Rarefaction waves in dusty gases

The propagation of normal rarefaction waves in dusty gases has been investigated numerically, using the modified random choice method with operator splitting technique. The effects of the dust parameters on the flow properties inside and behind the rarefaction wave are studied. The results are compared with those appropriate to a dust-free gas.     

Three-dimensional steady flows of stratified fluid and internal waves

A study is made of three-dimensional steady flows of an ideal heavy incompressible fluid stratified in each layer over a flat or asymptotically flat base. Mixed Euler-Lagrange variables are chosen in which surfaces of constant density, including the layer division boundaries, become flat and parallel to the plane of the base. The original problem is reduced to a nonlinear boundary-value problem for a system of three quasilinear equations in a plane layer. This system of equations is used to construct an asymptotic theory of long waves in the three-dimensional case, which has particular solutions in the first approximation in the form of solitons and soliton systems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 127–132, May–June, 1985.     

Non-linear water waves on shearing flows

This article is devoted to the study of the propagations of the nonlinear water waves on the shear flows. Assuming μ=kh is small andε/μ ²∼O(1), and the base flow is uniformly sheared, the modified Boussinesq equation is obtained. We calculate propagations of the single solitary wave with vorticity Γ=0,>0 and <0. The influences of the vorticity are manifested. At the end examples of the interactions of two solitary waves, moving in opposite and the same directions, are given. Besides the phase shift, there also occur second wavelets after head-on collision. The project supported by the National Natural Science Foundation of China     

Magnetovibrational flows in a magnetic fluid

A new type of flow in a magnetic fluid has been experimentally detected and investigated. The interaction between an alternating nonuniform magnetic field and a magnetic fluid leads to the parametric excitation of traveling capillary-gravitational waves which are the direct cause of the average flow. A necessary condition of formation of hydrodynamic flows in an alternating field is also the presence of time-dependent harmonics with multiple frequencies synchronized with the first harmonic, so that the time dependence of the ponderomotive force is generally pulsed. It is shown that for plane vibrational flows the classical theory cannot explain the high intensity of the average flows observed. It is suggested that the high intensity of magnetovibrational flows is related to the violation of the cylindrical symmetry of the traveling capillary-gravitational waves and the transition to a three-dimensional motion. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–133, January–February, 1998.     

Critical time for asymptotic waves in self-similar flows

The problem of shock wave formation within a self-similar flow is studied through the asymptotic wave methodology.The conditions for the breakdown of the perturbations are discussed in terms of the adiabatic index.     

Rarefaction shock waves in porous media that accumulate CO2, CH4, N2

In this paper, a porous medium whose core is built from a solid substance is considered. Such a medium can accumulate liquid and gaseous substances absorbing on the surface of the solid body and diffusing within its molecular lattice. The medium forms a so-called solid solution. A change in the values of the thermodynamic parameters of this medium leads to phase transitions in these substances. Besides, some other associated phenomena may occur. There are given the results of laboratory analyses concerning the relation between the specific volumeV of the solid solution formed by the coal with CO₂, CH₄, N₂ dissolved in it and its confining pressurep. This relation indicates the possibility of the propagation of a rarefaction shock waves in such a medium.A mathematical model of the generation of such waves and its specific applications to describe the initial boundary conditions affected during the experiments presented. The results of these experiments have confirmed the adopted model, particularly those aspects that are concerned with the specific sliced structures of the coal medium with the accumulated CO₂ and N₂, through which a rarefaction shock wave has passed (Figs. 10a, 10b, 11a, and 11b). The presented model explains the phenomena of sudden massive rock-and-gas outbursts, occurring in nature, e.g. as a result of disturbing the primary equilibrium of the rocks in the Earth crust which form a solid solution, by underground mining exploitation.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Certain nonisothermal flows of fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 83–92, May–June, 1990.     

Stability of non-newtonian fluid flows

The stability of non-Newtonian fluid films moving on inclined planes is studied within the framework of the two-parameter Ostwald-de Waele model taking into account surface tension and van der Waals forces. The problem is solved analytically in the linear formulation, and the evolution of finite-amplitude perturbations is determined numerically. Novosibirsk Military Institute, Novosibirsk 630117. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 75–80, May–June, 2000.     

