Stability of unsteady viscous flows

A study is made of the linear stability of plane-parallel unsteady flows of a viscous incompressible fluid: in the mixing layer of two flows, in a jet with constant flow rate, and near a wall suddenly set in motion [1]. The slow variation of these flows in time compared with the rate of change of the perturbations makes it possible to use the method of two-scale expansions [2]. The stability of nonparallel flows with allowance for their slow variation with respect to the longitudinal coordinate was investigated, for example, in [3–6]. The unsteady flows considered in the present paper have a number of characteristic properties of non-parallel flows [1], but in contrast to them are described by exact solutions of the Navier-Stokes equations. In addition, for unsteady planeparallel flows a criterion of neutral stability can be uniquely established by means of the energy balance equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, 138–142, July–August, 1981.I thank G. I. Petrov for suggesting the problem, and also S. Ya. Gertsenshtein and A. V. Latyshev for assisting in the work.     

On the obtaining of axisymmetric flows from plane-parallel flows

The obtaining of axisymmetric flows of incompressible and compressible fluids from plane-parallel flows by means of integral transformations relating harmonic and p-harmonic functions [1] is considered. A transformation is found that carries plane-parallel flows from elementary singularities into axisymmetric flows. It is shown that this transformation makes it possible to obtain the general form of the solution of axisymmetric problems of flow past bodies from the solution of plane-parallel problems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 113–121, September–October, 1982.     

Effect of friction in a turbulent boundary layer at low degrees of gas saturation

Gas saturation of the turbulent boundary layer on the surface of the entrance section of a channel, through which an incompressible fluid flows, has been investigated.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 150–153, March–April, 1972.     

Stability of two-dimensional curvilinear flows of an ideal barotropic fluid

It was established by Arnol'd [1] that the conservation laws for the energy and vorticity can be used to establish sufficient conditions of stability of two-dimensional curvilinear flows of an ideal incompressible fluid in the exact nonlinear formulation. It is shown below that one can obtain similarly conditions of stability of two-dimensional curvilinear steady flows of an ideal barotropic fluid in the linear approximation. One of the conditions has a significance similar to Rayleigh's criterion and its generalization by Arnol'd [1]; the other is the condition of subsonic flow. In addition, a variational principle is established and an expression found for the second variation of the corresponding functional; these can be used to prove the stability of these flows in the exact nonlinear formulation.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 5, pp. 19–25, September–October, 1981.I am sincerely grateful to V. L. Berdichevskii and A. G. Kulikovskii for constructive advice.     

Quasi-three-dimensional calculation of flow in blade passages of turbines

The flow in turbomachines is currently calculated either on the basis of a single successive solution of an axisymmetric problem (see, for example, [1-A]) and the problem of flow past cascades of blades in a layer of variable thickness [1, 5], or by solution of a quasi-three-dimensional problem [6–8], or on the basis of three-dimensional models of the motion [9–11]. In this paper, we derive equations of a three-dimensional model of the flow of an ideal incompressible fluid for an arbitrary curvilinear system of coordinates based on averaging the equations of motion in the Gromek–Lamb form in the azimuthal direction; the pulsation terms are taken into account in the equations of the quasi-three-dimensional motion. An algorithm for numerical solution of the problem is described. The results of calculations are given and compared with experimental data for flows in the blade passages of an axial pump and a rotating-blade turbine. The obtained results are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 69–76, March–April, 1991.I thank A. I. Kuzin and A. V. Gol'din for supplying the results of the experimental investigations.     

Stationary simple waves in an electrically conducting magnetizable fluid

A study is made of the analog of Prandt1—Meyer flow in an incompressible electrically conducting ideal fluid that is magnetizable in accordance with an arbitrary isotropic law. It is shown that inhomogeneity of the magnetization in a conducting fluid makes possible the existence of stationary simple waves with varying magnetic permeability. For a paramagnetic fluid magnetized to saturation, the equations of these waves are integrated completely in the case of a magnetic field parallel to the velocity. Some regions of such flows of magnetizable fluids are discussed in the present paper for the example of the problem of flow around a perfectly conducting profile.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 136–143, September–October, 1980.I thank I.E. Tarapov for his interest in the work and valuable comments made in a discussion.     

Unsteady flows of an inhomogeneous incompressible viscous fluid

This paper deals with a theoretical analysis of the transfer of reactive impurities by open and filtration flows of an incompressible viscous fluid. The first section of the paper studies the model of an inhomogeneous incompressible viscous fluid, which is widely used in meteorology and oceanology, with additional allowance for the drag of the magnetic field or porous medium. Another object of research in this paper is the model of filtration of an inhomogeneous incompressible fluid in porous media proposed by V. N. Monakhov (1977) (Section 2). In both models, hydrodynamic flows determine the motion of the mixture as a whole and the temperature and concentration distributions of the components of an inhomogeneous fluid are described by a common nonlinear system of equations of diffusive heat and mass transfer.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 44–51, March–April, 2005.     

Calculation of the trajectory of a plane free jet

A method is proposed for calculating the trajectory of a plane jet of an incompressible liquid, subjected to the action of two flows, directed at different angles to the original direction of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 178–182, May–June.     

Unsteady effects in weakly perturbed pulsatile channel flows

Pulsatile incompressible laminar flow in a plane channel with slight asymmetric deformation of the walls is considered on the basis of an asymptotic approach to the solution of the Navier-Stokes equations at large Reynolds numbers. It is shown that for extended deformations the change in the direction of the undisturbed flow in the wall regions is accompanied by a sharp increase in the amplitude of the perturbations; this is an essentially unsteady process. For flows with a small positive friction stress two classes of eigensolutions are obtained in the quasisteady approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 96–104, March–April, 1987.The author is grateful to V. V. Sychev and A. I. Ruban for a number of useful consultations in the course of the work.     

