On the necessity of including the turbulence experienced by an inertial particle in Lagrangian random-walk models

Many Lagrangian models have been developed in the literature in order to simulate the dispersion of particles in turbulent gas and liquid flows. The purpose of the present study is to critically analyze the impact of different fluid autocorrelation functions on the behavior of the dispersed phase in homogeneous isotropic turbulence. The “purely Lagrangian” autocorrelation, well-appropriate for turbulent diffusion problems, needs to be modified by other more sophisticated autocorrelation coefficients, including either space–time characteristics or better particle parameters to obtain appropriate numerical dispersion results in concordance with a recent theory.     

Adaptive resolution refinement for pseudospectral simulations of isotropic homogeneous turbulence

Pseudospectral simulations of homogeneous turbulence provide an important class of benchmark flow problems used for fundamental studies of turbulence and for numerical validation purposes. Depending on the numerical resolution, fully resolved computations of homogeneous turbulence can consume large amounts of central processing unit (CPU) time. Here, we present an approach analogous to adaptive mesh refinement for computations performed in physical space to adaptively refine the spectral resolution for pseudospectral computations of isotropic homogeneous turbulent flows. The method is applied to simulations of two-dimensional and three-dimensional isotropic homogeneous turbulence, and the results are compared with direct numerical simulations (DNS) performed using a fixed fine mesh. Significant savings in computational time are found in each case, with little to no compromise in the accuracy of the solutions.     

Interaction of a normal shock wave with a compressible turbulent flow

A speckle photographic method, which is sensitive to changes of gradients in fluid density, is applied for analyzing a compressible turbulent air flow with density fluctuations. Spatial correlation coefficients, turbulent length scales, and energy spectra are determined under the assumption of homogeneous isotropic turbulence. The experiments are performed in a shock tube where the flow is passed through a turbulence grid. Measurements are taken before and after the turbulent regime interacts with the normal shock wave reflected from the tube's end wall. Amplification of the turbulence intensity by the shock interaction process is verified quantitatively and is shown to be restricted to the lower wave numbers in the spectrum.A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988.To Professor Dr.-Ing. Klaus Gersten on the occasion of his 60th birthday     

Calculation of isotropic turbulence spectrum

The spectral function of isotropic turbulence is obtained on the basis of semi-empirical turbulence theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–164, November–December, 1974.     

Response of Generalized Thermoelastic Half-space with Voids to Mechanical and Thermal sources

The dynamic response of a homogeneous, isotropic, generalized thermoelastic half-space with voids subjected to normal, tangential force and thermal source is investigated. The displacements, stresses, temperature distribution and change in volume fraction field so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict the response of various sources in the Lord–Shulman (L–S) theory and Green–Lindsay (G–L) theory for an insulated boundary and temperature gradient boundary. Some particular cases have been deduced.     

Objective tensorial representation of the pressure–strain correlations of turbulence

An explicit algebraic model for the fluctuating pressure–strain rate correlations of turbulence is developed by the use of representation theorems for tensor-valued isotropic tensors, and by invoking the principle of objectivity. The resulting model differs from others by the absence of the vorticity tensor from its formulation. The new model is calibrated by reference to data from homogeneous shear flows, and its potential as a practical tool for the analysis of turbulent flows is demonstrated by numerical simulations of a benchmark two-dimensional shear layer.     

The decay of weak,homogeneous turbulence in the presence of a vertical body force and concentration gradient with a first-order reaction

The effects of buoyancy, produced by a uniform vertical concentration gradient and body force, on a homogeneous turbulent field accompanied by a first-order chemical reaction, are analysed by considering a simplified model. A system of two-point correlation equations, which contains mean concentration gradient and body force terms, is constructed from the Navier-Stokes, convective diffusion and continuity equations. By well-known methods, these equations are converted into equations for the spectrum functions in the wave-number space and solutions for different spectral tensors are obtained by neglecting the contributions of the triple correlation terms. For carrying out the numerical calculations, it is assumed that the turbulence is initially isotropic and the concentration fluctuations initially zero. It turns out that the turbulence decays with time, although the buoyancy forces do alter the rate of decay. The buoyancy forces can either extract energy from the turbulent field or feed energy into it, depending upon the direction of the body force and the concentration gradient. Spectra are displayed graphically for several values of the reaction rate parameter for stabilizing, as well as destabilizing, buoyancy forces.     

A new dynamic formula for determining the coefficient of Smagorinsky model

The most common method to determine the coefficient of Smagorinsky model now is to employ the Germano identity, however it is too complex and expensive in numerical calculation. In this letter we propose a new dynamic formula for determining the coefficient, which is based on the Kolmogorov equation of filtered velocity in physical space. The simplified formula is quite easy to implement in calculation. It is then verified in both homogeneous isotropic turbulence and wall-bounded turbulence by A Priori and A Posteriori tests.     

Direct simulation of compressible turbulence in a shear flow

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. We find that the growth of the turbulent kinetic energy decreases with increasing Mach number—a phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. We previously obtained the following results for isotropic turbulence: first, the normalized compressible dissipation is of O(M _t ² ), and, second, there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both these results have now been substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, U.S.A.     

Constitutive Equations of an Isotropic Hyperelastic Body

Stress—strain equations for an isotropic hyperelastic body are formulated. It is shown that the strain energy density whose gradient determines stresses can be defined as a function of two rather than three arguments, namely, strain–tensor invariants. In the case of small strains, the equations become relations of Hooke's law with two material constants, namely, shear modulus and bulk modulus.     

