Connection between the characteristics of the signal of a shadow instrument and the spectrum of the turbulence

The shadow method is one of the most widely used methods for investigating turbulence [1, 2]. Using a shadow instrument with photoelectric recording, there exists, in principal, the possibility of finding the statistical characteristics of the turbulence from the statistical characteristics of the random signal taken from the instrument. In the present work, an investigation is made of the connection between the mean value and the scattering of the signal of a shadow instrument and the energy spectrum of optical inhomogeneities in the medium.     

Vorticity of the velocity field for flow in a porous medium with random inhomogeneities

The vorticity field of the flow velocity in a porous medium with random inhomogeneities is considered in the correlation approximation of perturbation theory. The correlation tensor of the vorticity, the correlation between the vorticity and the permeability field, and the circulation of the velocity are calculated for three- and two-dimensional flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 157–160, July–August, 1982.     

Stability of compressed continuously inhomogeneous plate

The action of an external reactive medium on the components of operational structures often changes the physicomechanical properties of the material, which markedly affects its carrying capacity. This means that the real properties of the material, including the formation of such inhomogeneities, must be taken more thoroughly into account. In the present work, the stability of an isotropic plate whose elastic characteristics are continuous functions of the Cartesian coordinate is investigated.L'vov University, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 84–89, February, 1994.     

Interaction of local inhomogeneities of a fluidized bed

In connection with an analysis of transport processes in fluidized beds a study is made of the steady motion of a system of local inhomogeneities of the bed porosity, which are modeled by packets of particles. The interaction of the inhomogeneities is taken into account on the basis of a cell model. The velocity fields and the pressure distributions of the solid and gas phases together with the rising and sinking velocities of the system of packets are determined in the approximation of a double continuum. The flow regimes of the fluidizing agent are investigated. It is shown that with increasing concentration of packets in the bed the velocity of their motion decreases, and the circulation region of the dispersion medium surrounding a packet or trapped within it contracts. The dependence of the rate of flow of the fluidizing agent through the transverse section of the reactor on the concentration of packets in the bed is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 42–49, January–February, 1991.     

Dispersion of a filtration flow

In this paper we shall consider the transport of a dynamically neutral impurity in a porous medium containing random inhomogeneities. The original versions of the equations for the mean impurity concentration [1, 2] were based on the hyphothesis that the random motions obeyed the Markov principle, use being made of the diffusion equations of A. N. Kolmogorov. Later [3, 4] the method of perturbations was used to study the complete system of equations for the impurity concentration and random filtration velocity in the case of a constant, nonrandom porosity; after an averaging process this yields a generalized equation for the average concentration. In the limiting cases of small- and large-scale inhomogeneities in the permeability of the medium, the basic integrodifferential equation may be, respectively, reduced to parabolic and hyperbolic equations of the second order. In the present analysis we shall use the perturbation method to study the transport of an impurity by a flow when the filtration velocity of the latter fluctuates around inhomogeneities in the permeability field, the porosity of the medium in which the flow is taking place also constituting a random field, correlating with the field of permeability. We shall derive equations for the average concentration and should formulate the corresponding boundary-value problems for these equations; we shall also calculate the components of the dispersion tensor and shall consider the equilibrium sorption of an impurity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 65–69, July–August, 1976.The author is grateful to A. I. Shnirel'man for useful discussions.     

Percolation with a limiting gradient in a medium with random inhomogeneities

The coverage of a medium by percolation and the effective permeability of a medium with stagnant zones are determined. It is shown that effective permeability is a function of external conditions, particularly the average pressure gradient. Three-, two-, and one-dimensional flows are discussed. The theory of overshoots of random functions and fields beyond a prescribed level [1, 2] is used for the investigation. Overshoots of elements of the percolation field in media with random inhomogeneities are studied. Overshoots of energy being dissipated in a volume are discussed in particular; this permits an approximate determination of the coverage of an inhomogeneous porous medium by migration during percolation with a limiting gradient, i.e., in the case of formation of stagnant zones chaotically disseminated in the flow region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 159–165, September–October, 1970.The authors thank V. M. Entov for discussing the article and useful comments.     

Nonlinear interactions of langmuir waves in a weakly inhomogeneous plasma

Kinetic equations for the scattering of the waves of the one-dimensional spectrum by plasma particles are obtained for a weakly inhomogeneous plasma. The equation for the evolution of the spectrum of the short waves [k² > (m_e/m_i) D_e ^–2] trapped in the inhomogeneities of the plasma density differs significantly from the kinetic equation for the waves in a homogeneous plasma. The problem of localization on the spectrum of the Langmuir waves in regions near the minima of the plasma density is also considered. A solution of the kinetic equation for the waves, which describes this process, is obtained.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 6–13, November–December, 1972.In conclusion, the author thanks A. S. Kingsep for suggesting the problem and for directing the work.     

