Type of reflection of a near-wall shock wave in the process of diffraction from a square channel

The results of an experimental and numerical investigation of the process of diffraction of shock waves from a square channel at a ninety-degree convex corner are presented for various incident shock wave Mach numbers M₀ (1.4<M₀<7). The type of reflection of the near-wall fragment of the diffracting shock wave from the wall and the wave velocity are determined as functions of M₀, direction, and time. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 145–151, January–February, 2000. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 96-02-16170a).     

Quasi-cylindrical figures of equilibrium of a rotating fluid

The problem of the equilibrium shape of a steady rotating rectilinear infinite cord of ideal self-gravitating homogeneous fluid is considered. The question whether, apart from the obvious solution, namely, an infinite circular cylinder, noncylindrical equilibrium figures can exist is investigated. A search is carried out among axisymmetric figures with periodic surface structure (“wavy” cylinders). The period of the wave structure and, in the first approximation, the shape of the surface are found as functions of the angular velocity of rotation. Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–30, May–June, 2000.     

Optimization of the shape of a wing in a hypersonic nonequilibrium gas flow

A variational technique of obtaining the optimal shape of a low-aspect-ratio wing with allowance for the nonequilibrium character of the flow is developed. The technique is applied to the problem of determining optimal wing shapes under terrestrial atmosphere conditions. The real-gas effect on the optimal shapes and maximum lift-drag ratio is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 160–170, March–April, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00629).     

Uniform far field asymptotics of internal gravity waves from a source moving in a stratified fluid layer with smoothly varying bottom

The far field asymptotics of internal waves is constructed for the case when a point source of mass moves in a layer of arbitrarily stratified fluid with slowly varying bottom. The solutions obtained describe the far field both near the wave fronts of each individual mode and away from the wave fronts and are expansions in Airy or Fresnel waves with the argument determined from the solution of the corresponding eikonal equation. The amplitude of the wave field is determined from the energy conservation law along the ray tube. For model distributions of the bottom shape and the stratification describing the typical pattern of the ocean shelf eract analytic expressions are obtained for the rays, and the properties of the phase structure of the wave field are analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 111–120, May–June, 1998. This work was financially supported by the Russian Foundation for Basic Research (project No. 96-01-01120).     

Motion of a deformable droplet of magnetic fluid in a rotating magnetic field

The problem of the magnetic field-driven rotation of a magnetic fluid droplet in a viscous nonmagnetic fluid is solved analytically and experimentally. The shape of the droplet and the magnetic fields and velocities of both fluids are calculated in the weak-field approximation. The droplet is flattened for any relations between the parameters of the system. The instability of the axisymmetric shape of the droplet is established experimentally. A result of the instability is a sudden change in the droplet shape from a flattened ellipsoid of revolution to a triaxial ellipsoid elongated in the equatorial plane. The critical magnetic Bond number is determined. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 22–30, January–February, 2000. The work was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00182).     

Motion of a cylinder below the free surface of a fluid at large froude numbers

A method of solving the problem of the motion of a cylinder of given shape below the free surface of an infinitely deep heavy fluid is perfected for large Froude numbers. The motion of a circular cylinder is investigated at small distances from the free surface. Solutions of the problem are given for cylinders with noncircular cross-sections. Kazan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 34–45, July–August, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (projects Nos. 99-01-00169 and 99-01-00173).     

Propagation of a thermal detonation wave in a water-corium system

The problem of the unsteady propagation of a thermal detonation wave in a high-temperature-melt-water system up to the steady-state regime is considered on the basis of the three-dimensional and three-temperature vapor explosion model. The basic laws of wave evolution are analyzed and the wave structure is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 115–125, July–August, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 98-02-17766) and the International Science and Technology Center (project No. 408).     