Unsteady layered vortical fluid flows

An exact time-dependent solution of the system of Navier–Stokes equations governing large-scale viscous vortical incompressible flows is derived. The solution generalizes that describing the Couette flow. Two ways of preassigning the boundary conditions at the upper boundary of a fluid layer are considered. These are the time-dependent variation of the velocity value with the conservation of its direction and the variation of the angle at which the velocities parallel to the coordinate axes are directed. It is shown that at certain values of vorticity, viscosity, and the layer thickness the velocities within the layer can be severalfold greater than the given velocity at the boundary.     

Elastic waves in a turbulent fluid

It is shown that a turbulent flow can support elastic waves for which the fluctuating stress is essentially proportional to the strain field. These fluctuations are described by a hyperbolic system and hence they do not decay away from a solid boundary. Their behaviour is also consistent with Taylor's frozen field hypothesis that turbulent fluctuations are advected with the local mean flow speed.     

Nonlinear convective flows in multilayer fluid system

The nonlinear thermocapillary and buoyant-thermocapillary flows in a three-layer system, filling a closed cavity and subjected to a temperature gradient directed along the interfaces, are investigated. The nonlinear simulations of convective regimes are performed by the finite-difference method. The process of transition of unicell structures into multicell structures is studied.     

Shock waves in dense granular flows down a chute

Large scale, three dimensional computer simulations of monosized, viscoelastic, spherical glass particles flowing in an inclined duct were performed using a phenomenological model based on the modified Kelvin–Maxwell model. The particle flow rate in the model duct was regulated using a stationary wedge located in the middle of the duct. At low flow rates of glass particles, a continuous flow was observed similar to that excited by steadily and rapidly adding glass particles to the top of a heap. However, at high flow rates, a totally different situation arises where a flow with a different nature was established in the duct. The situation was found to be analogous to the case of a supersonic gas flow in a duct, where a curved-bow shock was observed to have formed on the upper edges of the duct adjacent to the wedge. In addition, in supersonic granular flows the viscous and conductance effects spread the shock changes over a finite shock layer.     

High speed flows and shock waves in astrophysical problems

Typical problems of high speed flows and shock waves in astrophysical environment are reviewed in the present paper. The emphases are especially to the solar wind acceleration, the jet structure of radio galaxies and Quasars, the galactic shock waves.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Stagnation flows for the Oldroyd-B fluid

Exact solutions to the plane and axi-symmetric stagnation flows of an Oldroyd-B fluid are reported. It is found that a steady flow is possible if the Weissenberg numberWi, defined by the product of the Maxwellian relaxation time and the shear rate at infinity, satisfies – 1/2 <Wi < 1/m, wherem = 1 in an axisym-metric flow andm = 2 in a plane flow. Furthermore, the fluid elasticity always decreases the boundary-layer thickness. An Oldroyd-B fluid with the parameters matched those of a typical Boger fluid behaves essentially like a Newtonian fluid in a stagnation flow.     

Shear flows of a thixotropic fluid

A thixotropic fluid with a viscosity dependent on a structural parameter, which satisfies a very simple kinetic equation, is examined. The stability and evolution of shear flows of such a fluid are investigated. Some classes of problems for which approximate solutions can be obtained are considered. Solutions are obtained for problems of changes in structure in oscillatory Couette flows. The apparent viscoelasticity of thixotropic fluids is analyzed. Some aspects of the thixotropic behavior of blood are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp.3–12, May–June, 1978.In conclusion, I thank S. A. Regirer for discussion of the work and useful comments.     

Three-dimensional conical viscous incompressible fluid flows

New exact solutions of the Navier-Stokes equations are obtained for steady-state three-dimensional conical flows. In this class of flows the velocity decreases in inverse proportion to the distance from the source and the input equations reduce to two-dimensional ones. It is shown that in the spherical coordinate system the equations of motion reduce to a single nonlinear equation with respect to a scalar function which depends on the polar angles. The case in which this equation reduces to the integrable Liouville equation is discussed. This makes it possible to obtain a wide class of three-dimensional solutions in analytic form. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 144–148, November–December, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00063).