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.     

Diffusion of a ring vortex

The diffusion of a ring vortex is investigated in the present paper with allowance for the influence of the initial radius of the toroidal vorticity distribution on the flow structure. The statement of the problem in such a formulation makes it possible to classify and reinterpret results obtained previously. A vortex pair is studied together with a vortex ring. The toroidal vorticity and stream function distributions are obtained analytically. The self-induced lift velocity of the ring vortex is found. The influence of inertial terms is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 10–15, November–December, 1987.     

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.     

Calculation of the aerodynamic characteristics of a helicopter lifting rotor subjected to air gusts

A numerical method of calculating the unsteady aerodynamic characteristics of a helicopter lifting rotor smoothly enveloped by an air gust arriving from an arbitrary direction is proposed. The problem is solved in the non-linear formulation for an incompressible medium. The flow over each blade is simulated by a system of discrete vortices. The deformation of the vortex trail from the blades under the influence of the gust is taken into account. The results of the calculations are reported.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 153–158, March–April, 1987.     

Asymptotic model of the axisymmetric breakdown of a vortex filament in an incompressible fluid

The axisymmetric flow of an incompressible fluid is considered. An exact solution of the Euler equations corresponding to the breakdown of a straight vortex filament of intensity ₀ into a vortex filament of lesser intensity and a conical vortex surface is obtained. It is shown that beyond the breakdown point in the region bounded by the conical vortex surface reverse flows occur. An investigation of the problem with allowance for viscous effects at large Reynolds numbers makes it possible to establish a relation between the free parameters entering into the solution of the Euler equations. The results obtained are useful for investigating the problem of the breakdown of a swirled jet, whose solution has recently been receiving much attention [1, 2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 47–52, November–December, 1989.     

Structure of the wake behind a cylinder in a fluid with a variable buoyancy frequency,studied with the help of echo sounding and optical observation

Acoustic sounding of the wake behind a circular cylinder and observation of the shadow pattern indicate that for a density gradient varying on distances of the order of the cylinder's vertical dimension two parametrically different vortex systems may coexist in the wake. In the particular case when the profile of the buoyancy frequency is symmetric and its axis coincides with the path along which the cylinder's axis travels, the vortex systems on both sides of the wake are nearly identical. However, if the axes do not coincide, then the structures of the upper and the lower parts of the wake are rather different.If the Froude number Fr=u/NR is based on the flow velocityu, the radius of the cylinderR, and the current value of the buoyancy frequencyN, then the observed flow pattern corresponds to known regime diagrams presented by several authors. In the present experimentsN was found using the characteristic periods of oscillation of the intensity of volume ultrasonic scattering.The vertical profiles of the coefficient of backscattering of ultrasound and the synchronous shadow flow patterns in the wake behind the body are subjected to simultaneous analysis.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–12, November–December, 1995.     

The flow in a planar-radial vortex chamber. 2. Vortex structure of the flow

A vortex structure of an air flow with a characteristic size of vortices comparable with the primary vortex size was observed in a vortex chamber of planar-radial geometry for the first time. The vortex component of the flow velocity along the chamber radius and its axis was calculated. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 41–49, January–February, 2000.     

Effect of the flow regime in an underexpanded jet issuing into a subsonic counterstream on the pressure distribution on a body

The pressure distribution on a cone with a half-angle =75°, from which a single central underexpanded jet issues into a subsonic counterstream, has been experimentally investigated. The effect of the flow regime in the jet on the pressure distribution is demonstrated. Generalized relations for the pressure on the body are obtained for various jet-flow momentum ratios J and flow Mach numbers M = 0.35–0.9; the Mach number M_a at the exit of the conical nozzle with half-angle _a=10° was equal to 2.9. The working medium of the jet and the flow was air with stagnation temperatures T_0a = T₀ 260–265°K. The ratio of the nozzle outlet radius to the radius of the maximum cross section of the cone _a/R_M=0.1.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 182–185, January-February, 1988.     

Analytic investigation of a nonlinear problem of the effect of buoyancy on the evolution of an annular vortex

The evolution of a heavy axisymmetric vortex whose density differs from that of the surrounding irrotational ideal fluid is investigated analytically. If the vortex had no buoyancy (i.e., if the densities were identical), it would preserve its shape and velocity. An approximate analytic solution of the problem is obtained. This solution describes two types of evolution of the vortex shape corresponding to different values of the initial velocity and small buoyancy. The spectrum of a nonlinear wave developing on the vortex boundary is estimated.Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 56–66, January–February, 1996.     

Calculation of the flow of an ideal fluid past a wing of finite thickness

The problem of irrotational flow past a wing of finite thickness and finite span can be reduced by Green's formula to the solution of a system of Fredholm equations of the second kind on the surface of the wing [1]. The wake vortex sheet is represented by a free vortex surface. Besides panel methods (see, for example, [2]) there are also methods of approximate solution of this problem based on a preliminary discretization of the solution along the span of the wing in which the two-dimensional integral equations are reduced to a system of one-dimensional integral equations [1], for which numerical methods of solution have already been developed [3–6]. At the same time, a discretization is also realized for the wake vortex sheet along the span of the wing. In the present paper, this idea of numerical solution of the problem of irrotational flow past a wing of finite span is realized on the basis of an approximation of the unknown functions which is piecewise linear along the span. The wake vortex sheet is represented by vortex filaments [7] in the nonlinear problem. In the linear problem, the sheet is represented both by vortex filaments and by a vortex surface. Examples are given of an aerodynamic calculation for sweptback wings of finite thickness with a constriction, and the results of the calculation are also compared with experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 124–131, October–December, 1981.     

