ALBERT

Description:    Approximate two-dimensional equations governing turbulent vortex flows in plane fluid layers are considered. The equations were derived by the author in his earlier studies using the shallow water approximation and neglecting circulatory flows in the layer cross-sections. It is shown that, due to the centrifugal effect in the vortex flow, return flows in the layer cross-sections have only a slight influence on the fluid flow in the plane layer and can be neglected. Content Type Journal Article Pages 327-331 DOI 10.1134/S0015462811020153 Authors S. Yu. Khripchenko Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The flow in the shock layer between a plane wedge and a plane attached shock is considered. The flow two-dimensionality is violated by the presence of a weak heat source in the shock layer. The relation between the mechanical actions of the disturbances singly reflected from the shock and those proceeding from the source and directly incident on the wedge surface is analyzed. The three-dimensional features of the field of the disturbances reflected from the shock are illustrated with reference to several examples. Content Type Journal Article Pages 299-307 DOI 10.1134/S001546281102013X Authors S. I. Arafailov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    Soluble vapor-gas bubbles performing small radial oscillations in a liquid are considered. The heat- and mass-transfer processes and temperature and concentration inhomogeneities in the vaporgas mixture are taken into account. Expressions for the damping rate of radial oscillations of soluble vapor-gas bubbles are obtained. In [1–3] the dynamics of vapor-gas bubble oscillations were considered for a gas insoluble in liquid. Content Type Journal Article Pages 286-290 DOI 10.1134/S0015462811020116 Authors Mona Al-Monnai N. S. Khabeev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The oil redistribution pattern in a compound vortex created by a uniformly rotating disk located on the bottom of a cylindrical tank is investigated. At the initial instant, a round spot of a lightweight oil is deposited on the free surface of the liquid at the center of the tank. In the course of the formation of the compound vortex, the oil is partially entrained into the interior of the liquid and forms a body of revolution. On the free surface, the spot loses the round shape, spiral branches stretch out from the appeared protrusions and cusps. The orientation of these branches is opposite to the direction of fluid rotation in the tank. Geometrical parameters of the structures for different flow regimes are studied. Content Type Journal Article Pages 214-224 DOI 10.1134/S0015462811020049 Authors E. V. Stepanova T. O. Chaplina Yu. D. Chashechkin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    An analytical procedure used in calculating the Stokes drift velocity (the drift motion initiated by the propagation of a capillary-gravity wave over an ideal fluid surface) is applied to the problem of the calculation of an analogous drift flow in a viscous fluid. An expression for the velocity of the Stokes drift modified with allowance for viscosity is constructed. The properties and the role of the modified Stokes drift in the general pattern of the drift in a viscous fluid are analyzed. Content Type Journal Article Pages 270-277 DOI 10.1134/S0015462811020098 Authors D. F. Belonozhko A. V. Kozin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    A new quasi-two-dimensional model of impurity propagation from a man-made source is devised on the basis of a three-dimensional model of hydrothermodynamics of mesoscale processes in the lower atmosphere with account for the thermal nonuniformity of the underlying surface in the environs of a large industrial city. The boundary conditions and the model coefficients are determined using the parametrization method. The results of numerical calculations are presented. The calculations are performed using parallelized algorithms on a cluster supercomputer of the Vyatka State University. They show that, due to the action of an inhomogeneous horizontal temperature gradient in the lower atmosphere, vortex flows can be formed above populated areas. The disturbed wind flow has a considerable effect on the impurity propagation pattern in the neighborhood of the sources. Content Type Journal Article Pages 332-339 DOI 10.1134/S0015462811020165 Authors A. V. Shatrov K. G. Shvarts Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The Rapoport-Leas mathematical model of two-phase flow is generalized to include the case of anisotropic porous media. The formula for the capillary pressure, which specifies the relationship between the phase pressures, contains a scalar function of a vector argument. In order to determine the scalar function, the capillary pressure tensor and the tensor inverse to the tensor of characteristic linear dimensions are introduced. The capillary pressure is determined by the contraction of the second-rank tensors with a unit vector collinear to the phase pressure gradients, also assumed to be collinear. It is shown that the saturation function introduced for isotropic porous media (Leverett function) can be generalized to include anisotropic media and is now determined by a fourth-rank tensor. Generalized expressions for the Leverett and relative phase permeability functions are given for orthotropic and transversely isotropic media with account for the hysteresis of the phase permeabilities and capillary pressure. Content Type Journal Article Pages 291-298 DOI 10.1134/S0015462811020128 Authors M. N. Dmitriev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The development of gravitational convection in a two-dimensional enclosure occupied by a viscous fluid with foreign inclusions (particles) is considered. At the initial instant of time, the fluid is at rest and, in a general case, the spatial distribution of the particle concentration is nonuniform. Under the action of the gravity force, the particles start to settle down, inducing the development of convective motion in the carrier phase. The mathematical description is based on the model of interpenetrating continua, which takes into account a finite particle volume fraction and a variation of the effective viscosity of the mixture due to the redistribution of the particles. A general two-fluid model of two-phase convection is proposed, the similarity parameters are determined, and specific cases of the model, corresponding to typical real situations, are considered. On the basis of numerical study of a number of examples of the development of slow convection in suspension, a quantitative estimate is obtained for the effective rate of sedimentation of heavy particles in vessels with inclined walls (the Boycott effect). The known experimental effect of horizontal-strata formation in settling suspension is modeled, and the development of instability on the lower boundary of settling suspension (“fingering” effect) is modeled. It is shown that, to realize the Boycott effect, it is necessary to form a particle concentration nonuniformity in the direction normal to the gravity force. The range of inclination angles of a tilted square vessel is determined, for which the effective sedimentation rate of the dispersed phase is maximal. Content Type Journal Article Pages 225-239 DOI 10.1134/S0015462811020050 Authors Yu. A. Nevskii A. N. Osiptsov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The results of mathematical modeling and experimental investigation of flows and heat transfer in supercritical media in the vicinity of the critical thermodynamic point under microgravity and terrestrial conditions are considered. The effects of thermal gravitational convection and thermoacoustics complicated by the adiabatic compression effect, as well as the special features of two- and three-dimensional supercritical structures, are discussed. The experimental results obtained aboard the space station Mir are interpreted. The projects of experiments aboard the International Space Station, together with their terrestrial applications, are discussed. Content Type Journal Article Pages 175-195 DOI 10.1134/S0015462811020025 Authors V. I. Polezhaev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The two-dimensional problem with an unknown boundary of the development of a periodic system of cavities in viscous bodies under finite deformations is considered. The solution of the periodic problem of the development of a system of similar cavities in a slow time-dependent flow of a Newtonian viscous fluid is derived. Content Type Journal Article Pages 262-269 DOI 10.1134/S0015462811020086 Authors V. M. Mirsalimov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The impact of the plane front of a rotational discontinuity, which has a circular polarization and propagates in the solar wind along the Sun-Earth radius, on the Earth’s bow shock and the magnetosheath is first investigated in the three-dimensional formulation. The most characteristic values of the solar wind parameters and the interplanetary magnetic field strength in the Earth’s orbit are considered. The global three-dimensional pattern of the flow is constructed as a function of the latitude and longitude of points on the bow shock and the intensities of all the waves appearing in the interaction which significantly depend on the angle of rotation of the magnetic field are found. The solution obtained is necessary to interpret the solar wind parameters and the interplanetary magnetic field measured by spacecraft located in the neighborhood of the Lagrange point and the Earth’s magnetosphere. Content Type Journal Article Pages 308-326 DOI 10.1134/S0015462811020141 Authors E. A. Pushkar Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The shallow water equations on a rotatable attracting sphere represent a system of hyperbolic equations on a compact manifold. These equations are derived in a spherical coordinate system from the integral laws of mass and total momentum conservation with account for the Coriolis and centrifugal forces. An analysis of the stability of discontinuous solutions with discontinuous waves and contact discontinuities is made using the closing law of total energy conservation, which represents a convex extension of the basic conservation-law system. The classes of stationary, one-dimensional (latitude-dependent only) exact solutions with contact discontinuities and discontinuous waves are constructed. Within the framework of the one-dimensional equations the test problem of wave flows resulting from the simultaneous break of two dams confining a fluid at rest in the vicinities of the poles is numerically modeled. Content Type