Comparison of approximate and exact models of leaching in the presence of a horizontal impermeable layer

In [1], the present author investigated an approximate model of two-dimensional flow in the case of leaching of soil in the presence of an impermeable layer when the depression curve is replaced by a fixed horizontal boundary. Later [2] the problem was solved with allowance for and the finding of the depression curve. In the present paper, the flow characteristics in approximate and exact formulations are compared for several variants on the basis of the results of calculations made on the basis of the obtained solutions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 3, pp. 168–173, May–June, 1982.I thank N, S. Kolodei for assistance in the calculations.     

Longitudinal-transverse interaction in a three-dimensional boundary layer

Three-dimensional flow is considered for an incompressible fluid in a boundary layer developing along a curved solid surface during interaction between it and a small uneven area (projection or depression) on the surface. It is shown that an important part in the formation of the flow round the uneven area may be played by the drop in the pressure across the boundary layer. Conditions are formulated under which this effect, which is connected with the action of centrifugal forces, is realized. On the assumption that the longitudinal dimension of the uneven area is of the order of Re^–3/14, its width of the order of O(Re^–3/7), and its height O(Re^–4/7), where Re is the Reynolds number, asymptotic equations are derived which describe the motion of the fluid in the neighborhood of the uneven area.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–50, May–June, 1987.     

Use of a three-parameter family of locally similar velocity profiles in the calculation of turbulent separation regions in a compressible gas

A method is proposed for calculating two-dimensional leading turbulent separation regions based on the use of integral relations of boundary layer theory and integral characteristics of a three-parameter family of locally similar velocity profiles. The method makes it possible to calculate the characteristics of a turbulent boundary layer, including friction and heat transfer, without separation of discontinuities and special regions and to do this in both attached and separated flow regions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza, No. 3, pp. 24–33, May–June, 1982.I thank V. N. Shmanenkov for interest in the work and L. V. Gogish for reading and discussing the draft.     

Strong evaporation of a filler from a porous body with a plane surface

The problem of strong evaporation of matter filling periodic rectangular semi-infinite channels in a porous two-dimensional body is solved by a method of direct statistical modeling. The depths of the channels, the outer surface elements of the body, and the distance from the outer to the evaporation surface are assumed equal in order of magnitude to the mean free path of the molecules. Boundary conditions are obtained for the gas dynamics equations in Euler form, making it possible to describe adequately the flow outside the Knudsen layer. The flow structure in this last is investigated as a function of the determining parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 130–134, March–April, 1986.In conclusion I express my gratitude to V. S. Galkin and N. K. Makashev for their discussion of the results obtained.     

Asymptotic behavior of the neutral curves of the linear stability problem for a laminar boundary layer

Asymptotic flow schemes corresponding to two branches of the solution for the neutral stability curve of a laminar boundary layer in an incompressible fluid are constructed. Two-term asymptotic solutions are obtained in the limit when the Reynolds number tends to infinity. The linear formulation of the problem is used and the flow is assumed to be two dimensional.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 39–46, September–October, 1981.I should like to thank O. V. Denisenko for making the numerical calculations.     

Ground water regime in an irrigated soil layer with lower lying strongly permeable pressure level

A solution is found to the problem of planar pressureless steady filtration from a system of equidistance channels of the same thickness through a soil layer to a lower lying pressure level in the case of uniform infiltration (evaporation) to the free surface. The unique solvability of the system of equations for the two unknown transformation parameters is established. The filtration flow rate from a channel is investigated analytically as a function of the infiltration intensity and the magnitude of the backwater.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 168–174, March–April, 1979.I thank N. S. Kolodei for assistance in the calculations and the simulation.     

Stability of the boundary layer of a non-Newtonian liquid obeying a power-type rheological law

The stability of the stationary (steady-state) laminar boundary layer of a non-Newtonian liquid obeying a power-type rheological law at a semiinfinite plate situated in a longitudinal flow is analyzed. An approximate formula is derived for estimating the minimum Reynolds number at which the flow loses stability with respect to slight two-dimensional perturbations. Calculations of the point of stability loss for aqueous solutions of carboxyl methyl cellulose are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 121–124, March–April, 1971.     

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.     

