Nonstationary waves in the continuously stratified flow of a fluid of finite depth

A theoretical investigation is made of the development of linear two-dimensional waves in a continuously stratified flow of an ideal incompressible fluid. The waves are generated by pressures that are independent of time and that are applied at time t=0 to a bounded region on the free surface of an initially undisturbed flow. The stationary internal waves generated by such a disturbance have been investigated in [1–3]. The nonstationary waves in a continuously stratified fluid that are generated by initial disturbances or periodic surface pressures applied to the entire free surface have been studied in [4–7] in the absence of a slow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 87–93, November–December, 1976.     

Influence of surface tension on damping of the oscillations of a viscous incompressible fluid in a cylindrical channel

A numerical calculation is made of small oscillations of a viscous incompressible fluid that fills half of a horizontal cylindrical channel. The calculation is made with and without allowance for surface tension. The results of the calculation show that allowance for surface tension increases the damping of the oscillations. The general properties of problems of the normal oscillations of a heavy and capillary viscous incompressible fluid were studied in [1–3], in which the possibility of applying the Bubnov-Galerkin method to these problems was pointed out. A method for calculating the oscillations of a viscous incompressible fluid that partly fills an arbitrary vessel at large Reynolds numbers was developed in [3–5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–132, May–June, 1980.     

Stable equilibrium of the surface of a capillary liquid in contact with the edge of a solid

The equilibrium conditions which must be satisfied at the free surface of a capillary liquid and at the line of its contact with the smooth surface of a solid are well known [1]. These conditions are equivalent to the condition of steady-state conditions for the potential energy [2, 3], and the question of the stability of the equilibrium states reduces to a study of the sign of its second variation [2–4]. The case is discussed below where the surface of the solid has a break at the line of contact with the free surface. Stable equilibrium states are identified with the points of a local minimum of the potential energy. The necessary and sufficient conditions for a minimum are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–6, January–February, 1974.The authors thank A. D. Myshkis for his evaluation of the results obtained.     

Flow past a plate under the free surface of a weightless liquid

A study is made of the nonlinear problem of the flow without separation of a perfect weightless liquid past a plate near the free surface. This problem was first posed by Gurevich [1]. At present, there are only a general solution to the problem [2–4] and some numerical calculations [5], which have been made under definite restrictions and are inadequate for detailed information about the interaction between the free surface and the plate. In the present paper, a complete investigation of the problem is given. Convenient computational formulas are obtained together with asymptotic expansions of them, and detailed calculations are made for all depths of the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 158–162, January–February, 1980.     

Flow and heat transfer of a viscous fluid when there is a phase transition

A study is made of the problem of the flow and heat transfer of a fluid formed by the phase transition (melting or sublimation) when the end of a rod touches a heated surface. Problems of this kind arise, in particular, when a heated surface is cooled by means of the heats of the phase transitions of materials with an energy content. A solution is obtained to a simplified system of heat and mass transfer equations obtained by estimating the order of magnitude of the various terms in the Navier-Stokes equations in a manner similar to that in [1–3]. The parameters that govern the process are identified, and an approximate analytic solution is found for the quasi-stationary case. The analytic solution is compared with a numerical solution obtained iteratively.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–131, May–June, 1931.     

Surface waves and stability of free surface of a magnetizable liquid

Linear theory of surface waves in a magnetizable liquid is examined. A stability criterion for a plane-free surface of a magnetizable liquid is studied for an arbitrary magnetization law.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 35–40, July–August, 1974.     

Investigation of the azimuthal instability of the surface of a liquid phase in a melting channel

The instability of the molten metal layer on the walls of a melting channel is considered. A dispersion relation for small azimuthal perturbations of the free surface of the melt is obtained and investigated numerically. It is shown that the onset of azimuthal, monotonically increasing deformations of the surface is possible. The characteristics and conditions of onset of the deformations are determined.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 21–27, July–August, 1996.     

Slow rotation of a sphere in a confined volume of a dilute gas

The axially symmetric motion of a gas in a volume confined between an external immobile surface of rotation and a coaxial surface of a rotating sphere is considered. A solution is obtained by the moment method based on the Boltzmann equation with a collision integral of Maxwellian molecules. The gas-velocity distribution and an expression for the friction torque exerted on the sphere are obtained for arbitrary Knudsen numbers and for an arbitrary shape of the outer surface. The proportionality of the gas slip velocity over the surface of the sphere to the friction strain is shown. The friction torque is investigated for specific shapes of the outer surface. The motion of a gas filling the space between concentric spheres, each of which rotates about an arbitrary axis, is treated. In the limiting case of small Knudsen numbers the expressions obtained are compared with the corresponding results for a continuous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–124, July–August, 1978.The authors are grateful to the participants of the seminars guided by G. I. Petrov and A. M. Golovnyi for discussions concerning this work.     

Optimization of Dynamic Plastic Deformation of Plates with a Complex Contour

A method for studying dynamic deformation of ideal rigid–plastic plates with a complex contour on a viscoelastic foundation is proposed. The method allows one to optimize the process of pulsed forming. The optimization parameters are the amplitude of the pulsed load, viscoelastic damping coefficients of the foundation, the surface density of the plate material, and the shape and supporting conditions of the edges. Numerical examples of simply– and doubly–connected plates are given. It is shown that different combinations of the control parameters of the process can ensure the same final shape of the plate formed.     

