Effect of continuous variation of the density of a liquid on the waves generated by moving surface pressures

This study investigates the plane linear problem of steady-state internal waves in an ideal incompressible liquid with nonuniform density. The waves are generated by surface pressures applied in a bounded region which moves at constant velocity. It is assumed that the density in the unperturbed state varies continuously with depth, remaining constant in the upper and lower layers and varying according to an exponential law in the middle layer. The problem may be regarded, in particular, as a hydrodynamic model for the study of internal waves produced by a cyclone moving over the surface of the ocean. Analogous investigations for a homogeneous liquid were carried out in [1–3]; internal waves for a liquid with the above-mentioned law of density variation but with stationary pressure changes which are periodic with respect to time were studied in [4]. Problems analogous to the one considered here, both for exponential variation of density in the entire layer and for the case of a nonuniform layer near the surface, were investigated in [5, 6]. An analysis of non-linear waves of the steady-state type with arbitrary distribution of vorticity and density with respect to depth was carried out in [7, 8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 55–62, November–December, 1973.     

Cathode electric-field-intensity-distribution function

The behavior of the distribution function for the electric field intensity at the cathode is considered including only nearest-neighbor effects and is compared with the behavior of the distribution function obtained when including the effects of many ions. Motion of ions in the near-cathode region and their nonuniform density there are taken into account in the calculations of the distribution function. It is shown that for a broad range of parameters the resultant distribution function differs little from the distribution function found when constant density is assumed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 29–34, May–June, 1973.     

Theory of vortical helical ideal gas flows in laval nozzles

An asymptotic solution is found for the direct problem of the motion of an arbitrarily vortical helical ideal gas flow in a nozzle. The solution is constructed in the form of double series in powers of parameters characterizing the curvature of the nozzle wall at the critical section and the intensity of stream vorticity. The solution obtained is compared with available theoretical results of other authors. In particular, it is shown that it permits extension of the known Hall result for the untwisted flow in the transonic domain [1]. The behavior of the sonic line as a function of the vorticity distribution and the radius of curvature of the nozzle wall is analyzed. Spiral flows in nozzles have been investigated by analytic methods in [2–5] in a one-dimensional formulation and under the assumption of weak vorticity. Such flows have been studied by numerical methods in a quasi-one-dimensional approximation in [6, 7]. An analogous problem has recently been solved in an exact formulation by the relaxation method [8, 9]. A number of important nonuniform effects for practice have consequently been clarified and the boundedness of the analytical approach used in [2–7] is shown.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–137, March–April, 1978.The authors are grateful to A. N. Kraiko for discussing the research and for valuable remarks.     

Hydrodynamic features of the exploitation of highly nonuniform source-type oil formations

The flow of a weakly compressible fluid in a highly nonuniform formation with block structure, classified as source-type, is considered. An analytic solution of the problem of fluid flow into a well in a bounded circular reservoir is obtained. On the basis of this solution the effect of the fluid offtake rate on the depletion of the reservoir is investigated. It is shown that in highly nonuniform media a number of unsteady effects, which cannot be described by the classical model with steady mass transfer, occur.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 113–120, September–October, 1993.     

Asymptotic solution of the euler equations in the shock layer on a blunt body in nonuniform flow with gas injection from the body surface

Supersonic nonuniform gas flow over blunt bodies without surface injection has previously been investigated by both numerical [1–3] and experimental [3] methods. The processes of surface vaporization under the influence of an intense heat flux, artificial gas injection and surface combustion [4] are all worthy of study. The problem of the interaction between a nonuniform supersonic flow and a body in the presence of intense gas injection from the surface is examined and an analytical solution is constructed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 126–134, November–December, 1989.     

Unsteady three-dimensional viscous shock layer in nonuniform gas flow in the neighborhood of a stagnation point

The combined influence of unsteady effects and free-stream nonuniformity on the variation of the flow structure near the stagnation line and the mechanical and thermal surface loads is investigated within the framework of the thin viscous shock layer model with reference to the example of the motion of blunt bodies at constant velocity through a plane temperature inhomogeneity. The dependence of the friction and heat transfer coefficients on the Reynolds number, the shape of the body and the parameters of the temperature inhomogeneity is analyzed. A number of properties of the flow are established on the basis of numerical solutions obtained over a broad range of variation of the governing parameters. By comparing the solutions obtained in the exact formulation with the calculations made in the quasisteady approximation the region of applicability of the latter is determined. In a number of cases of the motion of a body at supersonic speed in nonuniform media it is necessary to take into account the effect of the nonstationarity of the problem on the flow parameters. In particular, as the results of experiments [1] show, at Strouhal numbers of the order of unity the unsteady effects are important in the problem of the motion of a body through a temperature inhomogeneity. In a number of studies the nonstationary effect associated with supersonic motion in nonuniform media has already been investigated theoretically. In [2] the Euler equations were used, while in [3–5] the equations of a viscous shock layer were used; moreover, whereas in [3–4] the solution was limited to the neighborhood of the stagnation line, in [5] it was obtained for the entire forward surface of a sphere. The effect of free-stream nonuniformity on the structure of the viscous shock layer in steady flow past axisymmetric bodies was studied in [6, 7] and for certain particular cases of three-dimensional flow in [8–11].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 175–180, May–June, 1990.     

