The countercurrent flow in a gas centrifuge is simulated. Mechanical and thermal methods for its excitation are discussed; thermal restructuring, the thermal control of the velocity field, and a shift in the inversion point are analyzed; and the formation of overtone flows in the rarefaction zone is studied.

Vortex cascades of instabilities forming a core are studied. Large-scale linear waves in a fluctuating medium are described.

The motion of bubbles in a centrally symmetric gravitational field is numerically simulated using two-dimensional conservation laws (Euler equations). The dynamics of bubbles with various numbers of modes in the initial perturbation are studied. The numerical results reveal features that are substantially different from the plane case in a homogeneous gravitational field. Bubble perturbations nearly do not interact at the formation stage. The lowest modes are amplified in the course of the bubble evolution.

A generalization of the explicit hybrid monotone second-order finite difference scheme for the use on unstructured 3D grids is proposed. In this scheme, the components of the momentum density in the Cartesian coordinates are used as the working variables; the scheme is conservative. Numerical results obtained using an implementation of the proposed solution procedure on an unstructured 3D grid in a spherical layer in the model of the global circulation of the Titan’s (a Saturn’s moon) atmosphere are presented.

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2 M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.

The paper is devoted to studying the mechanisms of formation of cyclones in the Earth’s atmosphere with the help of numerical modeling using the complete system of gas-dynamic equations. The results of modeling have shown that cyclones can appear in horizontal stratified shear flows of warm and wet air masses with horizontal direction of gradients of the wind velocity components as a result of small disturbances of pressure which can be produced by Rossby waves.

It is proposed to use nonlinear processes in 2D plasma in the channel of a field-effect transistor for frequency conversion (multiplication). It is shown that excitation of shock waves in the channel of a field-effect transistor by means of alternating voltage with a frequency of 1010−1011 Hz applied to the transistor gate results in the appearance of high frequency harmonics in the terahertz range.

The formation of shock waves in the electron gas of a field-effect transistor is simulated taking into account the coupled hydrodynamic and electromagnetic processes approximated, respectively, by the shallow water equations and electrostatic potential equations.

The results of the theoretical analysis and computer simulation of the behavior of neutrally stable shock waves with real (van der Waals gas, magnesium) equations of state are presented. An approach is developed in which the region of the neutral stability of a shock wave for each pressure value in front of the wave is determined from the analysis of the equation of state. A simple algorithm is developed to determine the cause of acoustic perturbations (a shock front or an external source) immediately from the flow pattern. In contrast to the predictions of the linear theory, the amplitude of the perturbations of the neutrally stable shock wave decreases with time, although this process is noticeably slower than in the case of an absolutely stable shock wave.

The stability of the laminar flow between two rotating cylinders (Taylor-Couette flow) is numerically studied. The simulation is based on the equations of motion of an inviscid fluid (Euler equations). The influence exerted on the flow stability by physical parameters of the problem (such as the gap width between the cylinders, the initial perturbation, and the velocity difference between the cylinders) is analyzed. It is shown that the onset of turbulence is accompanied by the formation of large vortices. The results are analyzed and compared with those of similar studies.

The problem of an ambiguous representation of shocks at S-like shaped Hugoniot fragment (in P-u plane) is considered. The behavior of the shock wave in the region of its ambiguous representation containing the Hugoniot segment with fulfilled condition of shock wave instability L>1+2M has been studied numerically on the basis of the Navier-Stokes equations in one- and twodimensional formulations. Multidimensional modeling of the behavior of the periodically disturbed shock wave has shown the formation of a cellular detonation-like front structure.

A viscous incompressible fluid is taken in a space layer (a channel) periodic in two directions and supplied with either third periodic direction or two parrallel rigid walls with no-slip conditions. The fluid in motion is treated as a mechanical system with a series of its own modes being produced by restrictions imposed during the state of rest. When classified on different structures, the modes form a complete orthogonal system. The related spectral method is developed for the Navier-Stokes system in which a new equivalent form is used to account for the interaction between the average flow and the relevant correlations of disturbances.

