found that hydrographic features in our across-shelf hydrographic transects that appeared to represent the detached parcels of shelf water often reported in the literature were, in fact, part of the three-dimensional structure of shelfbreak eddies. Adequate alongshelf resolution, in particular, enabled us to determine that no detached parcels were present. The two prominent features of the eddy groups we found were plumes of lighter shelf water that protruded into slope water, curling "backward" opposite the direction of mean shelf flow, and neighboring cyclones with warmer, saltier slope water in their cores, partly or wholly encircled by the plumes. The plumes have the potential especially for producing vigorous across-front exchange of heat, salt, and nutrients and may play roles analogous to the "squirts" found on the California shelf.
The effective tidal viscosity in close solar-type binaries
NASA Astrophysics Data System (ADS)
Goldman, I.
2008-09-01
A major problem confronting the understanding of tidal evolution of close solar-type binaries is the inefficiency of the turbulent convection. The value of the effective viscosity estimated, in the framework of the mixing length theory (MLT), implies circularization timescales which are almost two orders of magnitude longer than observed. Moreover, the reduction of the effective viscosity due to the fast time-variation of the tidal shear in short period binaries, increases the discrepancy to about three orders of magnitude. This state of affairs has motivated suggestions that tidal orbital evolution, notably circularization occurs mainly during the pre-main-sequence phase. However, observational data accumulated over the recent decades imply that circularization does occur during the the main-sequence phase (Mazeh 2008). In this work, we examine the possibility that the apparent inefficiency of turbulent convection is merely a shortcoming of MLT approach. Indeed, a recent 3D numerical simulation (Penev et al. 2007), suggests that the true convective viscosity is probably larger than the MLT value and that the reduction due to the time-variation of the shear is not drastic. We employ a model for stellar turbulent convection (Canuto, Goldman & Mazzitelli 1996) to evaluate the effective viscosity both for a steady for and time dependent tidal shear. The model is physically based, self-consistent, and accounts for the full spectrum of the turbulent eddies. It has been found advantageous, compared to the MLT, in many applications. We use an analytic approximation to the turbulent spectrum to obtain the reduction of the efficiency due to the time-variation of the tide. The results are: (i) an enhanced effective viscosity (by a factor of ˜ 4.5), and more importantly (ii) only a mild reduction due to the time-variation of the tidal shear. Overall, for binaries with orbital period of 15 days the discrepancy is ``only" a factor of ˜ 30 down from a factor of ˜ 1000. These
Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.
ERIC Educational Resources Information Center
Leitze, Annette Ricks; Kitt, Nancy A.
2000-01-01
Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)
Distance geometry and geometric algebra
NASA Astrophysics Data System (ADS)
Dress, Andreas W. M.; Havel, Timothy F.
1993-10-01
As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)
Loop Virasoro Lie conformal algebra
Wu, Henan Chen, Qiufan; Yue, Xiaoqing
2014-01-15
The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.
Hopf algebras and Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Weinzierl, Stefan
2016-06-01
In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.
Large eddy simulation of incompressible turbulent channel flow
NASA Technical Reports Server (NTRS)
Moin, P.; Reynolds, W. C.; Ferziger, J. H.
1978-01-01
The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.
Minimum-dissipation models for large-eddy simulation
NASA Astrophysics Data System (ADS)
Bae, Hyunji Jane; Rozema, Wybe; Moin, Parviz; Verstappen, Roel
2015-11-01
Minimum-dissipation eddy-viscosity models are a class of subgrid scale models for LES that give the minimum eddy dissipation required to dissipate the energy of subgrid scales. The QR minimum-dissipation model [Verstappen, J. Sci. Comp., 2011] gives good results in simulations of decaying grid turbulence carried out on an isotropic grid. In particular, due to the minimum dissipation property of the model, the predicted energy spectra are in very good agreement with the DNS results up to the cut-off wave number unlike other methods. However, its results on anisotropic grids are often unsatisfactory because the model does not properly incorporate the grid anisotropy. We propose the anisotropic minimum-dissipation (AMD) model [Rozema et al., submitted for publication, 2015], a minimum-dissipation model that generalizes the QR model to anisotropic grids. The AMD model is more cost effective than the dynamic Smagorinsky model, appropriately switches off in laminar and transitional flow on anisotropic grids, and its subgrid scale model is consistent with the theoretic subgrid tensor. Experiments show that the AMD model is as accurate as the dynamic Smagorinsky model and Vreman model in simulations of isotropic turbulence, temporal mixing layer, and turbulent channel flow. H. J. Bae acknowledges support from SGF. W. Rozema and R. Verstappen acknowledge sponsoring by NWO for the use of supercomputing facilities and the financial support to attend the CTR SP 2014.
A family of dynamic models for large-eddy simulation
NASA Technical Reports Server (NTRS)
Carati, D.; Jansen, K.; Lund, T.
1995-01-01
Since its first application, the dynamic procedure has been recognized as an effective means to compute rather than prescribe the unknown coefficients that appear in a subgrid-scale model for Large-Eddy Simulation (LES). The dynamic procedure is usually used to determine the nondimensional coefficient in the Smagorinsky (1963) model. In reality the procedure is quite general and it is not limited to the Smagorinsky model by any theoretical or practical constraints. The purpose of this note is to consider a generalized family of dynamic eddy viscosity models that do not necessarily rely on the local equilibrium assumption built into the Smagorinsky model. By invoking an inertial range assumption, it will be shown that the coefficients in the new models need not be nondimensional. This additional degree of freedom allows the use of models that are scaled on traditionally unknown quantities such as the dissipation rate. In certain cases, the dynamic models with dimensional coefficients are simpler to implement, and allow for a 30% reduction in the number of required filtering operations.
Superparamagnetic nanoparticle-based viscosity test
NASA Astrophysics Data System (ADS)
Wu, Kai; Liu, Jinming; Wang, Yi; Ye, Clark; Feng, Yinglong; Wang, Jian-Ping
2015-08-01
Hyperviscosity syndrome is triggered by high blood viscosity in the human body. This syndrome can result in retinopathy, vertigo, coma, and other unanticipated complications. Serum viscosity is one of the important factors affecting whole blood viscosity, which is regarded as an indicator of general health. In this letter, we propose and demonstrate a Brownian relaxation-based mixing frequency method to test human serum viscosity. This method uses excitatory and detection coils and Brownian relaxation-dominated superparamagnetic nanoparticles, which are sensitive to variables of the liquid environment such as viscosity and temperature. We collect the harmonic signals produced by magnetic nanoparticles and estimate the viscosity of unknown solutions by comparison to the calibration curves. An in vitro human serum viscosity test is performed in less than 1.5 min.