Journal Article Pages 196-213 DOI 10.1134/S0015462811020037 Authors V. V. Ostapenko A. A. Cherevko A. P. Chupakhin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The steady-state advective flow in a long horizontal rectangular channel with rigid adiabatic boundaries in the presence of a uniform longitudinal pressure gradient is investigated. The stability of this flow with respect to perturbations of various types is studied. The dependence of the critical Rayleigh number on the Prandtl number is found for various aspect ratios. Content Type Journal Article Pages 240-249 DOI 10.1134/S0015462811020062 Authors T. P. Lyubimova D. A. Nikitin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    The results of experimental and numerical investigation of flow in a circular conical diffuser with a small conicity angle ensuring separationless flow are presented. The measurements are carried out in an air flow with the Reynolds number Re 2 in the diffuser exit section ranging from 600 to 3000. A considerable effect of the channel expansion on the flow pattern is found to exist. It is shown that, as distinct from a tube, in which only laminar flow can be realized as steady for Re 〈 2000, in the exit section of a diffuser with the generator slope of 0.3° and a length equal to 70 entry diameters a developed turbulent flow is formed for Re 2 〉 1000. For Re 2 〉 1300 this flow is steady, that is, almost independent of the turbulence level at the entry, and is determined by the Reynolds number Re 2 in the exit section. For Re 2 ≈ 1000 the turbulent flow continuously goes over into a laminar flow. The flow parameters measured at the diffuser exit correspond to calculations in accordance with the threeequation turbulence model. Content Type Journal Article Pages 278-285 DOI 10.1134/S0015462811020104 Authors A. I. Reshmin S. Kh. Teplovodskii V. V. Trifonov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description: In memory of Aleksei Alekseevich Barmin Content Type Journal Article Pages 169-174 DOI 10.1134/S0015462811020013 Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    A mathematical model describing small oscillations of a combined medium consisting of an ɛ-periodic porous viscoelastic material and a viscous compressible fluid filling the pores is considered. For this model an effective averaged model is developed and the convergence of the solutions of prelimiting problems, as ɛ → 0, to the solution of the averaged problem in the L 2 space norm is proved. Content Type Journal Article Pages 250-261 DOI 10.1134/S0015462811020074 Authors A. S. Shamaev V. V. Shumilova Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 2

Description:    A model and a numerical algorithm for studying unsteady gas flows in self-heated solid waste dumps are developed without regard for detailed chemical kinetics of the process. The results of the numerical experiments performed indicate the formation of vortex gas flows in the heat release site and its vicinity, which can considerably deteriorate the heat removal from the object under consideration. It is shown that both complete quenching of the energy release source and the attainment of a steady self-heating regime and unbounded heating of the object can occur depending on the initial and boundary conditions and the problem parameters. Content Type Journal Article Category Supplement: Vychislitel’naya Mekhanika Sploshnykh Sred (Computational Continuum Mechanics) Pages 826-834 DOI 10.1134/S0015462811050152 Authors V. A. Levin N. A. Lutsenko Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    Collision of plane fronts of a plane-polarized Alfvén discontinuity and a slow shock wave propagating in opposite directions at a certain angle is considered within the framework of an ideal magnetohydrodynamic model. The initial state of an infinitely conducting medium at rest with a frozen-in magnetic field is assumed to be given. Calculations are carried out for various values of the shock wave Mach number and the magnetic field strength using a special software which makes it possible to find an exact solution of the Riemann problem of breakdown of a discontinuity between the states downstream of the interacting waves by means of a computer. The wave flow structure is investigated and a bifurcation map of flow restructuring is constructed. Domains of the initial parameters for which the interaction differs qualitatively are distinguished. The parameters of the medium and magnetic field are found as functions of the angle between the colliding discontinuities and the inclination of the magnetic field. The results obtained may be used in investigations of magnetic reconnection. Content Type Journal Article Pages 782-793 DOI 10.1134/S0015462811050127 Authors A. S. Nosova E. A. Pushkar Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    he results of an investigation of hydrochloric acid treatment on micro and macroscales are presented. A petrophysical permeability-porosity dependence used in the averaged mathematical model and taking account of the wormhole formation effect on the level of individual pores is proposed. The values of the surface reaction rate on carbonate rock dissolving in hydrochloric acid are given from the results of laboratory studies. An optimum rate of hydrochloric acid plug injection is estimated and the constraints due to possible transition of the acidizing in the acid breaking of the formation are discussed. Content Type Journal Article Pages 736-743 DOI 10.1134/S0015462811050073 Authors T. A. Kremleva A. S. Smirnov K. M. Fedorov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    The relations for the temperature, velocity, and pressure fields on the interface between two regions occupied by a liquid and its vapor are derived from the balance laws. In contrast to the traditional relations, the relations obtained contain additional terms, responsible for certain physical phenomena on the interface and usually neglected in the force and energy flux balances. The problem of evaporation of a liquid layer is considered. An exact solution of this problem is constructed in the one-dimensional formulation. The evaporation rate is calculated for a specific liquid. Content Type Journal Article Pages 754-763 DOI 10.1134/S0015462811050097 Authors V. V. Kuznetsov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    Thermal-gravitational and thermocapillary convection is numerically modeled in the axisymmetric and three-dimensional approximations for the hydrodynamic model configuration corresponding to technological regimes of oxide crystal growth and taken as the basis in an international test. The salient features of the interaction between the convection and the flow driven by crystal rotation are studied at high Prandtl numbers. The flow and temperature fields occurring upon the generation of axisymmetric oscillations and the loss of axial symmetry are studied, analyzed, and compared with the results of other authors. Content Type Journal Article Pages 684-698 DOI 10.1134/S0015462811050024 Authors O. A. Bessonov V. I. Polezhaev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    A mathematical model of gas hydrate formation from microbial methane in marine sediments is proposed. An analytical solution of the problem is obtained, determining dimensionless parameters are distinguished, and numerical investigation is performed. In the region of main parameters a critical diagram of hydrate existence is plotted. It is shown that at small sediment accumulation rates microbial methane disperses due to diffusion of dissolved gas which does not reach saturation. If the sediment accumulation is intense, the region of possible hydrate formation falls within the region of stable thermodynamic states only at large depths. Correspondingly, in these cases, the probability of formation of hydrate-containing sediment layers is small. The most probable hydrate formation regime is realized at moderate sediment accumulation rates corresponding to Péclet numbers of the order of unity. Content Type Journal Article Pages 744-753 DOI 10.1134/S0015462811050085 Authors A. V. Egorov G. G. Tsypkin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    Three variants of the startup of an axisymmetric convergent-divergent nozzle are considered with the static pressures at the entry and exit of the nozzle being the same at the beginning of the process. The subsonic startup corresponds to open nozzle acceleration in air. The supersonic startup simulates the sudden opening of a cover at the nozzle inlet under supersonic flight conditions. A successful nozzle startup with the formation of steady supersonic flow along the whole channel is realized in the third variant of supersonic startup with gas injection through a small region of the wall of the divergent nozzle section. The investigation is performed numerically, on the basis of the Euler equations for axisymmetric gas flows. Content Type Journal Article Pages 775-781 DOI 10.1134/S0015462811050115 Authors Yu. V. Tunik Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    An approach to the solution of the two-dimensional Navier-Stokes equations on triangular unstructured grids is considered. The method is based on the key idea of the Godunov scheme, namely, the advisability of solving the Riemann problem of arbitrary discontinuity breakdown. In the calculations the derivatives with respect to space are approximated with both the first and the second order. However, as distinct from the conventional Godunov method, in calculating the fluxes across the cell boundaries the Riemann problem is solved using the Advection Upstream Splitting Method (AUSM). The concepts involved in the AUSM scheme are discussed. The solution of the discontinuity breakdown problem obtained within the framework of this approach is compared with the results obtained using the Godunov method. Numerical solutions of some problems of viscous and inviscid perfect-gas flows obtained on unstructured grids of different fineness and those obtained on structured grids are also compared. The effect of the spatial approximation order on the accuracy of numerical solutions is studied. Content Type Journal Article Category Supplement: Vychislitel’naya Mekhanika Sploshnykh Sred (Computational Continuum Mechanics) Pages 809-825 DOI 10.1134/S0015462811050140 Authors D. V. Kotov S. T. Surzhikov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    The linear problem of convective instability near the surface of a stratified two-component liquid medium (for example, saline sea water) is considered. The specificity of the problem consists in need to take into account both background stratifications and a difference in the transfer coefficients