Motion of a charged particle in crossed fields when the magnetic field is strongly inhomogeneous

We discuss the astrophysical problem [1] of the motion of a charged particle in crossed fields. In contrast with previous treatments [2–5] we allow strong inhomogeneities of the magnetic field.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 3–6, July–August, 1981.     

Nature of the state of the medium in the neighborhood of a cavity expanding into a dilating medium

Substantial changes in the state of a solid medium can occur under the expansion of a gas cavity therein. In particular, rupture of the brittle rock occurs. The nature of the motion of the ruptured rock differs substantially from the nature of the motion of the unruptured medium. Thus, a change in the density of the ruptured rock occurs under shear strains. This phenomenon is usually called dilatancy [1]. In addition, the strength characteristics also change under rupture of the rock. The stress state of a medium in the neighborhood of an expanding cavity at the time of cessation is analyzed in this paper. The influence of the ruptured rock characteristics on the magnitude of the residual stress is investigated. The radius of the rupture zone is determined and its dependence on the characteristics of the medium is investigated. The volume of the threshold space in the neighborhood of the cavity being formed because of dilatancy is calculated. The nature of the stress state in elastic-plastic media which do not dilate under plastic flow is also investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 143–152, May–June, 1979.     

Percolation model of two-phase flow through porous media

A physical model of the process of two-phase flow of immiscible fluids through a porous medium is developed and used to make an analytical calculation of the dependence of the relative phase permeabilities on the saturation of the medium by one of the phases. The theory is compared qualitatively with experiment for a model capillary radius frequency function and quantitatively with numerical calculations made on a computer. In both cases good agreement is obtained. The pressure dependences of the phase permeabilities are analyzed. The question of residual saturation with the wetting fluid after completion of the displacement process is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 88–95, January–February, 1987.     

Calculation of unsteady supersonic flow past a two-dimensional cascade of plates ween vorticity inhomogeneities of the flow act on it

In the framework of the linear theory of small perturbations the problem of unsteady subsonic flow past a two-dimensional cascade of plates has been considered in a number of papers. Thus, the unsteady aerodynamic characteristics of a cascade of vibrating plates were calculated in [1] by the method of integral equations, while the same method was used in [2, 3] to calculate the sound fields that are excited when sound waves Coming from outside or vorticity inhomogeneities of the oncoming flow act on the cascade. The problem of a two-dimensional cascade of vibrating plates in a supersonic flow was solved in [4, 5]. In [4] the solution was constructed on the basis of the well-known solution of the problem of vibrations of a single plate, while in [5] a variant of the method of integral equations was used which differed slightly from the usual formulation of this method [1–3]. The approach proposed in [5] is used below to calculate the unsteady flow past a two-dimensional cascade of plates in the case when vorticity inhomogeneities of a supersonic oncoming flow act on it. Equations are obtained for the strength of the unsteady pressure jumps arising in such a flow and the vortex wakes shed from the trailing edges of the plates. Examples of the calculations illustrating the accuracy of the method and its possibilities are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp, 152–160, May–June, 1986.     

Intense evaporation of a gas from a two-dimensional periodic surface

Evaporation (or condensation) of a gas is said to be intense when the normal component of the velocity of the gas in the Knudsen layer has a value of the order of the thermal velocity of a molecule, c_T=(2kT/m)^1/2. In this case the distribution function of the molecules with respect to their velocities in the Knudsen layer differs from the equilibrium (Maxwellian) value by its own magnitude. As a result of this, over the thickness of the Knudsen layer the macroparameters also vary by their own magnitudes. So in order to obtain the correct boundary conditions for the Euler gas dynamic equations, it is necessary to solve the nonlinear Boltzmann equation in the Knudsen layer. The problem of obtaining such boundary conditions for the case of a plane surface was considered in [1–11]. In the present study this problem is solved for a two-dimensional periodic surface in the case when the dimensions of the inhomogeneities are of the order of the mean free path of the molecules and the inhomogeneities have a rectangular shape. The flow in the Knudsen layer becomes two-dimensional, and this leads to a considerable complication of the solution of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 132–139, March–April, 1985.In conclusion the author would like to express his gratitude to V. A. Zharov for his valuable advice, and also V. S. Galkin, M. N. Kogan, and N. K. Makashev for discussion of the results obtained.     

Distortion of the shock front in a shock tube with a divergent conical transition section

The profile of the leading shock front in a gas has been experimentally investigated in shock tubes of variable cross section. It is shown that the presence of a conical transition section between the high-pressure and low-pressure chambers leads to the retention of inhomogeneities on the surface of the wave front (slopes, twists, and bends) over a length of 20–30 diameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 141–147, July–August, 1991.     

Ion-acoustic turbulence in a collisionless shock wave

The structure of a collisionless shock wave at the front of which ion-acoustic turbulence is excited is investigated. On the basis of the theory of anomalous resistance, equations are obtained for the oscillational spectrum and the particle distribution function in the plasma which, when known, make it possible to determine the magnetic field profile, density, and other macroscopic characteristics of the shock wave. The possibility of comparing theoretical predictions with experimental results from light scattering at the shock front is discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 38–43, May–June, 1974.The author thanks R. Z. Sagdeev and D. D. Ryutov for discussions of the work.     