Drift of a reacting droplet due to the chemoconcentration capillary effect

The motion of a droplet with a first-order chemical reaction taking place at its surface with the participation of a surfactant dissolved in the external medium is considered. Approximate expressions are obtained for the velocity and other characteristics of the autonomous motion of the droplet caused by the surface capillary forces due to the nonuniform distribution of the surfactant over the surface of the moving droplet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 51–61, May–June, 1990.     

Two-phase displacement of compressible fluids from stratified reservoirs

Mutual displacement equations are derived within the framework of the modified phase permeability model, taking the compressibility of one of the phases into account. A self-similar solution of one-dimensional displacement problems is obtained. The role of compressibility in displacement from nonuniform stratified reservoirs is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 74–83, March–April, 1993.     

Flow processes with change of regime in fractured reservoirs

Experimental and industrial observations indicate a strong nonlinear dependence of the parameters of the flow processes in a fractured reservoir on its state of stress. Two problems with change of boundary condition at the well — pressure recovery and transition from constant flow to fixed bottom pressure — are analyzed for such a reservoir. The latter problem may be formulated, for example, so as not to permit closure of the fractures in the bottom zone. For comparison, the cases of linear [1] and nonlinear [2] fractured porous media and a fractured medium [3] are considered, and solutions are obtained in a unified manner using the integral method described in [1]. Nonlinear elastic flow regimes were previously considered in [3–6], where the pressure recovery process was investigated in the linearized formulation. Problems involving a change of well operating regime were examined for a porous reservoir in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 67–73, May–June, 1991.     

Laminar boundary layer stability and delayed transition on a nonisothermal surface

The effect of a nonuniform surface temperature distribution on the boundary layer stability characteristics is further investigated. It is shown that the presence of fairly extensive areas of the surface within which the temperature of the body exceeds the free-stream temperature leads to the destabilization of the flow and the appearance of a local closed region of laminar flow instability.Paper presented at the Sixth All-Union Conference on Theoretical and Applied Mechanics (Tashkent, 1986). The results of references [8, 9], published after the conference, have been taken into account.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 52–57, March–April, 1989.     

Plane viscoplastic flow in narrow channels with deformable walls

The equations of motion of a continuum in a thin layer are derived for a given functional dependence of the stress tensor on the strain rate tensor. The general problem of viscoplastic flow is considered in the thin-layer approximation for boundary surface material points travelling in the lateral direction in a predetermined fashion.The projections of the continuum point velocity, pressure, flow rate through a cross-section of the channel, and the power of external forces are expressed as functions of the boundary deformation law. The problem of determining the channel boundary deformation law is formulated for a given boundary pressure distribution. The expressions for the continuum flow rate and pressure and the power of external forces written as functionals of the channel width allow formulation of the problems of controlling viscoplastic flows in thin layers and optimizing the processes.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 23–31, March–April, 1996.     

Solution of problems of unsteady flow through porous media with an extended fracture (barrier)

A method of constructing the potentials describing the elastic regime of flow through porous media is proposed. The flow is induced by the initial conditions in media with an extended fracture-drainage or barrier-curtain used, in particular, for blocking off polluted zones. The fracture and barrier are simulated by infinitely thin strata with permeability which is infinitely large for the fracture and infinitesimal for the barrier. Similar problems for steady processes were considered in [1–3].Chita. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 95–98, November–December, 1995.     

Quasi-one-dimensional approximation in two-dimensional problems of gas dynamics

A useful means of constructing approximate flow models is the hydraulic (for two-dimensional problems quasi-one-dimensional) approach, based on averaging the initial nonuniform flows over some direction or cross section [1]. In this case, at the expense of a rougher model it is possible to reduce the dimensionality of the problem. Here, this approach is extended to unsteady two-dimensional gas-dynamic processes; certain problems (flow around a cone or a blunt body, jet flows) are considered in the framework of the quasi-one-dimensional model obtained, and results are compared with the solutions of the corresponding two-dimensional problems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 136–143, March–April, 1989.     