and boundary conditions for two substances (heat and admixture concentration), as well as the thermocapillary effect. It is shown that there is a vast region of monotonic instability in the medium stable in accordance with all criteria previously known. The two-component nature of the medium makes the development of anomalously intense perturbations deeply penetrating into the hydrostatically stable medium possible. A dimensionless instability criterion is formulated and neutral curves are calculated. Content Type Journal Article Pages 699-706 DOI 10.1134/S0015462811050036 Authors L. Kh. Ingel Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    A retrospective problem consisting in the reconstruction of an apriori unknown initial state of a highly viscous, incompressible fluid from its known final state is studied. The fluid dynamics model in the Boussinesq approximation is described by the equations of Stokes, incompressibility, and thermal balance with the corresponding initial and boundary conditions. The problem is solved in the inverse direction of time using a new, specially developed iterative method which makes it possible to reduce the original unstable problem to a set of stable problems. The algorithm based on this method is realized on a parallel computer using the OpenFOAM package for engineering calculations. The computational efficiency of the algorithm is analyzed. Content Type Journal Article Category Supplement: Vychislitel’naya Mekhanika Sploshnykh Sred (Computational Continuum Mechanics) Pages 835-842 DOI 10.1134/S0015462811050164 Authors I. A. Tsepelev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    The conditions of existence of a stable rupture in a horizontal ferrofluid layer on a liquid base are determined experimentally. The characteristics of ruptures of ferrofluid, kerosene, and water layers are compared to estimate the effect of different physicochemical properties of the liquid pairs used. It is found that switching-on a magnetic field parallel to the ferrofluid layer surface initiates deformation of the rupture and its simultaneous motion along the field. The dependences of the geometric parameters of the rupture on the magnetic field strength and the magnetic susceptibility of ferrofluid are established. The possibility of closing the stable rupture under the action of a magnetic field is demonstrated. Content Type Journal Article Pages 707-714 DOI 10.1134/S0015462811050048 Authors K. A. Bushueva K. G. Kostarev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    Experiments on the determination of the trajectories and orientations of ellipsoids freely floating up in a viscous fluid under the gravity action are described. Content Type Journal Article Pages 715-725 DOI 10.1134/S001546281105005X Authors Yu. K. Bratukhin I. Yu. Makarikhin S. O. Makarov K. A. Rybkin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    The problem of static loading of the eye cornea by a flat stamp modeling an applanation tonometer is solved. The eye is treated as the composition of a soft shell (cornea) and an elastic element, which includes the sclera and tissues surrounding it, under the action of an internal pressure. The function determining the dependence of the intraocular volume on the intraocular pressure and the load applied is calculated. It is shown that over a wide range of physiologically admissible parameter values the dependences of the intraocular volume on the pressure at a fixed load and of the pressure on the load at a fixed volume are almost linear. The relationship between the coefficients determining these dependences is investigated. The possibility to find the elastic characteristics of the individual eye from a limited number of measurements is discussed. Content Type Journal Article Pages 673-683 DOI 10.1134/S0015462811050012 Authors I. N. Moiseeva, Institute of Mechanics, Moscow State University, Moscow, Russia A. A. Stein, Institute of Mechanics, Moscow State University, Moscow, Russia Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    Using an asymptotic small-perturbation method, the flow around a strongly heated sphere at small Reynolds numbers Re ≪ 1 is considered with account for thermal stresses in the gas in the higher-order approximations, beyond the Stokes one. It is assumed that the value of the Prandtl number Pr is arbitrary and the temperature dependence of the viscosity is described by a power law with an arbitrary exponent. In the O (Re 2 ) and O (Re 3 ln(Re)) approximations, the drag force of a heated sphere is found over a wide range of the ratios of sphere’s temperature to the gas free-stream temperature T W / T ∞ . The limits of applicability of the first (in Re) approximation are investigated, including the negative-drag effect, attributable to the action of the thermal stresses. The results are compared with numerical calculations of the flow around a hot sphere. The limits of applicability of the approximations found are examined. Similar results are obtained for the standard Navier-Stokes equations in which the thermal stresses are neglected. Content Type Journal Article Pages 794-808 DOI 10.1134/S0015462811050139 Authors V. Yu. Aleksandrov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    The negative corona discharge in a hot turbulent air jet is investigated experimentally and theoretically, within the framework of a discrete dischargemodel making it possible to determine its frequency characteristics. When using the discrete dischargemodel, in contrast to describing the discharge as a continuous electric charge motion, it is assumed that, like in the experiment, the charge is transferred within the discharge space by separate portions. This was noted in an old monograph [1]. Some results on this subject were presented in [2]. In [3], a discrete model of the corona discharge was developed and realized numerically for a system of spherical electrodes in the presence of a hydrodynamic source at the center of the system. In the present study, certain results earlier obtained are generalized. An approximate, using similarity and dimensional methods, model is proposed for the negative corona discharge in a hot turbulent air jet and the frequency discharge characteristics under these conditions are investigated experimentally. Content Type Journal Article Pages 726-735 DOI 10.1134/S0015462811050061 Authors A. B. Vatazhin D. A. Golentsov V. A. Likhter E. K. Kholshchevnikova Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    A system of electrogasdynamic final-control elements (plasma actuators) intended for increasing the stability of the boundary layer on a swept wing is considered. The actuators operate on the basis of dielectric barrier discharge. The physical model of the discharge in the air is formulated in the diffusion-drift approximation with account for three charged ionized-gas components, namely, electrons, positive nitrogen and oxygen ions, and negative oxygen ions. The boundary conditions on the dielectric surface are formulated with account for finite desorption and recombination rates of the charged particles. The numerical modeling for an actuator system of particular geometry shows a slight influence of the negative ions on the bulk force generated by each actuator. The main actuator parameters, such as the total longitudinal force and heat release, are shown to considerably depend on the dielectric permeabilities of insulation layers separating the external and internal electrodes. The expressions are derived that make it possible to estimate the gas velocity induced by the bulk force action of the dielectric barrier discharge on the gas flow. Content Type Journal Article Pages 764-774 DOI 10.1134/S0015462811050103 Authors A. P. Kuryachii D. A. Rus’yanov V. V. Skvortsov S. L. Chernyshev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 5

Description:    The gravity field and vibration effect on the flow of a viscoplastic fluid layer along an inclined solid surface is investigated. The rheological properties of the fluid are described using the Williamson equation. The vibrations are shown to have a considerable effect on the fluid layer flow intensity and direction; in particular, they generate a considerable mean fluid flow even in the cases in which the fluid is at rest in the absence of the vibrations. Content Type Journal Article Pages 24-33 DOI 10.1134/S0015462811010030 Authors D. V. Lyubimov A. V. Perminov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The linear hydrodynamic stability of the plane Couette flow of a suspension with a finite volume fraction of the particles is considered. The two-phase medium flow is described within the framework of the model of mutually penetrating continua which allows for the finiteness of the volume occupied by the particles. In the main flow the phase velocities are the same, while gravity is not taken into account. The stability of disperse flows with both uniform and nonuniform particle distributions is studied. The linearized system of the equations of suspension motion with the no-slip boundary conditions imposed on solid walls is reduced to the eigenvalue problem for an ordinary differential fourth-order equation in the stream function. The eigenvalues are sought using the orthogonolization method. The parametric investigation of the stability characteristics of the disperse flow is performed. It is shown that in the case of the uniform spatial distribution of the particles in the main flow, the presence of an admixture in the flow leads to a slight variation in the wave decay rates, while the flow remains stable for any permissible combinations of the dimensionless governing parameters. In the case of nonuniform distribution of inclusions the flow loses stability already for low Reynolds numbers on a wide range of the dimensionless governing parameters. Content Type Journal Article Pages 64-71 DOI 10.1134/S0015462811010078 Authors S. A. Boronin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The possibility to relate the nature of the forced expiration tracheal sounds with the sound radiation by a separated flow that arises in the region of dynamic trachea constriction during forced expiration is investigated. A mathematical model of forced expiration is used for estimating. The calculated form of the time dependence of the sound intensity during forced expiration qualitatively corresponds to the experimental dependence obtained experimentally for normal subjects. The results should be taken into account in the physical explanation of tracheal sound generation mechanisms and in the justification of using the tracheal sound characteristics in the diagnostics of human lung pathologies. Content Type Journal