Interaction of continuous-spectrum waves with each other and with discrete-spectrum waves

The nonlinear problem of the evolution of an initial perturbation in Couette flow is solved in the quadratic approximation and it is shown that the energy of the initial perturbation is transmitted to the main flow so that its profile is somewhat modified. The evolution of the initial perturbation in a fluid with a very simple model flow profile which, in addition to continuous-spectrum waves, also admits the existence of a single neutral mode of the discrete spectrum is then investigated. It is shown that as a result of the linear resonant interaction of the discrete-spectrum and continuous-spectrum waves disturbances that grow linearly with time may be formed. A flow that does not contain exponentially growing modes will be unstable with respect to certain initial disturbances; this instability is called algebraic [6, 7]. A physical interpretation of this effect is given. From this interpretation it is clear that algebraic instability is possible in a fluid with flow profiles of a more general type, in which there are neutral or weakly damped discrete-spectrum modes having a critical layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 116–123, July–August, 1989.The author is grateful to G. I. Barenblatt, S. Ya. Gertsenshtein, M. A. Mironov, S. A. Rybak, O. S. Ryzhov, and E. D. Terent'ev for their interest and useful comments.     

Effect of an impermeable inclusion in the underlying highly permeable pressurized horizon on the conditions of ground water in an irrigated layer of soil

The problem of plane, nonpressurized, steady-state filtration through a layer of soil into an underlying pressurized horizon, which contains an impermeable section at the top, with uniform infiltration on the free surface is solved in a hydro-dynamic formation. A constructive solution of the problem is given with the help of the method of P. Ya. Polubarinova-Kochina; representations are obtained for the characteristic dimensions of the flow scheme and the depression. The case of limiting flow — no head in the bottom, highly permeable layer — studied in [1] is noted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–5, May–June, 1986.The author thanks V. N. Emikh for useful remarks and discussions.     

Thermocapillary convection mechanism due to the absorption of spatially periodic laser radiation

This paper deals with the problem of the occurrence of regular convection in a fluid layer with a single free surface following the absorption of a light wave with an intensity distribution spatially periodic in the plane of the layer due to the temperature dependence of the surface tension. The velocity and temperature profiles in the medium are determined. It is shown that, other things being equal, the response of the system to the light wave is greatest when the period of the interference intensity pattern is of the order of twice the thickness of the layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti 1 Gaza, No. 5, pp. 47–50, September–October, 1985.The authors wish to thank N. T. Pashchenko, N. V. Tabiryan, and Yu. S. Chilingaryan for valuable discussions.     

Asymptotic representation of the solution in the hodograph plane in transonic flow problems around profiles

The flow around a slender profile by an ideal gas flow at a constant, almost sonic, velocity at infinity is considered. The behavior of the perturbed stream in the domain upstream of the compression shocks sufficiently remote from the streamlined body is studied. The question is investigated of what conditions the solution in the hodograph plane satisfies when it corresponds to a flow without singularities on the limit characteristic in the physical flow plane. It is known that cases are possible when a regular solution in the hodograph plane loses its regularity property upon being mapped into the physical plane [1]. A regular flow on the limit characteristic can be continued analytically downstream into the supersonic domain between the limit characteristic and the shock. The requirement of analyticity of the streamlined profile is essential for realizability of the flow under consideration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 84–88, January–February, 1976.In conclusion, the author is grateful to O. S. Ryzhov for discussing the research.     

Flow around a sphere by a two-phase supersonic jet

Results are presented of a calculation of the flow around a sphere of a two-phase supersonic jet, discharging into a vacuum. Calculations were performed by the determination method with use of a difference grid constructed on the basis of characteristic ratios [1], The parameters of the unperturbed jet were determined with the two-velocity and two-temperature model of mutually penetrating flows of continuous media (gas and particles) [2, 3] by the network method [4]. In calculating the flow around the sphere, as in [5–7], it was assumed that the particles do not affect the gas flow in the shock layer. An analysis of the effect of particles on gasdynamic parameters in a shock layer was performed in [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 171–176, November–December, 1978.The authors are grateful to A. N. Nikulin for providing the program for calculation of flow about a blunt body by a uniform supersonic flow.     