Some features of flexural-gravity wave propagation in the presence of a crack in sheet ice

The effect of a crack in an ice sheet on the propagation of surface flexural-gravity waves in a basin of constant depth is analyzed. The ice sheet is simulated by two floating semi-infinite fragments of a thin elastic isotropic plate. As the boundary-contact conditions on the line of contact between the parts of the plate the conditions of continuity of displacements for arbitrary slopes simulating one ice-floe overlying on another and free-edge conditions (crack) are considered. The dependence of the amplitude characteristics of the perturbations on the thickness of the ice, its degree of compression, the incident wave frequency, the depth of the basin, and the form of the boundary-contact conditions is investigated. Problems of wave diffraction on inhomogeneities of an elastic plate were solved in [1, 2], and on a crack in the ice sheet in [3, 4].Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 144–150, March–April, 1996.     

Model of a fracture as an emitter of elastic vibrations

During the past two decades a new method has begun to be intensively developed for the investigation of fracture processes which is based on recording the mechanical vibrations generated by the defects of a medium [1]. The new method's problems include: extraction of a useful signal from the extraneous noises, identification of the type of defect, determination of its characteristic dimensions, and an estimate of the danger of the situation which has developed. The solution of the problems indicated has great meaning in such practical applications as nondestructive quality control and the engineering diagnostics of materials and manufactured goods. Therefore, the investigation of the spectrum of the signals produced by the formation of macroscopic fractures, such as the terminal and, consequently, most dangerous phase of fracture, is of great interest. The kinematical characteristics of a fracture as an emitter of elastic vibrations are formulated in this paper. The spatial and time spectra of the dynamical motions caused by the appearance of a growing fracture in a thin plate are discussed. Relationships are derived between the spectral characteristics of propagating disturbances and the parameters of the fracture.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 160–166, March–April, 1976.The author thanks L. I. Slepyan for valuable discussion and attention to this research.     

Flow of a viscous heat-conducting gas and binary mixtures in a sink

The class of exact solutions of the one-dimensional Navier-Stokes equations corresponding to gas flows from a spherical source or sink has been investigated analytically and numerically on a number of occasions (see, for example, [1, 2]). Here, the solution for a sink is considered in the presence of heat transfer from the ambient medium. Apart from seeking the solution itself, the object of the investigation was to establish the conditions of transi tion from viscous to inviscid flow in the sink as the Reynolds number tends to infinity. As shown in [3], for zero heat flux at an infinitely remote point there is no such transition for flow in a sink. The sink flow characteristics of a binary gas mixture are investigated in detail. In the transonic flow region an asymptotic solution is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 56–62, January–February, 1989.     

Instability of a compound liquid jet

In the linear Rayleigh theory [1] the degree of stability of a jet is determined by the viscosity and inertia characteristics of the fluids and the interphase surface tension. The stability of a jet in an infinite medium increases with increase in the viscosity of both the jet and the medium [2, 3]. The presence of two interfaces is responsible for various features of the development of instability in a liquid layer on the surface of a cylinder, and in particular a layer on the inner surface of a cylinder is more unstable than one on the outer surface [4]. In [5, 6] the breakup of a hollow jet in an external medium was investigated. In this paper we examine, in the linear approximation, the stability of a compound jet of nonmiscible liquids with respect to small axisynmetric perturbations of the interfaces. The instability characteristics are given for jets with inviscid and very viscous outer shells. The conditions governing the suppression of rapidly growing instabilities of the inner part (core) of the jet by a viscous shell are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–8, July–August, 1985.     

Transmission of waves in a liquid through absorbing layers and subsequent interaction of the waves with an obstacle

The propagation of waves in porous media is investigated both experimentally [1, 2] and by numerical simulation [3–5]. The influence of the relaxation properties of porous media on the propagation of waves has been investigated theoretically and compared with experiments [3, 4]. The interaction of a wave in air that passes through a layer of porous medium before interacting with an obstacle has been investigated with allowance for the relaxation properties [5]. In the present paper, in which the relaxation properties are also taken into account, a similar investigation is made into the interaction with an obstacle of a wave in a liquid that passes through a layer of a porous medium before encountering the obstacle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–53, March–April, 1983.     

Large-scale turbulence in a thin layer of nonisothermal rotating fluid

The dynamics of large-scale nonisothermal turbulence in a thin rotating layer of fluid are investigated. An hierarchical model, obtained by averaging the initial Boussinesq equations with respect to the vertical coordinates and subsequently projecting the two-dimensional equations onto a basis consisting of a system of axisymmetric spiral vortices of progressively decreasing scale, is proposed. It is shown that the presence of horizontal temperature inhomogeneities leads to a considerable increase in the turbulence decay time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 48–55, July–August, 1988.