Radiative relaxation kinetics of shock-heated xenon

The kinetics of the ionization and radiation processes taking place in xenon heated in strong shock waves (Mach numbers on the interval 10–20) are numerically investigated. A fairly complete model of the medium and the processes is used. The influence of the radiation efficiency is taken into account on the assumption that the radiation layer is homogeneous and isotropic at every instant of time. The calculated distribution of plasma brightness temperature along the luminous layer is compared with that measured in shock-tube experiments. The experimental data are satisfactorily described by the modeling.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 157–163, November–December, 1992.     

On the spectrum of magnetic field and scalar impurity fluctuations in acoustic turbulence

The fluctuations of a magnetic field in acoustic turbulence are examined. An equation is derived for the spectral tensor of homogeneous magnetic field fluctuations. In a certain limit case the spectrum of steady-state pulsations is obtained in the presence of an external source. It is shown that three kinds of spectra exist in an inertial subdomain, each of which corresponds to a definite domain in wave space. Analogous results have been obtained for the fluctuations of a homogeneous scalar impurity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 26–31, March–April 1971.In conclusion, the author grateful to R. Z. Sagdeev for discussing the results obtains at a seminar.     

Nonlinear Antiplane Deformation of an Elastic Body

The antiplane elastic deformation of a homogeneous isotropic prestretched cylindrical body is studied in a nonlinear formulation in actual–state variables under incompressibility conditions, the absence of volume forces, and under constant lateral loading along the generatrix. The boundary–value problem of axial displacement is obtained in Cartesian and complex variables and sufficient ellipticity conditions for this problem are indicated in terms of the elastic potential. The similarity to a plane vortex–free gas flow is established. The problem is solved for Mooney and Rivlin—Sonders materials simulating strong elastic deformations of rubber–like materials. Axisymmetric solutions are considered.     

Group properties and invariant solutions of equations of an electric field in the case of nonlinear ohm's law

The group properties of one-dimensional nonstationary equations of an electric field in homogeneous isotropic media with nonlinear conductivity are considered. The nonlinear Ohm's laws for which these equations have the broadest symmetry properties are determined. Ordinary differential equations determining invariants solutions are obtained; the order of the equations is lowered or they are integrated to the end.Translated from Zhurnal Prikladnoi Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 28–36, May–June, 1972.     

Spectral transport model for turbulence

The spectrum of inhomogeneous turbulence is modeled by an approach that is not limited to regimes of large Reynolds numbers or small mean-flow strain rates. In its simplest form and applied to incompressible flow, the model depends on five phenomenological constants defining the strength of turbulence coupling to mean flow, turbulence transport in physical and wave-number space, and mixing of stress-tensor components. The implications for homogeneous isotropic turbulence are investigated in detail and found to correspond well to the conclusions from more fundamental theories. Under appropriate limiting conditions, a turbulent system described by the model will relax over time into a state of approximate spectral equilibrium permitting a reduction to a one-point model for the system that is substantially like the familiar K- model. This yields preliminary estimates of the present model's parameters and points to the way to improved modeling of flows beyond the applicability of the K- method.     

Turbulent cascade modeling of single and bubbly two-phase turbulent flows

The analysis of turbulent two-phase flows requires closure models in order to perform reliable computational multiphase fluid dynamics (CMFD) analyses. A spectral turbulence cascade-transport model, which tracks the evolution of the turbulent kinetic energy from large to small liquid eddies, has been developed for the analysis of the homogeneous decay of isotropic single and bubbly two-phase turbulence. This model has been validated for the decay of homogeneous, isotropic single and two-phase bubbly flow turbulence for data having a 5 mm mean bubble diameter. The Reynolds number of the data based on bubble diameter and relative velocity is approximately 1400.     

Influence of a longitudinally compressed elastic plate on the nonstationary wave motion of a homogeneous liquid

In a linear formulation, a study is made of the influence of a longitudinally compressed elastic isotropic plate on the nonstationary wave motion of a stream of homogeneous liquid of finite depth on which the plate floats. The waves are generated by periodic (in time) normal stresses applied to a restricted region of the plate surface and beginning at a certain initial time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 68–75, September–October, 1980.     

Numerical Simulation of Isotropic Turbulence Dynamics

The Karman-Howarth closed equation is used to describe the behavior of homogeneous isotropic turbulence. A numerical solution is obtained by the collocation-grid and finite-difference methods using moving grids. The predicted results are compared with experimental data on the decay of fully developed and weak turbulence. The numerical realization of the Loitsiansky-MilHonshtchikov asymptotic solution has been made.     

Lyapunov analysis for fully developed homogeneous isotropic turbulence

The present work studies the isotropic and homogeneous turbulence for incompressible fluids through a specific Lyapunov analysis. The analysis consists in the calculation of the velocity fluctuation through the Lyapunov theory applied to the local deformation using the Navier-Stokes equations, and in the study of the mechanism of energy cascade through the finite scale Lyapunov analysis of the relative motion between two particles. The analysis provides an explanation for the mechanism of energy cascade, leads to the closure of the von Kármán-Howarth equation, and describes the statistics of the velocity difference. Several tests and numerical results are presented.     

Oblique incidence of an electromagnetic wave on a parabolic plasma layer

We consider the oblique incidence of a sinusoidal electromagnetic wave (with the electric vector in the plane of incidence) on a parabolic layer of a plane-layered isotropic plasma. The reflection and transmission factors are obtained, and also the electromagnetic-plasma wave conversion factor.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 27–33, May–June, 1969.The author thanks R. Z. Sagdeev for useful discussions, and A, A. Galeev and A. M. Fridman for discussion of the results.