Problem of the motion of annular vortices in an ideal fluid

The study discusses problems in the numerical modeling of axisymmetric flows of an incompressible fluid induced by a continuous vortex region or vortex sheet by means of a discrete system of vortex rings.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 68–75, May–June, 1987.     

Development of vortical motions of an incompressible fluid in the cavity of a rotating body

Vortical nonstationary viscous incompressible flows in the space between coaxial cylinders or hemispherical segments rotating with a constant angular acceleration about a stationary axis of symmetry are analyzed numerically for Reynolds numbers Re — 1–10. It is shown that laminar circulating motions are realized. Two vortices form in the flow. The positions of these vortices depend substantially on the geometry of the rotating cavity.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 47–52, March–April, 1995.     

Vorticity enhancement in convergent incompressible flows: Nonself-similar solution of the Navier-stokes equations

The enhancement of vorticity in convergent viscous incompressible flows is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 100–107, May–June, 1989.The author is grateful to S. V. Bulanov for discussion of the results and useful advice and also to Yu. K. Krasnov for discussing studies [2, 3].     

Application of a differential equation for turbulent viscosity to the analysis of plane non-self-similar flows

A differential equation of the kinetic-energy balance of turbulence is used in a number of papers to close the equations describing average motion in turbulent flows. On the basis of this relation, a differential equation for turbulent viscosity is obtained herein. Numerical computations are carried out for incompressible non-self-similar turbulent and transition flows in awake, a jet, and a boundary layer; universal constants in the equation for the viscosity are refined. The flow in a wake and boundary layer with high longitudinal pressure gradients is investigated by analytical and numerical methods. Dimensionless criteria determining the nature of the effect of the pressure gradient on the average flow and turbulent viscosity are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 114–127, September–October, 1971.The author is greateful to I. P. Smirnov, S. Yu. Krasheninnikov, and V. B. Kuz'mich for aid in compiling the program for the numerical computations and to L. L. Bychkov for processing the computational results and plotting the graphs.     

On an attempt to simplify the Quartapelle–Napolitano approach to computation of hydrodynamic forces in open flows

In this paper we are interested in the Quartapelle–Napolitano approach to calculation of forces in viscous incompressible flows in exterior domains. We study the possibility of deriving a simpler formulation of this approach which might lead to a more convenient expression for the hydrodynamic force, but conclude that such a simplification is, within the family of approaches considered, impossible. This shows that the original Quartapelle–Napolitano formula is in fact “optimal” within this class of approaches.     

Helical flows with multiple circulation in channels of simple shape

A general solution is obtained for the problem of the helical motion of an incompressible liquid along a channel with a cross section in the shape of an annular sector or a triangle. The possible use of the solutions so obtained in order to describe secondary flows with repeated circulation in channels of simple shape (ring, circle, square, rhomb, rectangle, equilateral triangle) is demonstrated. The theory is in agreement with experiment. In one particular setting, problems as to the helical motion of an ideal incompressible liquid in channels of simple configuration were solved in [1, 2]. In this paper flows of a more general form with repeated circulation are considered, several vortices occurring inside the tube cross section.Deceased.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 32–38, March–April, 1973.     

Approximate solution of the problem of the flow of a conducting liquid in a duct with rectangular cross section

An approximate analytic solution is constructed for the problem of the fully developed stationary flow of a viscous incompressible liquid with a finite isotropic conductivity in a duct of rectangular cross section in the presence of an external magnetic field at right angles to nonconducting walls. An investigation is made of the extent to which flows in ducts with two electrodes parallel to the field resemble flows with four nonconducting walls. Theoretical and experimental investigations devoted to this problem are reviewed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 33–40, September–October, 1970.     

Onset of convection regimes with double period in a periodic field of external forces

We investigate the onset of secondary convective flows in the Rayleigh problem (in a horizontal layer of a viscous incompressible liquid with free boundaries) in the presence of a parameter that varies with time and has a period T, namely the temperature gradient or the intensity of the gravitational field.Translated from Zhurnal Prikladnoi Mekhanlki i Tekhnicheskoi Fizlki, No. 6, pp. 65–70, November–December, 1972.     

Method of narrow strips for nonlinear problems of a stratified fluid

Plane steady flow is considered for an ideal incompressible stratified fluid in a gravitational field of force. It is a characteristic feature of these flows that the density is constant and Bernoulli's constant remains the same along a streamline. Internal waves arise because of ponderability in the stratified fluid; they are not due to the presence of a free surface. These wave motions are studied in detail in the linear formulation, but flows of the solitary wave type can be described only by nonlinear equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–178, March–April, 1986.     

Branching of secondary modes in the flow between rotating cylinders

The steady secondary flows (Taylor vortices) of a viscous incompressible fluid between concentric rotating cylinders are studied. The range of wave numbers a and Reynolds numbers R in which there are several secondary flow modes is determined. The branching of these modes is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp.47–53, January–February, 1977.     

Jet flow of ideal fluid past a flexible shell

A detailed study is made of Kirchhoff flow of an ideal, incompressible, and weightless fluid past a flexible shell with one or two fixed points. It is shown numerically that when the pressure is decreased in a soft balloon multisheeted flows and a wavelike deformation of the balloon are possible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 43–48, November–December, 1982.