Some problems in the theory of plane jets of conducting fluid

Using the boundary-layer equations as a basis, the author considers the propagation of plane jets of conducting fluid in a transverse magnetic field (noninductive approximation).The propagation of plane jets of conducting fluid is considered in several studies [1–12]. In the first few studies jet flow in a nonuniform magnetic field is considered; here the field strength distribution along the jet axis was chosen in order to obtain self-similar solutions. The solution to such a problem given a constant conductivity of the medium is given in [1–3] for a free jet and in [4] for a semibounded jet; reference [5] contains a solution to the problem of a free jet allowing for the dependence of conductivity on temperature. References [6–8] attempt an exact solution to the problem of jet propagation in any magnetic field. An approximate solution to problems of this type can be obtained by using the integral method. References [9–10] contain the solution obtained by this method for a free jet propagating in a uniform magnetic field.The last study [10] also gives a comparison of the exact solution obtained in [3] with the solution obtained by the integral method using as an example the propagation of a jet in a nonuniform magnetic field. It is shown that for scale values of the jet velocity and thickness the integral method yields almost-exact values. In this study [10], the propagation of a free jet is considered allowing for conduction anisotropy. The solution to the problem of a free jet within the asymptotic boundary layer is obtained in [1] by applying the expansion method to the small magnetic-interaction parameter. With this method, the problem of a turbulent jet is considered in terms of the Prandtl scheme. The Boussinesq formula for the turbulent-viscosity coefficient is used in [12].This study considers the dynamic and thermal problems involved with a laminar free and semibounded jet within the asymptotic boundary layer, propagating in a magnetic field with any distribution. A system of ordinary differential equations and the integral condition are obtained from the initial partial differential equations. The solution of the derived equations is illustrated by the example of jet propagation in a uniform magnetic field. A similar solution is obtained for a turbulent free jet with the turbulent-exchange coefficient defined by the Prandtl scheme.     

Motion of a drop with allowance for thermocapillary forces

A study is made of the motion of a drop in a viscous medium of nonuniform temperature when the dependence of the surface tension on the temperature at the interface of the two media gives rise to additional tangential stresses leading to thermocapillary convection in fluids. The motions of a spherical drop and a deformed drop (when the surface of the drop is determined in the process of finding the solution) are considered. The shape of the drop surface is calculated for different values of the parameters of the problem. Dependences are obtained for the Reynolds number of the thermocapillary drift of drops in the absence of body forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 80–86, July–August, 1982.     

Two-scale semiempirical theory of turbulent boundary layers and jets

To characterize the turbulence of boundary layers in the energy-bearing interval of wave numbers several turbulence scales are sometimes used (for example, [1, 2]). In particular, the universality of the semiempirical model of turbulence [2] can be extended in this way. A turbulence model with one equation (energy balance of the turbulence) has been constructed and used [3–6] and it has been established that the number of problems that can be solved for a universal choice of the values of the empirical coefficients increases appreciably if not one but two turbulent scales are used. In the present paper, it is shown that the introduction of a second scale makes it possible to take into account the interaction of shear layers in flows with two shear layers (for example, a channel or jet), and also to take into account the influence of turbulence of an external flow on a boundary layer. The interaction of shear layers is taken into account in theories containing a transport equation for the turbulent frictional stress _t (for example, [7]), in which the essence of the interaction reduces to diffusion of _t from layer to layer. In the present paper, a predominant volume interaction effect is assumed. It takes the form of a difference between the interaction of large-scale vortices with a shear deformation motion in flows with one and two shear layers, and also in the presence of turbulence in an external flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 8, pp. 17–25, November–December, 1982.     

Equations for the migration of natural gases in porous media

Equations are given for the equilibrium and nonequilibrium migration of natural gases in variable and invariable porous media. In numerous works [1–4], migration has been considered principally in geological-geochemical terms, the qualitative side of the phenomenon being mainly investigated; its physicomathematical aspects have been inadequately studied [5, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 152–158, September–October, 1971.     

Averaging of stochastic evolution equations of transport in porous media

A study is made of the problem of averaging the simplest one-dimensional evolution equations of stochastic transport in a porous medium. A number of exact functional equations corresponding to distributions of the random parameters of a special form is obtained. In some cases, the functional equations can be localized and reduced to differential equations of fairly high order. The first part of the paper (Secs. 1–6) considers the process of transport of a neutral admixture in porous media. The functional approach and technique for decoupling the correlations explained by Klyatskin [4] is used. The second part of the paper studies the process of transport in porous media of two immiscible incompressible fluids in the framework of the Buckley—Leverett model. A linear equation is obtained for the joint probability density of the solution of the stochastic quasilinear transport equation and its derivative. An infinite chain of equations for the moments of the solution is obtained. A scheme of approximate closure is proposed, and the solution of the approximate equations for the mean concentration is compared with the exactly averaged concentration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 127–136, September–October, 1985.We are grateful to A. I. Shnirel'man for pointing out the possibility of obtaining an averaged equation in the case of a velocity distribution in accordance with a Cauchy law.     

Asymptotic of the electromagnetic field above a layerlike anisotropic medium of high conductivity

The model of an anisotropic, layerlike medium is often employed in problems of electromagnetic probing, and many papers have been written on the propagation of an electromagnetic field in such media. A systematic exposition of such problems was set out by Tikhonov, Sku-garevskaya, and Dmitriev [1–6]. In this paper we shall construct an asymptotic for the electromagnetic field of a point source lying above a layerlike medium of finite anisotropy having a fairly high longitudinal and transverse conductivity, or in which the source lies at a considerable height above the medium. The principles here laid down for the construction of the asymptotic indicate quite clearly under what circumstances the asymptotic is feasible, and if necessary allow the next approximations to be taken into account.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 175–188, March–April, 1966.