Effect of internal linear waves on the hydrodynamic characteristics of a vortex source

The results of an investigation to estimate the effect of surface and internal waves on the hydrodynamic characteristics are presented for the problem of the uniform motion of a vortex source in a three-layer fluid. The behavior of the lift force and wave drag is studied in the neighborhood of the critical Froude number. Some results of the numerical experiments are presented. An analogous investigation is also carried out for the motion in a two-layer fluid beneath a rigid top and in the presence of a bottom.Omsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 146–153, September–October, 1996.     

Vortex motion of a disperse mixture

A study is made of the motion of fine spherical particles in a given steady vortex flow of an incompressible fluid. The results are given of an investigation into the Lyapunov stability of a particle trajectory coincident with the vortex axis, and of trajectories from which the distance to the vortex axis is determined by the condition of equality of the radial components of the force of the phase interaction and of the centrifugal force which acts on the particle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 167–169, November–December, 1984.     

Radiation and scattering of sound from a vortex ring

The mechanisms of generation and scattering of sound by a vortex ring are investigated on the basis of fluid dynamics. The vortex ring can serve as a simple dynamic model of the large-scale structures observed in shear flows. Moreover, it is probably the most easily studied vortex element that can be created experimentally. The sound scattering investigation also served to determine the extent to which the vortex is affected by sound, its selectivity with respect to such parameters as the acoustic frequency, the angle of incidence of the wave, etc. The perturbed motion is considered against the background of the steady-state motion of the ring. The perturbed motion in the vortex core is determined on the basis of linear incompressible fluid dynamics. Two terms of the expansion in the M number of the far acoustic field generated by the perturbations in the core are found in accordance with Lighthill's theory. The acoustic power and directivity of the radiation and the acoustic instability growth rate are calculated. It is shown that the scattering of sound by the vortex ring is a resonance effect, and the scattering amplitude near resonance is determined. The acoustic action on the hydrodynamic structure of the flow in the core of the ring is especially intense near the resonances and extends over a period short as compared with the characteristic time of the acoustic instability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 83–95, May–June, 1987.     

Hydrodynamic characteristics of a vortex source performing translational motion in a multilayer heavy fluid

The problem of translational motion of a vortex source in a three-layer fluid bounded by a bottom from below is considered. The fluid in each layer is perfect, incompressible, heavy, and homogeneous. Based on the previously developed method, formulas for disturbed complex velocities of the fluid in each layer and the wave drag and lift force of the vortex source are obtained. The vortex motion is considered near the interface of two semi-infinite fluid media and in a two-layer fluid with different conditions at the boundary. In all cases, the hydrodynamic characteristics of the vortex source are given as functions of the Froude number. In a number of problems, these characteristics have discontinuities at the transition through the critical Froude numbers. The character of these discontinuities is studied analytically. Omsk Department of Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, Omsk 644099. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 140–146, September–October, 2000.     

Internal waves arising in the presence of the unsteady motion of a source in a continuously stratified fluid

A general approach to the investigation of linear internal and surface waves in a stably stratified fluid, arising from different types of perturbations, is presented in [1]. The methods of calculation of the internal waves generated by the motion of a mass source are developed for particular cases of steady horizontal motion in a continuously stratified fluid in [2] and arbitrary motion in an unbounded exponentially stratified fluid in [3]. Internal waves generated by other types of perturbations have also been investigated but only for particular cases of motion (see, for example, [4]). This paper presents a method for the calculation of unsteady, linear, internal gravity waves arising in an inviscid incompressible fluid with continuous stable stratification.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–130, July–August, 1985.     

Thermal structure of convective vortex lattices

The thermal structure of the convective motions of a rotating plane layer of fluid is experimentally investigated in the regular vortex structure regime. It is found that in such a system the intense vortex motion leads to a temperature distribution such that the mean fluid temperature falls linearly from the bottom of the layer to the surface, the temperature gradient being determined by the rate of rotation and depth of the fluid. By dimensional analysis it is shown that this gradient corresponds to heat transfer in which the Nusselt number isolines are parallel to the convection curve. The horizontal structure of the temperature field is investigated; it corresponds to motion in which the fluid descends within a narrow vortex-sink and rises along the edges of a cylinder which determines the characteristic dimension of the structure in rotating fluid convection.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 160–166, November–December, 1987.The author wishes to thank G. S. Golitsyn for his constant interest in the work.     

Plane vortex flow induced by a mass source (sink) in a rotating viscous fluid

A solution of the self-similar type, describing the development with time of a plane vortex flow excited by an axisymmetric mass source (sink) in a rotating viscous fluid, is obtained. Sources of two kinds — impulsive and of constant strength — are considered. The solutions for the velocity and vorticity fields are expressed in the form of functions similar to incomplete gamma functions and are presented in the form of graphs for various flow Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 172–175, July–August, 1991.     

Asymptotic theory of vortex breakdown

Axisymmetric breakdown of a vortex in a steady flow of incompressible fluid is investigated by means of an asymptotic analys is of the Navier-Stokes equations for large Reynolds number (R). A criterion for vortex breakdownis formulated. The region of slow motion resulting from vortex breakdown is shown to be bounded by an ellipsoid with length of order R^–1/4 and thickness of the order R^–3/8.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 78–90, May–June, 1993.     

Solution of a problem of flow in a porous medium with limiting gradient

For the law of flow in a porous medium with limiting gradient studied previously in [1], an exact solution is found for the problem formulated in [2] of the plane steady motion of an incompressible fluid in a channel with a rectangular step. Particular cases of the solution obtained are given; these represent the solutions of the problem of flow past a broken wall and of motion from a point source in a strip.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–78, January–February, 1985.     