Article Pages 16-23 DOI 10.1134/S0015462811010029 Authors A. I. Dyachenko G. A. Lyubimov I. M. Skobeleva M. M. Strongin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The solution of the inverse boundary-value problem for a wing airfoil with slot air suction from the outer flow on its upper surface and control jet injection from its rear is generalized to include the case of the flow around such an airfoil in the presence of a screen. The complications due to the double connectivity of the flow region are overcome by means of introducing a fictitious flow beneath the screen. The solution is constructed using a numerical-analytical iteration procedure. Formulas for recalculating the aerodynamic characteristics and the velocity distribution over the airfoil surface to different flight regimes and suction-injection device operation regimes are derived. The effect of the injected jet energy, the airfoil-screen spacing, and the slope of the rectilinear airfoil undersurface on the aerodynamic and geometric characteristics of the airfoil, namely, the shape and the lift coefficient, is studied. The reliability of the results is confirmed by the results of calculations using the Fluent program. Content Type Journal Article Pages 34-43 DOI 10.1134/S0015462811010042 Authors R. A. Gaifutdinov N. B. Il’yinskii Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    Three-dimensional large eddy simulation is used to solve the problem for a homogeneous forest canopy. The development of the Kelvin-Helmholtz instability above the canopy leads to the formation of coherent structures in the atmosphere flow, which are reproduced in the calculations. The statistical characteristics of the flow obtained from the numerical modeling are compared with experimental data. The passive admixture transfer from the canopy to the clean atmosphere is studied for two cases, namely, for constant and variable coupled concentration of the impurity in the canopy. Content Type Journal Article Pages 138-147 DOI 10.1134/S0015462811010169 Authors K. A. Gavrilov D. Morvan G. Accary D. V. Lyubimov S. Meradji O. A. Bessonov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    Detonation combustion of hydrogen-air mixtures entering an axisymmetric convergent-divergent nozzle at a supersonic velocity is considered. The nozzle geometry does not ensure gas self-ignition; for this reason, forced ignition is used, which, under certain conditions, leads to the formation of stationary detonation combustion in the case of both uniform and nonuniform hydrogen distribution at the channel entry. The nonlinear problem of the stability of these combustion regimes against periodic disturbances of the hydrogen concentration in the oncoming flow is numerically solved. The study is performed on the basis of the two-dimensional gasdynamic Euler equations for a multicomponent reacting gas. A detailed model of chemical reactions is used. Content Type Journal Article Pages 115-121 DOI 10.1134/S0015462811010133 Authors Yu. V. Tunik Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    In a plane formulation, we consider a viscous-fluid jet flowing out of a rectangular channel and interacting with a horizontal solid substrate surface in the presence of gravity. The mathematical problem is formulated within the creeping flow approximation. For the numerical solution, a boundary-element method is used. The kinematic parameters of the jet and the evolution of the free surface are studied for different values of governing parameters. The critical values of the distance from the channel outlet to the solid wall are found. For the heights, greater than the critical value, the jet loses stability, which is manifested in the periodic buckling of the jet. A flow regime characterized by damped oscillations is described. Content Type Journal Article Pages 44-50 DOI 10.1134/S0015462811010054 Authors M. A. Ponomareva G. R. Shrager V. A. Yakutenok Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The motion of an inertial dispersed admixture near a plane cylinder immersed in a steady-state hypersonic dusty flow in the presence of an oblique shock wave interacting with the bow shock is considered. It is assumed that the free-stream particle mass concentration is small and the particles do not affect the carrier flow. The III and IV shock wave interaction regimes are considered. The gas flow parameters in the shock layer are calculated from the numerical solution of the full Navier-Stokes equations for the perfect gas. A TVD second-order finite-difference scheme constructed on the basis of a finite volume method is used. For calculating the dispersed-phase parameters, including the concentration, the full Lagrangian method is used. On a wide range of variation of the particle inertia parameters, the patterns of the particle trajectories, velocity, concentration, and temperature in the shock layer are studied. The possibility of aerodynamic focusing of the particles behind the shock wave intersection point and the formation of narrow beams with a high particle concentration is revealed. These beams impinge on the cylinder surface and result in a sharp increase in the local heat fluxes. The maximal possible increase in the heat fluxes caused by the particles colliding with the cylinder surface is estimated for the flows with and without the incident oblique shock wave. Content Type Journal Article Pages 51-63 DOI 10.1134/S0015462811010066 Authors I. V. Golubkina A. N. Osiptsov V. I. Sakharov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    Within the framework of the fractal mobile-immobile medium model describing non-Fickian effects occurring in admixture seepage due to particle adhesion to the solid matrix, an expression for the admixture flux is derived. Flow discretization intended for finite-difference calculations is proposed and used as a basis for a conservation-law scheme for solving the model equations with account for admixture sources. Several one-dimensional test problems of admixture propagation in an imposed seepage flow are solved using the approach developed. Content Type Journal Article Pages 148-157 DOI 10.1134/S0015462811010170 Authors B. S. Maryshev T. P. Lyubimova D. V. Lyubimov M. -C. Néel Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The propagation of acoustic waves in two-fraction mixtures of gas with vapor, droplets and solid particles of different materials and sizes in the presence of phase transitions is investigated. A mathematical model is presented, the dispersion and wave equations are obtained, and the dispersion curves are calculated. The relative sonic velocity and the attenuation decrement on the wave length are analyzed as functions of the oscillation frequency for an “air-vapor-liquid droplet-sand particle” mixture. Using the fast Fourier transform, the propagation of pulse disturbances in the two-fraction disperse systems is calculated. Content Type Journal Article Pages 72-79 DOI 10.1134/S001546281101008X Authors D. A. Gubaidullin A. A. Nikiforov E. A. Utkina Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The gas flow in the zone of interaction between an oblique shock and a centered isentropic rarefaction wave is studied using the direct statistical simulation method for solving the Boltzmann equation. The data of calculations of the shock and rarefaction wave structures, flow fields, and streamlines are given for the free-stream Mach number M ∞ = 6, 4 and 2. The formation of the interaction zone is simulated by a gas flow past a double-plane wedge in which the break of the generating line leads to formation of the centered isentropic rarefaction wave. The results of calculations of this flow in solving the Boltzmann equation are given in the Euler approximation. Content Type Journal Article Pages 122-130 DOI 10.1134/S0015462811010145 Authors V. N. Gusev A. I. Erofeev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The paper outlines the theoretical studies of flows and heat transfer in near-critical media in the vicinity of the critical thermodynamic point under microgravity and terrestrial conditions. The criteria determining the characteristics of thermal gravitational convection and thermal acoustics complicated by the adiabatic compression effect, the distinctive features of convection generation, and the hierarchy of non-Boussinesq mathematical models and the their calibration on the basis of the Boussinesq model are discussed. Content Type Journal Article Pages 1-15 DOI 10.1134/S0015462811010017 Authors V. I. Polezhaev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The interaction of disturbances in the compressible boundary layers on both impermeable and porous surfaces is considered in the linear and nonlinear approximations (weakly-nonlinear stability theory) in the presence of surface cooling. The regimes of moderate (Mach number M = 2) and high (M = 5.35) supersonic velocities are considered. It is established that surface cooling leads a considerable change in the linear evolution of the disturbances, namely, the first-mode vortex disturbances are stabilized, whereas the second-mode acoustic disturbances are destabilized, the variation degree being determined by the temperature factor. A porous coating used for controlling flow regimes influences the stability in the opposite fashion. For vortex waves the nonlinear interactions in three-wave systems at M = 2 are considerably attenuated in the presence of cooling. It might be expected that the cooling of the surface can delay the laminar regime for M = 2 and accelerate transition to turbulence for M = 5.35. Content Type Journal Article Pages 399-411 DOI 10.1134/S0015462811030057 Authors S. A. Gaponov N. M. Terekhova Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    The pairwise hydrodynamic and electrostatic interaction between micrometer-sized water droplets at small distances between them due to their evaporation and the presence of an electric charge on at least one of them is considered. The velocities of the steady-state motion of charged water drops with radii of 1 and 10 µm evaporating in air are calculated. It is shown that at small distances between the drops the joint action of hydrodynamic attraction and polarization interaction, always of attraction type, favor the coalescence of the drops (or drops and solid particles), leading to the displacement of the maximum of the function of drop distribution over size to the region of greater sizes and the gravity sedimentation of large drops. At large distances between the drops, when the short-distance hydrodynamic and polarization attractive forces become smaller than the long-distance Coulomb repulsion forces between likely charged particles, this distance tends