Evolution of a single vortex in a uniform nonequilibrium medium

The problem of the evolution of a single vortex in a nonequilibrium medium with a temperature-or density-dependent energy release was solved. In a medium that is stable against small perturbations, the vortex passes to a new stationary state, and no vortex breakdown occurs. For a temperature-dependent energy release, analytical solutions that define changes in the characteristics of the vortex were obtained for high and low relaxation times. The solutions were compared with the results of numerical simulation by the Godunov method.     

Turbulent diffusion in a compressible medium

This paper examines the diffusion of impurity particles in a compressible turbulent medium and compares it to diffusion in an incompressible medium. The turbulent diffusion coefficients are calculated using exact formulas expressed in terms of the Green’s function describing impurity transport in an infinite homogeneous, isotropic, stationary turbulent medium. To obtain an approximate expression for the Green’s function, numerical solutions of the nonlinear DIA (direct interaction approximation) equation (which in this paper are obtained for the first time for the case of compressible turbulence) are employed. Two types of turbulence are examined, acoustic and a mixture of shock waves. These are described by different generalized spectra. Finally, it is shown that compressibility significantly enhances the diffusion coefficient in the case of acoustic turbulence and reduces it in the second case. Zh. éksp. Teor. Fiz. 114, 930–945 (September 1998)     

Dissipation of vortex disturbances in a vibrationally nonequilibrium diatomic gas

The influence of the vibrational relaxation on suppression of the Kelvin??Helmholtz instability in an evolving shear layer of a vibrationally nonequilibrium diatomic gas is studied numerically on the basis of equations of two-temperature aerohydrodynamics. Planar waves with the maximum growth rates, which were computed within the framework of a linearized system of equations of inviscid two-temperature gas dynamics, are used as the initial disturbances. It is shown that relaxation of the nonequilibrium vibrational mode at excitation levels, which can be obtained in diatomic gases in nozzle flows, in underexpanded jets, or in flows with moderate laser pumping, is accompanied by noticeable suppression of vortex disturbances. The associated relative enhancement of dissipation of kinetic energy of a large vortex structure averaged over its ??lifetime?? reaches approximately 13 %.     

Conservation laws for cosmological perturbations

We briefly recall the problem of defining conserved quantities such as energy in general relativity, and the solution given by introducing a symmetric background. We apply the general formalism to perturbed Robertson-Walker spacetimes with de Sitter geometry as background. We relate the obtained conserved quantities to Traschen's integral constraints and mention a few applications in cosmology.     

Conservation laws in a directed sandpile model

We derive a complete set of conservation laws for a directed sandpile model originally studied by Dhar and Ramaswamy, and discuss the rather minimal effect of these laws on the dynamics of avalanches.     

Conservation laws in acoustics

The method earlier proposed by the author for obtaining a complete set of conservation laws is applied to a number of simple acoustic problems. Some of the conservation laws presented are derived for the first time. Special attention is given to the physical interpretation of the results.     

Conservation laws for polynomial quantum Hamiltonians

A construction method for the conservation laws for a broad class of polynomial quantum Hamiltonians is proposed. Also the classification of irreducible representations of some nonlinear commutation relation is given.     

Conservation laws in general relativity

In recent years an increased interest in General Relativity Theory (GRT) has been apparent among theoretical physicists, mathematicians, astronomers and geophysicists. At the same time, the necessity of rinding a final and generally satisfactory solution of a very important problem, namely that of conservation laws, has become topical. Surprising difficulties have been encountered in the attempt to transfer these concepts to General Relativity Theory. In the course of a few years a comprehensive literature has resulted and now the time is ripe for a thorough summary of the results attained so far.The authors would like to thank Dr. P. Burcev from the Dept of Theoretical Physics, J. E. Purkyn University in Brno, and Dr. K. Kucha from the Dept. of Theoretical Physics, Charles University in Prague, for their permanent interest in this work and for valuable discussions.     

Conservation laws and self-consistent sources for a super-CKdV equation hierarchy

From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy.     

Conservation laws in Bimetric gravitation theories

In the bimetric theory of gravitation with a flat-space background metric conservation laws for energy and momentum are considered in several different forms. In the bimetric theory with a constant-curvature background metric a previous error in the energy-momentum relation is corrected.     

Nonparaxial vortex vector solitons in a nonlinear cubic medium

The propagation of narrow three-dimensional wave beams in a nonlinear cubic medium has been analyzed taking into account all vector components of the wave field, including radial, angular, and longitudinal ones. Soliton solutions to the Maxwell equations in the form of vortex solitons are found, and their properties are investigated.     

Global visualization and quantification of compressible vortex loops

The physics of compressible vortex loops generated due to the rolling up of the shear layer upon the diffraction of a shock wave from a shock tube is far from being understood, especially when shock-vortex interactions are involved. This is mainly due to the lack of global quantitative data available which characterizes the flow. The present study involves the usage of the PIV technique to characterize the velocity and vorticity of compressible vortex loops formed at incident shock Mach numbers ofM=1.54 and1.66. Another perk of the PIV technique over purely qualitative methods, which has been demonstrated in the current study, is that at the same time the results also provide a clear image of the various flow features. Techniques such as schlieren and shadowgraph rely on density gradients present in the flow and fail to capture regions of the flow influenced by the primary flow structure which would have relatively lower pressure and density. Various vortex loops, namely, square, elliptic and circular, were generated using different shape adaptors fitted to the end of the shock tube. The formation of a coaxial vortex loop with opposite circulation along with the generation of a third stronger vortex loop ahead of the primary with same circulation direction are of the interesting findings of the current study.     

非局域非线性介质中的拉盖尔-高斯涡旋呼吸子和涡旋光孤子

在圆柱坐标系下,利用分离变量的方法求得了非局域克尔介质中拉盖尔-高斯光束传输的精确解析解。当输入功率等于临界功率时,光束演变为拉盖尔-高斯涡旋光孤子,是一种旋转的多环光孤子;当输入功率接近于临界功率时,光束在传输过程中形成拉盖尔-高斯涡旋呼吸子。结果表明,低阶的拉盖尔-高斯孤子呈现中空多峰亮环分布。