Effect of homogeneous stratification of the fluid on the dynamics of a kármán vortex street behind a circular cylinder

The experimental results of studying the effect of homogeneous stratification of the fluid on the conditions of generation of a Kárman vortex street [1] developing in the wake of a cylinder in steady horizontal motion are described. In a homogeneous medium at Reynolds numbers Re >5 two symmetrical regions of vorticity of opposite sign are formed behind the cylinder and move together with the latter. As the speed of the cylinder increases, the link between the vortices and the cylinder grows weaker, the vortices are stretched out along the flow and at Re > 40 begin to separate alternately, forming a vortex street in the wake. At first, the frequency of vortex separation increases sharply with increase in Re, but then levels off. It is found that in a uniformly stratified fluid the onset of vortex separation from the moving cylinder is delayed. The dependence of the critical Reynolds number (onset of vortex separation) on the internal Froude number is obtained. The effect of stratification of the fluid on the frequency of separation of the vortices in the Kármán street is investigated. The effect of the Froude number on the dependence of the Strouhal number on the Reynolds number is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 83–86, January–February, 1986.In conclusion the authors wish to thank A. T. Onufriev for his interest in their work and useful discussions of the results.     

Secondary thermocapillary motions of soliton type

An exact analytic solution is obtained for the problem of the stability of the axisymmetric thermocapillary motion due to a point heat source of constant power located on the horizontal free surface of a viscous fluid. Analytic expressions are found for monotonic neutral disturbances of hydrodynamic and thermal type. The critical values of the dimensionless source power for disturbances with arbitrary quantum numbersl andm are determined, together with the secondary motions near the stability threshold. An exact solution of the problem of the axisymmetric thermocapillary motion due to a spherical heat source is presented and its stability is investigated. It is shown that it is always possible to select physical heater properties such that for arbitrarily small source power, the axisymmetric motion is unstable relative to the vortex motion. A comparison is made with experiment.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 20–27, July–August, 1992.     

Theory of nonstationary vortices in an ideal fluid

Equations that describe the evolution of a region with nonzero vorticity are formulated. These equations are solved on a bounded time interval for regions having the shape of a sphere or a circular cylinder at the initial time. It is shown that a spherical vortex formed in a medium at rest begins to move, and is stretched in the direction of the motion; a cylindrical vortex, under the influence of the nonuniform intensity of the vorticity on its boundary, changes both the magnitude and direction of its velocity, and describes a curvilinear trajectory. Expressions are obtained which describe the initial evolution of a fluid sphere of one density in a fluid medium of another density.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–11, November–December, 1980.     

Motion of an intense vortex on a rotating globe

The evolution of an initially circular vortex is considered in terms of the relation between its dimensions and the screening scale — the radius of deformation of the quasigeostrophic single-layer model in the betaplane. It is shown that the beta-effect causes the displacement of the center of the vortex as a result of wave drift and secondary flows of dipole structure, whose development is analyzed asymptotically. It is found that with increase in the radius of deformation relative to the dimensions of the vortex the velocity of its center with respect to latitude becomes greater than the velocity with respect to longitude. The change in the intensity of the vortex due to the motion of its center with respect to latitude is estimated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 68–77, March–April, 1988.     

Long-wave instability of a vortex ring

The instability of barrel-shaped vibrations of a vortex ring in an ideal fluid is investigated. These vibrations, stable for a vortex ring with a piecewise-uniform vorticity profile, appear to be unstable for a vortex ring with a smooth vorticity profile. The instability growth rate is found on the basis of the energy balance equation determining the energy transport from perturbations with negative energy in the critical layer to perturbations with positive energy in the rest of the flow. The curvature of the vortex ring, by virtue of which the perturbations with energies of different signs appear to be connected, plays a prominent role in the mechanism under consideration.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 72–78, November–December, 1995.     

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.     

Flow of a vortical stream in the neighborhood of the critical point

A study was made of the axisymmetric flow of a viscous incompressible fluid in the neighborhood of the critical point of an obstacle when steady-state vortices oriented in the direction of the angular coordinate are introduced into the oncoming flow. A solution is presented of the equation for the transfer of a vortex in the case of an external flow containing a single largesize vortex in the low-frequency part of the spectrum. Using a finite integral Hankel transform, the problem is reduced to the solution of a system of ordinary differential equations. It is shown that a sufficiently large-size vortex can have a considerable effect on the structure of viscous flow near an obstacle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 85–89, November–December, 1970.     

Dynamics of thin vortex rings in a low-viscosity fluid

In order to describe the unsteady flow of a viscous fluid induced by a toroidal vorticity distribution we use the two-scale expansion method [6], By this means we obtain a vorticity distribution in the core of the thin vortex ring that is consistent with the external potential flow. The time dependence of the flow characteristics obtained confirms the experimental results for the inertial regime. The interaction of coaxial vortex rings is investigated as an example.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 52–59, September–October, 1992.     

Vortex on the surface of a viscous fluid

The system of Navier-Stokes equations is solved for boundary conditions corresponding to the case when an axisymmetric tangential transversal load acts at the surface of a gravity viscous incompressible fluid of infinite depth. An integral representation is obtained for the shape of the free surface under the prolonged effect of a stationary vortex load. The example of a tangential load, similar to a concentrated vortex, is examined. In this case a column is squeezed out of the fluid, the height of the column being directly proportional to the square of the moment of the transverse tangential forces and inversely proportional to the square of the product of the dynamic fluid viscosity and the area of the tangential stress distribution. The depth of the annular funnel being formed in front of the column is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–132, July–August, 1978.     

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.