to increase. These phenomena give a microphysical explanation to the phenomenon of electrostatic blooming in optically dense smokes and mists. Content Type Journal Article Pages 437-443 DOI 10.1134/S0015462811030100 Authors S. I. Grashchenkov A. I. Grigoryev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    The stability of boundary flows occurring near an inclined plane or a cylinder executing longitudinal periodic oscillations is studied within the framework of a system of embedded models (homogeneous fluid, stratified viscous fluid, and fluid in the presence of diffusion). It is shown that in a stratified fluid the resonance boundary-oscillation frequency, at which the boundary layer thickness increases without bound, exists not only in the problem with a plane boundary but also in the case of oscillations of an inclined cylinder. Taking diffusion into account leads to the boundary layer splitting into viscous and diffusion sublayers with considerably different thicknesses and properties. Nevertheless, the fact itself of the existence of the resonance oscillation frequency turns out to be stable and the resonance takes place also in the models of stratified flows with allowance for diffusion. Content Type Journal Article Pages 835-842 DOI 10.1134/S0015462810060013 Authors V. G. Baidulov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    Using a coloring method, the pattern of the transport of a compact spot of markers in a composite vortex created by a uniformly rotating disk, which is located on the bottom of a cylindrical tank, is investigated. The markers were formed by droplets of an aqueous solution of uranyl or ink, which fell down on the free surface of the fluid. In a quiescent fluid, the spot of the markers was transformed into a slowly sinking cascade of vortices. The markers introduced at the center of the cavity on the composite-vortex surface formed a spiral branch. For a non-central introduction of the markers, two spiral branches were formed, one growing in the direction of the fluid rotation and the other growing in the direction, opposite to the rotation. The markers penetrate into the interior of the composite vortex along isolated cylindrical surfaces. The geometrical parameters of the flow are presented. Content Type Journal Article Pages 843-858 DOI 10.1134/S0015462810060025 Authors E. V. Stepanova Yu. D. Chashechkin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    Heterogeneous water-air mixture flows in the presence of capillary forces are investigated. It is shown that for moderate pressure and temperature gradients the distribution of the water saturation function can be determined from a nonlinear differential equation with a coefficient dependent on the porous medium parameters, the water viscosity, and the capillary pressure. The water-air mixture flow behind the ice melting front is considered. Content Type Journal Article Pages 942-951 DOI 10.1134/S0015462810060128 Authors G. G. Tsypkin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    On the basis of the methods of the theory of codimension-two bifurcations of cylindrically symmetric hydrodynamic flows, using computer calculations, the motions of a fluid between rotating permeable coaxial cylinders are investigated near the intersection of the bifurcations corresponding to the origin of a stationary regime of the Taylor vortex type and self-oscillations with azimuthal waves. Content Type Journal Article Pages 880-888 DOI 10.1134/S0015462810060050 Authors V. V. Kolesov M. N. Romanov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    The velocity fields and the parameters of a finite-width liquid film moving along the bottom of a mini- and a microchannel under the action of a gas flow are calculated. The investigations are performed for different levels of gravity. It is found that the thin liquid film distorts the velocity field in the gaseous phase. In contrast to the minichannel flow, in the microchannel the film surface is not leveled with increase in the gravity force. Content Type Journal Article Pages 924-929 DOI 10.1134/S0015462810060104 Authors M. V. Bartashevich O. A. Kabov V. V. Kuznetsov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    The noise effect on the stability of equilibrium in systems with slowly varying parameters is investigated. With reference to some model examples and for the case of convection in a closed region in the presence of gravity modulation it is shown that taking the noise into account is of key importance at low modulation frequencies, since it can even change the sign of the effect: modulation leads to equilibrium stabilization in the absence of the noise and to destabilization in its presence. Content Type Journal Article Pages 859-865 DOI 10.1134/S0015462810060037 Authors D. V. Lyubimov T. P. Lyubimova B. S. Maryshev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    On the basis of the molecular dynamics simulation method the trajectories of hydrogen molecules reflected from a graphite surface are calculated with account for its structure and the thermal motion of carbon atoms. The velocity distribution after the reflection is obtained as a function of the velocity magnitude and direction of the incident molecules and the surface temperature. In the case of heat transfer between symmetric surfaces in the free-molecular regime, the energy accommodation coefficients are calculated for hydrogen on graphite as functions of the gas and wall temperatures. The results obtained are in agreement with experimental data. Content Type Journal Article Pages 975-981 DOI 10.1134/S0015462810060153 Authors V. L. Kovalev A. N. Yakunchikov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    The breakup of liquid bridges under the action of capillary forces is used for studying the rheology of suspensions under stretching. The experiments were performed with suspensions of finegrained (3–30 µm) sand in glycerin for sand volume fractions up to 0.465. The bridge thinning process was registered using an electro-optical measuring device and videofilming. The results were analyzed on the basis of a theory developed earlier for the thinning of a liquid bridge under the action of capillary forces. It is found that, for fairly slow stretching realized in the initial stage of the thinning, the rheological behavior of the suspensions considered agrees with the model of a Newtonian viscous fluid. Along with this, the measured effective viscosity of the suspension turned out to be approximately two-fold greater than the suspension viscosity under shear. The origin of this discrepancy is analyzed. With increase in the stretching rate, in the final stage of the thinning, the weakening of the suspension occurs, which is manifested in the formation of a local rapidly thinning neck in the bridge, similar to that observed in the breakup of plastic materials. Content Type Journal Article Pages 952-964 DOI 10.1134/S001546281006013X Authors A. N. Alexandrou A. V. Bazilevskii V. M. Entov A. N. Rozhkov A. Sharaf Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    An unsteady process of matter extraction from a porous body is considered. The body is modeled by a system of semi-infinite capillary tubes connected with a system of closed-end channels, so that the matter transfer rate in the flow (large-size channels) is composed of two components. The first is a constant velocity component, while the second is a time-periodic addition to the former component, which is assumed to have a small amplitude. Analytical dependences for the matter concentration in the porous body are derived both in the main approximation and with account of the correction for the periodic forcing of the system. Content Type Journal Article Pages 930-941 DOI 10.1134/S0015462810060116 Authors A. I. Moshinskii Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    In numerical calculations of vortex evolution the effect of nonlinear terms related with the parametrization of the Ekman bottom boundary layer in the barotropic vortex equation is demonstrated. It is shown that taking these terms into account can lead to the coalescence of mesovortices formed as a result of the barotropic-instability-induced breakdown of an annular vortex, as distinct from the conventional parametrization of the bottom friction by a linear term, when a symmetric system of mesovortices, or the so-named vortex crystal, is formed. Content Type Journal Article Pages 905-908 DOI 10.1134/S0015462810060086 Authors N. P. Malikova M. S. Permyakov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    The state of a gas in the neighborhood of an infinitely thin permeable membrane whose sides have different temperatures is investigated. The dimensions of orifices in the membrane are much less than the mean molecular free path. The gas temperatures and pressures on both sides of the membrane outside the nonlinear Knudsen layers adjacent to the membrane and variations in these parameters in the Knudsen layers are determined. The investigation is carried out by solving the Boltzmann kinetic equation by means of the direct simulation Monte-Carlo method. The semiempirical Maxwell method is also used for consideration of the molecular flows on both sides of the membrane when analyzing the temperatures and the pressures. The solution to the nonlinear problem is compared with the solution to the linear problem of a jump temperature near a nonisothermal porous body obtained earlier. Content Type Journal Article Pages 965-974 DOI 10.1134/S0015462810060141 Authors A. I. Erofeev O. G. Friedlender Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    The effect of an ultrasonically-absorptive coating on laminar-turbulent transition on cones with different nose bluntnesses is experimentally investigated. The experiments were performed with a cone with the semi-vertex angle of 7° set at zero incidence in the Mach 8 flow for three Reynolds numbers. A material with a chaotic micropore structure was used as the ultrasonically-absorptive coating. One side of the model, along its generator, was coated with the porous material, while the second represented a rigid surface. The laminar-turbulent transition location was determined from the results of heat flux distribution measurements. The heat flux fluctuations were also measured on the model surface. It was found that the laminar region length increased with an increase in the bluntness radius. The ultrasonically-absorptive coating with a chaotic microstructure effectively stabilizes the boundary layer for all bluntness radii considered, increasing the laminar region length by 30 to 85%. Content Type Journal Article Pages 898-904 DOI 10.1134/S0015462810060074 Authors D. A. Buntin