Equations and forms of motion of a jet flowing onto a liquid

A nonlinear theory is constructed for a thin jet of nonviscous, incompressible, weightless fluid flowing from a nozzle onto the surface of an immobile heavy liquid. The theory is asymptotically (over jet thickness) more accurate than that presented in [1]. Forms of the flow are studied as functions of nozzle, jet, and heavy liquid parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 20–28, November–December, 1976.     

Boundary conditions on a rigid surface in a two-phase flow

A study is made of the boundary conditions on a rigid surface in a two-component disperse flow. Appropriate boundary conditions are obtained for the kinetic equation and macroscopic equations of a pseudogas of solid particles proposed in [1–3]. The reasons for the occurrence of bubbles in two-phase systems are discussed. On the basis of the similitude parameters of the kinetic equation of the pseudogas, disperse systems are classified generally on the basis of the concentration of solid particles and their diameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 46–51, May–June, 1980.I thank V. P. Myasnikov for suggesting the problem and for a helpful discussion.     

Stability of flow of a viscous liquid down an inclined plane

Using the Navier-Stokes equation the stability of a layer of viscous liquid flowing down a solid surface under gravity is studied in the linear formulation. The effect of surface tension and the inclination of the solid surface on the limits of stability are examined also. Curves are calculated for the neutral stability with respect to two types of perturbations — surface waves and shear waves.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskol Fiziki, No. 2, pp. 172–176, March–April, 1975.     

Calculation of the stability characteristics of a boundary layer with blowing in the presence of a negative pressure gradient

A study is made of the viscous and inviscid stability of self-similar Falkner-Skan flow on a permeable surface in a wide range of blowing intensities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 60–64, March–April, 1984.     

Action of an explosive plastic wave on a plate

The action of a transient loading on an infinitely elastic plate, freely covering the surface of an ideal compressible liquid, was discussed in [1–3]. A review of work on the dynamics of a plate under the action of a transient loading is given in [4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 131–136, July–August, 1976.     

Propagation of a turbulent jet impinging on a plane surface in an external stream

The results of an investigation of the three-dimensional vortex zone which forms near a plane surface when a turbulent jet impinges on it in an external stream are presented. Problems of this kind occur, for example, in a study of the effects of the entry of exhaust gases into the air intakes of engines when aircraft with thrust reversers turned on fly through an airport and when vertical-take-off-and-landing aircraft move near the earth [1–3]. The structure of the vortex zone and the temperature distribution in it are established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 56–62, September–October, 1978.In conclusion, the author thanks A. N. Sekundov and S. Yu. Krasheninnikov for attention to the work and a discussion of its results.     

Cylindrical equilibrium surfaces of a capillary liquid and their stability

We consider the plane problem of the equilibrium of a capillary surface. We study the stability of a two-dimensional surface with respect to plane and spatial disturbances. We give data which can be used for deciding the question of the stability of any symmetric equilibrium surface in a field of gravitational forces and in conditions of weightlessness. We solve the problems of the stability of a liquid in a rectangular and a sectorial channel and also the problem of the separation of a plane drop from a horizontal wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 57–68, January–February, 1976.The authors are grateful to A. D. Myshkis and A. D. Tyuptsov for their evaluation and their useful comments.     

Dynamics of a diverging liquid meniscus in a capillary,taking into account the specific properties of thin films

The theory of the diverging meniscus of a Newtonian liquid for capillary flow conditions at low meniscus velocities, in which the thermodynamic and Theological features of thin wetting films appear, is set forth. Two cases are considered: thermodynamically stable wetting film with high viscosity in the boundary layer on a completely wetted solid surface and a thermodynamically unstable film on a conditionally wetted solid surface exhibiting a liquid slip effect.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 72–82, May–June, 1976.The author wishes to express his appreciation to A. G. Grivtsov and V. S. Yushchenko for valuable assistance in the computer calculations.     

Propagation of two-dimensional plastic waves in a thick plate

A study is made of the propagation and interaction of two-dimensional waves of high amplitude in a thick plate. A monotonically decreasing pressure is applied to the surface of the plate. Deformations are assumed to be large; the problem is formulated and solved in Lagrangian variables. An approximate method for constructing the fronts of the shock waves is proposed. The pressure and particle velocity at an arbitrary point and at an arbitrary instant of time are determined by the method of characteristics. A numerical example is given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 100–106, January–Febraury, 1971.     

Supersonic condensation of a monatomic gas

The problem of steady supersonic condensation of a monatomic gas on a plane evaporating surface is solved in the Knudsen layer by the direct statistical modeling method. The domain of existence of the solution of the problem is determined. The results of calculating the structure of the Knudsen layer near the surface are presented. A topological picture of the solutions of the strong evaporation and subsonic and supersonic strong condensation problems is given as a function of the Mach number, determined from the normal velocity component, and the other governing parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 171–175, May–June, 1990.     

Laminar boundary layer on a partly moving surface in the presence of blowing or suction

Planar and axisymmetric flows of a multicomponent compressible gas in a laminar boundary layer with nonzero tangential component of the velocity on a permeable surface are considered. The asymptotic solutions of the boundary-layer equations obtained earlier [1–4] for large values of the blowing and suction parameters are generalized to the case when the velocity vector of the blown or extracted gas makes an acute angle with the surface of the body, this angle depending on the longitudinal coordinate. The region of applicability of the asymptotic formulas is estimated on the basis of the results of numerical solution of the boundary-layer equations. The results are given of some calculations of the boundary layer on a partly moving surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 28–36, September–October, 1979.We thank G. A. Tirskii and G. G. Chernyi for a helpful discussion of the results.