Solution of linear problems of the uniform motion of a vortex source in a multilayer fluid

A method of solving linear problems of the uniform motion of a vortex source in a multilayer fluid having an arbitrary finite number of layers is proposed. As an example, the problem of the motion of a vortex source of given intensity in a three-layer fluid is solved. Formulas for the complex velocities and hydrodynamic reactions are obtained.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 127–132, May–June, 1995.     

Formation of a vortex ring during the rise of a heated air mass in the stratified atmosphere

The motion of a strongly heated air mass in the earth's atmosphere is studied numerically. The turbulence effects are modeled by the assignment of constant coefficients of viscosity and thermal conductivity. It is shown that a vortex torus is formed during the rise of a hot mass initially having a spherical shape. The velocity, density, and temperature distributions over the significant time interval are obtained for a series of variants differing in the values of the Reynolds and Prandtl numbers. A satisfactory correspondence between the integral characteristics (altitude of rise, dimensions of disturbed region) and the data obtained by the approximate method of A. T. Onufriev [1] is established for several variants.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 186–189, March–April, 1978.The author thanks L. A. Chudov for guidance of the work.     

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.     

Investigation by experiment and calculation of a supersonic stream adjacent to a wall in an accompanying supersonic flow

In well-known papers devoted to the investigation of supersonic streams adjacent to a wall, the authors, as a rule, restrict themselves to the case of a subsonic blast. In the present paper we determine the velocity field and the concentration field of an admixture of helium in a plane supersonic stream of air (M₁=2.18), propagating along a surface in an accompanying supersonic flow of air (M₂=2.7 and 3.8). In the boundary layer approximation a numerical calculation is made of the non-self-similar isobaric flow, using the equation for the turbulent viscosity [1] as the closing relationship. Results of the calculation are compared with experimental data.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 25–32, July–August, 1972.     

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.     

Inviscid evolution of incompressible swirling flows in pipes: The dependence of the flow structure upon the inlet velocity field

This paper analyses the influence of the inlet swirl on the structure of incompressible inviscid flows in pipes. To that end, the inviscid evolution along a pipe of varying radius with a central body situated inside the pipe is studied for three different inlet swirling flows by solving the Bragg–Hawthorne equation both asymptotically and numerically. The downstream structure of the flow changes abruptly above certain threshold values of the swirl parameter (L). In particular, there exist a value L_r above which a near-wall region of flow reversal is formed downstream, and a critical value L_f above which the axial vortex flow breaks down. It is shown that the dependence upon the pipe geometry of these critical values of the swirl parameter varies strongly with the inlet azimuthal velocity profile considered. An excellent agreement between asymptotic and numerical results is found.     

Reynolds number dependence of two-dimensional laminar co-rotating vortex merging

The paper reports unsteady Navier–Stokes calculations of laminar two-dimensional co-rotating vortex merging for various Reynolds numbers. The unsteady, incompressible two-dimensional Navier–Stokes equations were solved with fourth-order Runge–Kutta temporal discretization and fourth-order symmetric compact schemes for spatial discretization. Calculations of the unsteady Taylor vortex benchmark showed that fourth-order accurate solutions for all primitive variables were indeed achieved. Calculations for a pair of equal-strength co-rotating vortices show good agreement with reported direct numerical simulation and experiments for the evolution of the separation distance and core radius. It is found that the time required for merging is inversely proportional to the square root of the Reynolds number. According to previous experimental research, it was also found that complete merging in laminar regime undergoes four stages with physical meaning. The physical mechanism responsible for the merging process is investigated and it is found that the antisymmetric vorticity dynamics plays an important role until full merging.     

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.     

Nonlinear interaction of a large vortex with a boundary layer

The nonlinear problem of boundary layer instability under the influence of a plane vortex is investigated for high Reynolds numbers. The vortex occupies the entire thickness of the boundary layer and has a longitudinal dimension of the order of the Tollmien-Schlichting wavelength. The initial vortex is rapidly swept away by the flow, inducing a Stokes layer near the surface of the plate. Expanding, this layer reaches the dimensions of the viscous sublayer of free interaction theory, where wave packet generation takes place. In the case in question a feature of the nonlinear stage of development of the disturbances is the formation of a concentrated vortex, which arises in the Stokes layer and grows rapidly, whereas the wave packet propagated ahead of it remains linear. From the calculations there emerges a tendency for the new vortex to be formed above the wail, whereas the maximum vorticity of the vortex generated in the Stokes layer corresponds to the wall itself.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 70–77, January–February, 1993.The authors are grateful to V. V. Kozlov for his interest in their work.     

The pinch-off process in a starting buoyant plume

The vortex ring formation process of a starting buoyant plume was studied experimentally using digital particle image thermometry and velocimetry (DPITV). The vortex ring was observed to pinch-off, or become disconnected, from the trailing plume. Pinch-off occurred at non-dimensional times, or formation numbers, between 4.4 and 4.9. The observed pinch-off process is consistent with an explanation based upon the Kelvin–Benjamin variational principle. This is analogous to the pinch-off of a vortex ring generated using a piston–cylinder apparatus, suggesting that pinch-off is a general component of the vortex ring formation process for various generation mechanisms.