Instability of combined convective flow in a vertical layer

In the present paper, a study is made of the stability of plane-parallel flow induced by a transverse temperature difference between the boundaries of a layer and a longitudinal pressure gradient. This problem was solved earlier by the author [3] in a purely hydrodynamic formulation without allowance for thermal factors; the results then obtained correspond to the limiting case of small Prandtl numbers. In the paper, a numerical solution to the problem with the complete formulation is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1982.I thank G. Z. Gershuni for supervising the work, and also M. A. Gol'dshtik and V. N. Shtern for a helpful discussion.     

Computation of the two-dimensional viscous incompressible fluid flow with separation at the nlet edge around a cascade

A complex flow consisting of an outer inviscid stream, a dead-water separation domain, and a boundary layer, which interact strongly, is formed in viscous fluid flows with separation at the streamlined profile with high Re numbers. Different jet and vortex models of separation flow are known for an inviscid fluid; numerical, asymptotic, and integral methods [1–3] are used for a viscous fluid. The plane, stationary, turbulent flow through a turbine cascade by a constant-density fluid without and with separation from the inlet edge of the profile and subsequent attachment of the stream to the profile (a short, slender separation domain) is considered in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 34–44, May–June, 1978.     

Influence of acoustics and the flow regime in the boundary layer on nozzle walls on the mixing layer of an immersed jet

Experimental determinations were made of the width of the mixing layer and the level of turbulent pulsations in the initial section of a subsonic circular immersed jet for different parameters of the boundary layer on the nozzle walls and in the presence of acoustic excitation. It was established that the rate of expansion of the turbulent mixing layer depends on the flow regime in the boundary layer. For laminar initial boundary layer, external acoustic excitation can lead to a decrease in the expansion velocity of the mixing layer and of the intensity of the velocity pulsations on the jet axis within the initial section. If the frequency and amplitude of acoustic excitation at which a decrease in the rate of expansion of the mixing layer and of the pulsation intensity was observed remained unchanged, the influence of the acoustics disappeared when the boundary layer became turbulent. The acoustic vibrations influenced the subsonic jets by generating vortex perturbations when they interact with the edge of the nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 36–42, November–December, 1982.We are grateful to K. I. Artamonov, now deceased, for support and discussing the results, and O. I. Navoznov and S. F. Agafonov for help in organizing and performing the experiments.     

Dispersed phase motion in laminar boundary layer flow over a wedge

The motion of a dispersed phase in the laminar boundary layer on a wedge is considered with allowance for the effect of not only the Stokes force, which coincides in direction with the flow velocity, but also the transverse force (Saffman force) resulting from the transverse nonuniforrnity of the flow over the individual particle [1–3].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 34–42, November–December, 1993.In conclusion, the authors wishes to thank S. V. Manuilovich for assisting with the numerical calculations.     

Wave flow of a liquid film in a horizontal separator

The calculation of the motion of separated moisture in a linear horizontal separator is made on the basis of the analysis of the development of the waves in a flow of a thin layer of liquid along a vertical surface without allowance for the transverse flow of mass [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–176, March–April, 1985.     

An approximate method of determining the vorticity in the separation region as the viscosity tends to zero

In accordance with the Prandtl—Batchelor theorem, the vorticity in a separation region is constant in a laminar flow with vanishingly small viscosity. Batchelor proposed that the vorticity should be determined by matching the inviscid flow and the boundary layer at the edge of the separation region. An approximate method is constructed and, under a number of simplifying assumptions, used to consider a flow with a separation region in a rectangular trough.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 10–15, January–February, 1982.I thank N. A. Slezkin and the participants of his seminar for several discussions of the work and helpful comments.     

Hypersonic viscous flow around extended bodies

The characteristic feature of flow around an extended body is the interaction of the thickened boundary layer with the external nonviscous flow. This phenomenon becomes more significant at low Reynolds numbers and high Mach numbers. Theoretical investigation of this interaction is difficult because of the presence of shock waves, which are characteristic of hypersonic velocities; the position and curvature of these shock waves depend on the state of the boundary layer developing in conditions of pronounced vorticity of the external flow. With increasing rarefaction of the flow, the problem begins to take on an elliptic character, and this necessitates the use of methods of investigation of more general form than the classical boundary-layer theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 164–166, March–April, 1976.The authors thank V. G. Farafonov and V. N. Arkhipov for guidance and assistance in the work.