Constructively, the analysis of the phenomenon of turbulence must and can be performed through direct numerical simulations of mechanics supposed to be inherent to secondary flows. This one reveals itself through such instances as large vortices, structural instabilities, vortex cascades and principal modes discussed in this paper. Like fragments of a puzzle, they speak of a motion ordered with its own nuts and bolts, however chaotic it appears at first sight. This opens an opportunity for a multi-oriented approach of which a prime ideology seems to be a rational combination of grid, spectral and statistical methods. An attempt is made to bring together the above instances and produce an alternative point of view on the phenomenon in question when based on the main laws of conservation.

The work is devoted to a two-dimensional numerical study of an interaction between a transverse vortex and a composite wave that can exist in a thermodynamically nonideal medium. A model equation of state typical for shock compression processes involving phase transitions, high degree of ionization or endothermic chemical reactions is used. The composite wave consists of an upstream absolutely stable shock, a small-amplitude nonbreaking compression wave, and a downstream neutrally stable shock known as spontaneously emitting shock. The problem formulated allows to consider behavior of perturbed absolutely and neutrally stable shocks in a single computational experiment. It is shown that the front of the upstream absolutely stable shock quickly recovers its initial form and the acoustic and entropy disturbances are strongly damped. By contrast, the neutrally stable shock generates weakly damped outgoing acoustic waves long time after the interaction; i.e., the shock is a source of sound. This phenomenon increases the post-shock acoustic noise level in an initially turbulent flow.

A numerical analysis is presented of two-dimensional interaction between a transverse vortex and a composite compression wave that can exist in a thermodynamically nonideal medium. It is shown that the interaction of a composite wave involving a “neutrally stable” shock with a vortex generates weakly damped outgoing acoustic waves; i.e., the shock is a source of sound. This phenomenon increases the post-shock acoustic noise level in an initially turbulent flow.

Physical models of the development of turbulence in free shear flows and in accretion discs are proposed. The models are based on the results of numerical simulations of turbulent flow development. The main idea of the proposed theory of turbulence in free shear flow is stated as follows: the onset of turbulence begins with the formation of large vortices. The formation and evolution of large-scale turbulence in accretion discs are considered. It is shown that the kinetic energy of vortices forming in a turbulent flow is a virtually constant fraction of the initial kinetic energy of the rotating matter of an accretion disc. A possible mechanism explaining the transfer of angular momentum by large vortices that form in the disc without any noticeable heating of the matter is suggested. Keywords: Accretion discsLarge-scale turbulenceAngular momentum transfer Acknowledgements The authors wish to express their gratitude to the Russian Foundation for Basic Research for grants 06-02-16608, 06-01-00152 and 06-01-00558 and to the Programme of the Presidium of the Russian Academy of Sciences No. 4 and No. 14 for their support of this work. We also thank the Joint Supercomputer Center for providing power parallel supercomputer resources for the numerical simulation.

We consider the motion of a bubble in a central acceleration field created by gravity or a centrifugal force. In the former case, the bubble moves outwards from and, in the latter, towards the center. We have calculated the characteristic time needed for a bubble to leave or reach the center. The solution obtained provides insight into the processes of thermonuclear supernovae and combustion; in other words, into the interaction between a flame and a turbulent vortex. In the case of combustion, a light bubble of burnt material propagates towards the axis of a strong turbulent vortex faster than it drifts in the direction of rotation of the vortex. It is expected that the development of bubbles should prevent the formation of “pockets” at the flame front, similar to those predicted by a simplified model of turbulent combustion in a constant density flux. In the case of a thermonuclear supernova in a deflagration burning regime, it is shown that light products of burning rise from the center of the white dwarf substantially more rapidly than the thermonuclear flame front propagates. As a result, a flame cannot completely burn the central part of the star, and instead is pushed to the outer layers of the white dwarf. The effect of bubble motion (large-scale convection) makes spherically symmetric models for thermonuclear supernovae unrealistic, which is of prime importance for the supernova spectrum and energy. The motion of bubbles is even faster in the case of a rotating white dwarf; under certain conditions, the centrifugal force may dominate over the gravitational force. To test this theory, we have carried out numerical simulations of supernovae explosions for various sizes of the burned region in the core of the presupernova. We have derived a relation between the rate of large-scale convection and the size of the burned region, which is specified by the rate of the deflagration in the thermonuclear burning.