S. V. Lukashevich A. A. Maslov A. N. Shiplyuk Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    The behavior of a light cylindrical body of circular cross-section under horizontal vibration in a rectangular cavity filled with a fluid is experimentally investigated. At critical vibration intensity the body is repelled from the upper side of the cavity and takes up a stable suspended position, in which the gravity field is balanced by the vibrational repulsive force, executing longitudinal oscillations. As the vibrations are intensified, the gap between the cylinder and the wall widens. A new form of instability, namely, the excitation of the tangential motion of the body along the vibration axis, is found to exist on the supercritical range. The cylinder is at a finite distance from the upper side of the cavity and the tangential motion is due to the loss of symmetry of the oscillating motion. The transition of the cylinder to the suspended state and its return to the wall, as well as the excitation of the average longitudinal motion and its cessation, occur thresholdwise and have a hysteresis. The body dynamics are studied as a function of the dimensionless vibration frequency. Content Type Journal Article Pages 889-897 DOI 10.1134/S0015462810060062 Authors A. A. Ivanova V. G. Kozlov V. D. Shchipitsyn Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    Thermocapillary flows in an infinitely long liquid cylinder surrounded by a coaxial gas layer with a controlled flow rate and the stability of such flows are investigated. In the layers a constant axial temperature gradient is maintained. An exact solution of the equations of motion describing the steady-state flow in this two-phase system is derived. Possible flow regimes and their stability in the linear approximation are studied. It is shown that in the liquid phase the thermocapillary flow can be completely stopped by the gas flow at the expense of the interaction between mechanical stresses at the interface. The results obtained indicate the possibility of controlling thermocapillary flows and their stability by means of gas flows. Content Type Journal Article Pages 866-879 DOI 10.1134/S0015462810060049 Authors I. I. Ryzhkov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    The purpose of the study is to present an explicit self-consistent algebraic model of the Reynolds stresses (nonlinear turbulent viscosity) for calculating two-phase flows laden with small heavy particles. The model is tested by means of comparing with the results of the solution of a system of differential equations for all components of the Reynolds stresses and the data of direct numerical calculations in a homogeneous shear flow with particles. Content Type Journal Article Pages 909-923 DOI 10.1134/S0015462810060098 Authors V. M. Alipchenkov L. I. Zaichik Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 45 Journal Issue Volume 45, Number 6

Description:    The interaction between gravity convection and Marangoni convection in a horizontal rectangular channel filled with a liquid containing a surfactant and a drop of another liquid is numerically investigated. For large Schmidt numbers the occurring oscillatory regime of solutal convection is analyzed. In the model with a surface phase the effect of the adsorption and desorption processes on the convective flow structure is determined. The corresponding initial and boundary value problem is solved using a difference method. Content Type Journal Article Pages 131-137 DOI 10.1134/S0015462811010157 Authors R. V. Birikh R. N. Rudakov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The formation of differential rotation in a rotating cylindrical layer heated locally is investigated numerically. In the simulations performed, geometric parameters (the layer height and radius and the heating area), the kinematic viscosity, the heat flux, and the angular velocity of the cylinder were varied. Integral characteristics of differential rotation are obtained. The dependence of the relative angular momentum of the layer on various parameters is investigated. Content Type Journal Article Pages 158-168 DOI 10.1134/S0015462811010182 Authors A. N. Sukhanovsky Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The deformation and rupture of a liquid film, suspended between two solid walls, under the action of a localized thermal load is considered. For studying this process, a two-dimensional model is used, which describes the motion of a thin layer of a viscous non-isothermal liquid under microgravity conditions. For modeling the dynamics of the liquid, the Navier-Stokes equations in the “vorticity—stream function” variables are used. A numerical analysis of the influence of thermal loads on the deformation and the mechanism of the rupture of freely suspended films is performed. Is is shown that for a certain width of the thermal beam acting on the film free surface the rupture of the film may occur with the formation of a droplet. The results of the solution of model problems are presented. Content Type Journal Article Pages 108-114 DOI 10.1134/S0015462811010121 Authors A. S. Ovcharova Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The results of numerical investigations of the problem of flow through a porous reservoir in the process of its water flooding with addition of a sediment-forming component are given. The mathematical model is based on the mass conservation laws for each of the considered phases and components supplemented with the equations of motion and constitutive relations necessary to close the system of equations. In solving the problem, an empirical dependence of the sediment formation intensity on the content of the sediment-forming component in the aqueous solution with allowance for variation in the effective porosity of the medium is used. The main features in solving the sediment-formation problem are distinguished using the empirical dependence and a contrastive analysis of the effect of choosing this dependence on the solution results is carried out. It is shown that the neglect of the experimental results in the mathematical formulation can lead to not only unjustified overestimated results in realizing the method but also give a distorted pattern of the entire process of sediment formation in fluid flow through a water-flooded porous reservoir. Content Type Journal Article Pages 90-96 DOI 10.1134/S0015462811010108 Authors G. R. Idrisova L. A. Kovaleva M. V. Mavletov A. A. Musin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The stability of vertical steady-state flows in geothermal water-above-steam systems is considered. The steam compressibility and the capillary forces on a phase interface are taken into account. A domain of the physical parameters of the geothermal system, where vertical steady-state flows exist, is found. The linear stability of these flows is analyzed, namely, the dispersion relation is obtained, the stability diagram is constructed, and the possible types of loss of stability are found using asymptotic and numerical methods. The effect of the steam compressibility and other physical parameters on vertical steady-state flows and their stability is analyzed. Content Type Journal Article Pages 97-107 DOI 10.1134/S001546281101011X Authors V. E. Odintsova Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    A model of nonisothermal binary mixture flow through a porous medium, applicable over a wide range of thermobaric conditions, including temperatures higher than the critical mixture temperature, is proposed. A nonclassical approach used for modeling the mixture properties makes it possible to uniformly describe its single-, two- and three-phase thermodynamic equilibria and the corresponding flows under sub- and supercritical thermodynamic conditions. The wide application of thermodynamic methods to determining the real mixture properties leads to a nonstandard mathematical model in which the conservation laws are closed with a conditional extremum problem, not finite or differential equations. A dispersion analysis of the model equations is performed and the characteristic velocities in zones of different mixture phase states are determined. Content Type Journal Article Pages 80-89 DOI 10.1134/S0015462811010091 Authors A. A. Afanasyev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 1

Description:    The problem of viscoelastic fluid flow in a convergent-divergent channel is considered. A mathematical model and the results of numerical investigations are presented. A model of the differential type is used to describe the rheological properties of viscoelastic fluids. A comparative analysis of the flow parameters of generalized Newtonian and viscoelastic fluids in the channels considered is carried out on the basis of the results of numerical calculations. Content Type Journal Article Pages 412-417 DOI 10.1134/S0015462811030069 Authors E. K. Vachagina G. R. Galiullina G. R. Khalitova Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    Numerical modeling of the temperature distribution, the velocity fields, and the dopant (Ge:Si) concentration during germanium crystal growth by the floating zone method under microgravity is carried out. The time-dependent three-dimensional problem is solved using the difference method. The deformations of the free surface of a liquid bridge and of crystallization and melting fronts are neglected. The relaxation of axisymmetric flow regimes to a steady state is observed, whereas the unsteadiness of three-dimensional flows develops with time. Content Type Journal Article Pages 479-489 DOI 10.1134/S0015462811030148 Authors T. P. Lyubimova R. V. Skuridin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    The interaction between a viscous incompressible fluid layer and walls of a channel formed by two concentric discs moving perpendicularly to their planes due to vibration of the base on which the channel is mounted is investigated. The case of two absolutely rigid discs with elastic suspension and the case in which one of the discs is an elastic plate with the rigid restrain on the edges are considered. The velocity and pressure distributions over the fluid and the laws of motion of the walls and their frequency characteristics which make it possible to determine the resonance vibration frequencies of the mechanical system considered are found. Content Type Journal Article Pages 375-388 DOI 10.1134/S0015462811030033 Authors L. I. Mogilevich V. S. Popov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    New results of the series of experimental and numerical investigations of the self-oscillatory regimes of plane vertical jet spouting from beneath the free surface of a heavy incompressible fluid