Effect of surface and internal waves on the hydrodynamic characteristics of a contour in the linear approximation

A method of solving the problem of the motion of an elliptic contour in a three-layer fluid is developed within the framework of the linear theory. The results of calculating the hydrodynamic contour loads and the shape of the interfaces are presented for the following problems: the motion of a contour beneath an interface between two media and in a two-layer fluid both beneath a rigid lid and a free surface. On the basis of the numerical experiment it is concluded that surface and internal waves have a significant effect on the hydrodynamic characteristics of the contour. Omsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 121–127, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00093).     

Nonlinear effects caused by pulsed periodic supply of energy in the vicinity of a symmetric airfoil in a transonic flow

Changes in the structure of a transonic flow around a symmetric airfoil and a decrease in the wave drag of the latter, depending on the energy-supply period and on localization and shape of the energy-supply zone, are considered by means of the numerical solution of two-dimensional unsteady equations of gas dynamics. Energy addition to the gas ahead of the closing shock wave in an immediate vicinity of the contour in zones extended along the contour is found to significantly reduce the wave drag of the airfoil. The nature of this decrease in drag is clarified. The existence of a limiting frequency of energy supply is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 64–71, May–June, 2006.     

Internal waves induced by moving periodic perturbations applied to the surface of a stratified fluid

Investigations of internal wave generation by moving perturbations are of considerable interest for submarine navigation, hydroacoustics, ocean seismology, etc. The main results for perturbations of constant intensity were published in [1–3]. In the present paper we continue the investigations and study moving perturbations whose intensity varies periodically in time. The perturbations are approximated by surface shape variations or an external pressure on the surface. The vertical displacement of the water particles relative to the equilibrium position is obtained in the form of a series in terms of waves modes for a given density stratification. A calculation algorithm and a program for computing each of the wave modes have been compiled. The boundaries of the wave regions and constant-phase lines are constructed and the displacement amplitudes are calculated. It is shown that there are resonance relations between the oscillation frequency and the perturbation velocity for which the displacement for a given mode becomes infinite (in the linear theory). Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 130–135, July–August, 1994.     

Emulsion flow through a porous medium with allowance for interphase mass transfer between the components

A new model of the flow of two miscible, mutually-insoluble fluids in a porous medium with the formation of an emulsion and adsorption of the fluid components on the skeleton is proposed. The model takes into account the effect of interphase mass transfer on the emulsion dynamics and the active porosity. A continuous general solution of the one-dimensional model and the problem of breakdown of a discontinuity is constructed. The flow regimes generated in displacement problems which depend on the shape of the adsorption isotherms and the densities of the fluid components are considered. The time dependence of the production rate is constructed for frontal displacement regimes and for displacement regimes with the formation of a zone of mixing (Riemann wave) of the initial reservoir and injected fluids. These functions coincide, at least qualitatively, with the experimental data [1] indicating an initial increase in production rate even against a background of falling reservoir pressure, transition through a maximum, and subsequent decline. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 77–88, January–February, 1997. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 96-01-00991).     

Uniform expansion of a gravitating gas in the presence of a pressure gradient

Within the framework of the Newtonian mechanics, we studied the possibility of the formation of a uniformly expanding gravitating gas due to the passage of a detonation wave through a freely compressible medium (dust). The formulation of the problem is associated with the modeling of the large-scale expansion of the Universe. At the same time, the results obtained can also be applied to the calculation of the consequences of the spherical collapse of other gaseous masses. A class of exact solutions taking the pressure gradient into account is derived. Possible changes in the system behavior, as compared to with case of uniform pressure studied in [1], are analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 176–182, July–August, 1998. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 97-01-00196).     

Azimuthal wave motions on the surface of a rotating fluid cylinder

Wave motions in a fluid cylinder rotating about the axis are investigated within the framework of the linear theory. The cylinder is assumed to be fairly long. This makes it possible to restrict attention to the study of the plane oscillation pattern. The fluid is assumed to be ideal and incompressible. The models in which the fluid particles are confined by gravitational (body) or/and capillary forces (surface stress forces) are considered. A mode analysis is carried out and the dispersion relations are constructed. Traveling and steady-state waves on the surface of the fluid cylinder are investigated; qualitative effects ("wave inertia") are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–133, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00221). An erratum to this article is available at .     