in reservoirs of limited dimensions are presented. The experiments were performed on a rectangular-in-plan setup with near-bottom regime of fluid discharge. For several widths of the near-bottom orifices in the end walls of the setup the dependence of the self-oscillation period on the jet flow rate is studied. A considerable difference of these dependences from those earlier obtained in the case of the spouting with fluid discharge over a weir is found to exist. On certain ranges of control parameters it is established that the fountain self-oscillation periods are similar in value to those of natural oscillations of standing waves in the setup. A fairly narrow jet velocity range is revealed on which a hysteresis effect, that consists in the difference between the flow-rate-dependences of the self-oscillation period with gradual increase or decrease in the flow rate, is observable. The results of numerical calculations carried out using the STAR-CD software package are in good agreement with the experimental data. Content Type Journal Article Pages 418-424 DOI 10.1134/S0015462811030070 Authors V. P. Karlikov S. L. Tolokonnikov O. V. Trushina Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    The wave processes in an actively-dissipative dispersive medium described by a nonlinear evolutionary fourth-order equation are considered. With the use of traveling-wave variables analytical solutions in the form of solitary waves and kinks are obtained for certain combinations of the problem parameters. The stability of the exact solutions obtained is studied. The processes of formation of stable periodic oscillations are considered for different model parameters. The control parameter ranges, on which periodic structures can be formed, are determined. Content Type Journal Article Pages 425-432 DOI 10.1134/S0015462811030082 Authors N. A. Kudryashov P. N. Ryabov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    The instability of supersonic underexpanded submerged air jet outflow from a nozzle with a central cone in the form of two convergent interlaced spirals is described. A technique for controlling this structure by means of extending the central cone streamwise is proposed. It is shown that the central cone position makes it possible to control the gas outflow and to go over from the Mach reflection regime to the regime of wave spiral and gaseous phase condensation, which before were not observable. The results of the measurements of the dynamic head of jets issuing from the nozzle with and without the central cone are presented. Content Type Journal Article Pages 433-436 DOI 10.1134/S0015462811030094 Authors Kh. Khasanov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    A three-dimensional computer model of nonequilibrium aerophysics of the spacecraft entering in the Martian atmosphere and landing on the planet surface is presented. The model is based on the system of Navier-Stokes equations, the energy conservation equation in the form of the Fourier-Kirchhoff equation for the translational temperature, the system of equations of vibrational kinetics for six vibrational modes of N 2 , O 2 , CO 2 and CO molecules, and the equation of selective thermal radiation transfer in the multigroup spectral approximation. The results of two-dimensional and threedimensional calculations of the nonequilibrium flowfield and the convective and radiative heating of the EXOMARS spacecraft surface are presented. The calculations are performed on regular multiblock curvilinear grids using the NERAT-2D and NERAT-3D computer codes developed in the Institute for Problems in Mechanics of the Russian Academy of Sciences. Content Type Journal Article Pages 490-503 DOI 10.1134/S001546281103015X Authors S. T. Surzhikov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    The hypersonic rarefied gas flow over blunt bodies near the symmetry plane is investigated for the regime transitional from continuum to free-molecular. Three rarefied gas flow regimes are considered depending on the relationship between the determining parameters of the problem. For all regimes, at small Reynolds numbers, asymptotic solutions of the thin viscous shock layer equations near the symmetry plane of blunt bodies are obtained in the form of simple analytical expressions for the heat transfer, skin friction and pressure coefficients as functions of the gas-dynamic parameters of the free-stream flow and the geometric parameters and temperature of the body. With decrease in the Reynolds number these coefficients approach their values in free-molecular flow (with the accommodation coefficient equal to unity). From comparison with the data calculated using the direct simulation Monte Carlo method, the accuracy and applicability limits of the analytical solution are estimated. Content Type Journal Article Pages 444-455 DOI 10.1134/S0015462811030112 Authors I. G. Brykina Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    The state of the art and the recent advances in cosmic gasdynamics are reviewed with emphasis placed on the problems of the solar wind/interstellar medium interaction and the solar wind flow past cometary atmospheres. Certain new problems that need to be solved are formulated and discussed. Content Type Journal Article Pages 341-362 DOI 10.1134/S001546281103001X Authors V. B. Baranov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    Unsteady viscous incompressible flows in a spherical layer due to an increase in the rotation velocity of the inner sphere with constant acceleration are investigated. The acceleration starts at the Reynolds numbers Re corresponding to a stationary flow and ends at Re higher than the stability limit of the stationary flow, whereupon the rotation velocity of the inner sphere remains constant. The outer sphere is fixed and the spherical layer thickness is equal to the inner sphere radius. The inner sphere acceleration effect is studied on both the formation of one of two possible secondary-flow structures after the acceleration has been stopped, namely, traveling azimuthal waves with wavenumbers of 3 or 4, and on the change in the flow structure during the action of the acceleration. It is shown that not only an increase in the acceleration but also a decrease in Re corresponding to the acceleration onset can lead to an increase in the deviation of the instantaneous velocity profiles from their stationary values and can be accompanied by a variation in the secondary flow wavenumber. Content Type Journal Article Pages 363-374 DOI 10.1134/S0015462811030021 Authors D. Yu. Zhilenko O. É. Krivonosova Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    Comprehensive numerical modeling of the processes occurring in the combustion chamber of a solid propellant rocket engine during the stabilization of the design operation mode is performed. The self-consistent problem considered includes nonstationary operation of an ignition device, warmup and ignition of a solid propellant charge followed by its nonstationary burning, nonstationary threephase homogeneous-heterogeneous flow of the combustion products in the combustion chamber, in the nozzle, and behind the engine nozzle unit, engine depressurization, and nozzle unit plug blowing-out. The results of the calculations are presented. Content Type Journal Article Pages 467-478 DOI 10.1134/S0015462811030136 Authors G. N. Amarantov M. Yu. Egorov S. M. Egorov D. M. Egorov V. I. Nekrasov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    An isothermal steady rarefied gas flow in a long channel (tube) of elliptical or rectangular cross-section under the action of a given pressure gradient (Poiseuille flow) is studied on the basis of the Bhatnagar-Gross-Krook model. The solution is obtained using a conservative higher-order method. The velocity field in a channel cross-section is investigated as a function of the rarefaction degree and the cross-section geometry parameters. The main calculated function is the gas flow rate through the tube. The solutions obtained are compared with the available results. Content Type Journal Article Pages 456-466 DOI 10.1134/S0015462811030124 Authors V. A. Rykov V. A. Titarev E. M. Shakhov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    The dependence of the eigenvalues characterizing the disturbance propagation in hypersonic boundary layers on the temperature factor and the surface motion velocity is investigated. The eigenvalues are shown to decrease with an increase in the wall enthalpy. The results of the study are important for formulating well-posed problems for the time-dependent two-dimensional boundary layer equations and for developing adequate computational models. Content Type Journal Article Pages 389-398 DOI 10.1134/S0015462811030045 Authors D. Yu. Bogatyrev I. I. Lipatov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 3

Description:    The shock wave structure of flow around a V-wing and its properties determining the conical flow topology are numerically investigated within the framework of the inviscid gas model on a wide range of the angles of attack and yaw when in the disturbed supersonic flow either nonsymmetric Mach interaction between the shocks attached to the leading edges of the wing or a shockless flow in the compressed layer on the windward cantilever is realized. The subranges of the angles of attack and yaw with the disturbed flow properties characteristic of the wing of the given geometry are determined. It is found that at high angles of attack, when the branching point of the bow shock beneath the leeward cantilever generates an intense contact discontinuity, the structure of the conical flow in the shock layer on the windward cantilever involves a singularity of a new type which can be characterized as a “vortical” Ferri singularity. It is located above the point of convergence of the streamlines proceeding from the leading edges of the wing, at the vertex of the corresponding contact discontinuity. Flow patterns with the point of convergence of the streamlines proceeding from the leading edges located in the elliptical flow region, which is placed at a local maximum of the pressure distribution over the surface are also found. The range of the angles of attack and yaw on which this new property of supersonic conical flows is realized in the presence of a branched shock system is determined. Content Type Journal Article Pages 634-646 DOI 10.1134/S0015462811040132 Authors M. A. Zubin N. A. Ostapenko A. A. Chulkov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    The results of an experimental investigation of self-oscillatory jet outflow into a plane channel with air injection in its dead-ended part are presented. It is found that at fixed channel geometry and water supply system the main flow parameters depend on the air injection rate and the relative cavity volume. It is shown that with increase in the gas injection at a fixed cavity volume the self-oscillation intensity monotonically increases and the oscillations considerably change in nature, whereas the Strouhal number varies only slightly. At a fixed air injection coefficient the self-oscillation amplitude decreases with increase in the cavity volume and the self-oscillations stop at a certain threshold value. The flow pattern evolution with increase in the injection coefficient is studied in detail using high-speed filming. The developed surge flow pattern is described in detail. Content Type Journal Article Pages 548-557 DOI 10.1134/S0015462811040053 Authors I. I. Kozlov S. A. Ocheretyanyi V. V. Prokof’ev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    Within the Karman family of exact solutions of the Navier-Stokes equations, some non-selfsimilar solutions are considered to the problem of unsteady incompressible flow between two rotating disks one of which moves along a common rotation axis. Three classes of the flow regimes are studied: (i) a flow between the non-rotating disks, (ii) a flow between the disks rotating with identical angular velocities, and (iii) a flow between the disks rotating with opposite velocities. Examples of exact rotationally symmetric solutions for the inviscid-fluid equations, satisfying the no-slip conditions, are given. Content Type Journal Article Pages 558-564 DOI 10.1134/S0015462811040065 Authors D. V. Knyazev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    A plane steady-state two-layer fluid flow under the coupled action of the buoyancy and Marangoni forces is considered. The system is oriented at an arbitrary angle with respect to the gravity force. Exact solutions generalizing the Ostroumov-Birikh solution are obtained and their stability is studied in the framework of a linear theory. On the basis of numerical calculations, the influence of the inclination angle, the thickness of the layers, and the wall heating conditions on the instability mechanisms is investigated. Content Type Journal Article Pages 525-535 DOI 10.1134/S001546281104003X Authors V. B. Bekezhanova Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    The problem of interaction of a weak shock wave with a periodically disturbed phase interface between compressible fluids is solved in the linear approximation. A criterion of the Richtmyer-Meshkov instability is derived. Content Type Journal Article Pages 514-524 DOI 10.1134/S0015462811040028 Authors O. E. Ivashnev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    The behavior of a system of two immiscible isothermal fluids in a cylindrical reservoir under circularly polarized vibrations orthogonal to the cylinder axis is considered. The fluctuating flow is studied with account for dissipation in the near-interface vortex layer. Different mean flow generation mechanisms are discussed. It is shown that the main role in the generation is played by nonlinear processes in the near-interface boundary layer, which can be taken into accounted by applying effective boundary conditions. The mean flow structure and intensity are studied. The results obtained are compared with experimental data. Content Type Journal Article Pages 536-547 DOI 10.1134/S0015462811040041 Authors D. V. Lyubimov G. L. Khil’ko Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    Using a representation of the solutions for the shape of the hydraulic fracture crack opening and the pressure distribution along the crack in the form of a series expansion in Tchebychev polynomials of the second kind, a technique of finding the expansion coefficients is proposed and the curves for crack opening shape and pressure distribution are constructed at various injection rates. This enables one to clarify the dependence of the crack shape on the injection rate. Content Type Journal Article Pages 603-612 DOI 10.1134/S0015462811040107 Authors E. V. Teodorovich A. A. Trofimov I. D. Shumilin Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    For a theoretical derivation of bubble coalescence conditions, nonlinear forced oscillations of two closely spaced spherical bubbles subjected to the action of a periodic external pressure field are considered. The equations, asymptotic with respect to a small distance between the bubble surfaces, are derived to describe the approach of the bubbles under the action of (i) the Bjerknes attraction force averaged over the oscillation period and (ii) the viscous drag. It is shown that due to nonlinear interaction of the viscous drag with the radial and translational oscillations of the bubbles a unidirectional repulsive force is generated, which prevents the approach of the bubbles. The coalescence of the bubbles is possible when the nondimensional parameter combined from the amplitude and frequency of the external pressure field, the bubble radius, and the fluid viscosity is greater than a certain critical value. The obtained coalescence condition is qualitatively confirmed by experiments. Content Type Journal Article Pages 579-595 DOI 10.1134/S0015462811040089 Authors A. G. Petrov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    The immersion of a cylindrical solid in an undisturbed fluid is numerically investigated. Wave formation accompanying this process and the dependence of the wave parameters on those of the body are studied. The shallow water model in a cylindrical coordinate system is used. A total variation diminishing (TVD) scheme is applied on a C-type difference grid, according to Arakawa’s classification. Content Type Journal Article Pages 658-664 DOI 10.1134/S0015462811040156 Authors V. A. Levin L. V. Nadkrinichnyi Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    The results of experimental and numerical investigations of heat transfer to a cylindrical flatended model in underexpanded high-enthalpy air jets, including those flowing out through cylindrical heads of an elongated channel, are presented for the case of the operating parameters of the 100-kW VGU-4 plasma gun. Content Type Journal Article Pages 623-633 DOI 10.1134/S0015462811040120 Authors A. N. Gordeev A. F. Kolesnikov V. I. Sakharov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    A method for the on-line testing of small volumes of biological fluids is presented. The method is based on the ability of some liquids to form, when stretched, long thinning filaments, liquid bridges. Measuring the filament thinning rate makes it possible to determine the rheological parameters of the fluid. The method was tested on synthetic polymer solutions and biological fluids, such as saliva, bronchial sputum, follicular fluid, and chicken egg albumen and yolk. The results evidence that this technique can be used in various biomechanical applications, in particular, for disease diagnostics and treatment monitoring. Content Type Journal Article Pages 613-622 DOI 10.1134/S0015462811040119 Authors A. V. Bazilevsky V. M. Entov A. N. Rozhkov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    The effects of unsteady cavitation interaction between a coaxial system of a continuous water jet and a surrounding annular gas jet and a counter-streaming water flow in a cylindrical tube is investigated both experimentally and numerically. The distinctive features of the mechanism of the formation of regular self-oscillatory interaction regimes and their salient features are studied. The dependence of the mean self-oscillation frequency on the ratio of the counter-streaming water flows is determined at different gas jet flow rates. The Froude number effect on the self-oscillation frequency is analyzed. The dependence of the maximum value of the longitudinal displacement of the nose of a developed oscillating cavity penetrating into the counter stream and of the displacement amplitude on the flow rate of the supplied gas is determined. The idea on the pressure distribution in the cavity in different stages of flow development is obtained. The nature of the dependence of the self-oscillation frequency on the degree of tube flow blockage by the cavity is established. Content Type Journal Article Pages 596-602 DOI 10.1134/S0015462811040090 Authors V. P. Karlikov A. V. Rozin S. L. Tolokonnikov Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    The problem of gas flow around a plane cascade of oscillating blades is numerically solved using the ANSYS CFX package. The blade surface displacement is taken into account using a movable grid generated before the beginning of the calculations at each time step. The calculated and experimental data are compared. The calculated results are used for determining the blade stability against flutter. Content Type Journal Article Pages 665-671 DOI 10.1134/S0015462811040168 Authors S. V. Rusakov N. V. Shuvaev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    The restoration and Reynolds analogy coefficients are calculated for a laminar self-similar boundary layer on a permeable plate over the entire possible range of variation in the Prandtl number and the injection and suction parameter. Content Type Journal Article Pages 565-578 DOI 10.1134/S0015462811040077 Authors I. I. Vigdorovich A. I. Leont’ev Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    Unsteady three-dimensional conjugate natural convection in a closed vertical cylinder with a local energy source under convective heat transfer to its surroundings is mathematically modeled in the “vector potential—velocity vorticity—temperature” variables. The temperature and velocity fields, together with the dependences of the mean Nusselt number at the energy source surface on a complex of the governing parameters controlling the formation of different regimes of mass, momentum, and energy transfer, are obtained. Content Type Journal Article Pages 647-657 DOI 10.1134/S0015462811040144 Authors M. A. Sheremet Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4

Description:    The classic Prandtl slope flow model is generalized to include nonlinear turbulent friction and rotation. Several general regularities are established. In particular, a universal expression for the mass flux along the slope and a relationship between the surface velocity components, both independent of the friction law, are obtained. The applicability of the model to describing katabatic winds on fairly large horizontal scales is discussed. Content Type Journal Article Pages 505-513 DOI 10.1134/S0015462811040016 Authors L. Kh. Ingel Journal Fluid Dynamics Online ISSN 1573-8507 Print ISSN 0015-4628 Journal Volume Volume 46 Journal Issue Volume 46, Number 4