Optimum clearance of a gas hydrostatic thrust bearing with maximum load capacity

The optimum design of a gas hydrostatic thrust bearing clearance is obtained using the methods of calculus of variations. The variational problem of determining the clearance shape giving the maximum load capacity is solved for a given external pressurization and various journal speeds. The structure of the optimum solution is found on the basis of the gas lubrication approximation with and without constraints on the height of the bearing pad (pocket). The calculation results embrace all possible values of the parameters. A comparison with optimum liquid bearings is carried out. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–78, July–August, 2000. The work was carried out with support from the Russian Foundation for Basic Research (projects Nos. 99-01-01211 and 96-15-96158).     

Thermal convection in an acoustic field

The linear stability of flow in a horizontal fluid layer is investigated within the framework of thermoacoustic convection. The flow is initiated by a longitudinal temperature gradient and the propagation of an acoustic wave in the fluid. Instability modes corresponding to perturbations of both plane and longitudinal roller and oblique wave type are detected. Using weakly nonlinear analysis, it is shown that these regimes develop softly; the stability of various secondary flows is investigated for small supercriticalities. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 10–21, May–June, 2000. The work was carried out with partial support from the Program of State Support for Leading Science Schools (grant No. 96-015-96084).     

Modification of the burnett equations and shock wave structure

Questions of the applicability of simplifying modifications of the Burnett equations are studied with reference to the problem of the shock wave structure in a monatomic gas. As distinct from the complete system of Burnett equations, the order of the systems of modified equations is the same as that of the Navier-Stokes equations, and the equations are stable with respect to shortwave perturbations. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 164–176, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-01244).     

Interaction of a supersonic pulse jet with an obstacle

The nonstationary interaction between a supersonic pulse jet and a flat plate perpendicular to the jet axis is studied experimentally and numerically. The time dependences of the pressure and heat flux at various points on the obstacle and the spatial distribution of the density are obtained experimentally. The nonstationary flow is calculated numerically by the Godunov method. The experiments and calculations reveal the effect of the reflected starting shock wave and the front part of the swirled gas outflow on the distribution of the dynamic and thermal loads acting on the plate, in both time and space. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 45–51, March–April, 1998. This research was carried out with partial financial support from the Russian Foundation for Fundamental Research (project No. 96-02-16170).     

Waves in a heavy two-layer liquid excited by an oscillating sphere

An approximate solution of an initial-boundary-value problem appropriate for the semiaxist>0 (t is time) is constructed for a system of integrodifferential equations which describes the waves excited in an initially stationary unbounded heavy two-layer fluid by a vertically oscillating sphere located at a distance from the interface that is significantly greater than its radius. The shape of the steady-state wave is found by passing to the limit as time increases indefinitely. The wave resistance experienced by the sphere during the transient process and in the steady-state regime is studied as a function of frequency. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–133, March–April, 1998.     

On local perturbations of a boundary layer with small skin friction

This paper studies the effect of two-dimensional surface irregularities on the flow in a plane steady boundary layer with small skin friction in an incompressible fluid. A detailed analysis is carried out for the flow regime with a given pressure gradient determined on the scale of the small irregularity by its shape. It is shown that there is a critical value of the height (depth) of the irregularity at which the skin friction first becomes zero, and the nonuniqueness of the corresponding solution is established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 87–97, November–December, 1998. The work was financially supported by the Russian Foundation for Basic Research (project No. 97-01-00354).     

Thin airfoils of minimum wave drag with given chord, longitudinal section area, and lift

The problem of profiling optimal airfoils at small incidence in a supersonic stream in order to achieve the minimum wave drag coefficient for given chord, longitudinal section area, and lift coefficient is studied. It is demonstrated that a trailing flat end face plays an important role even for very thin airfoils. Moscow, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–157, July–August, 1998. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-01825).