Effect of high-frequency vibrations on the stability of advective flow

The stability of plane convective flow in a horizontal layer with a longitudinal temperature gradient under the action of longitudinal vibrations is considered. The behavior of small normal plane and spiral perturbations is investigated. It is shown that the vibrations enhance the stability with respect to almost all types of perturbations. The sole exception is plane thermal waves whose existence domain extends toward low Prandtl numbers. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–22, January–February, 1998. The work was supported by the Russian Foundation for Fundamental Research (project No. 94-01-01730).     

Stability of Poiseuille flow in the presence of a longitudinal magnetic field

The stability of the plane flow of an electrically conducting fluid with respect to small perturbations was studied at large Reynolds numbers in the presence of a longitudinal magnetic field. The dependence of the critical Reynolds number on the electrical conductivity is investigated. At large Reynolds numbers, a new branch of instability and a sudden change in the critical Reynolds numbers is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 45–53, May–June, 2008.     

Determination of the shape of the shocks ahead of a transverse jet injected into a supersonic flow

The three-dimensional shape of the shock wave formed ahead of a sonic jet flowing out into a supersonic flow through the surface of a sharp cone is determined. The shape of the wave in the longitudinal and transverse cross-sections of the model is constructed using schlieren photographs taken for various angles of rotation and freestream Mach numbers M=1.75–3. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 41–44, March–April, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 95-01-00709a).     

Model of a strong discontinuity for the equations of spatial long waves propagating in a free-boundary shear flow

The long-wave equations describing three-dimensional shear wave motion of a free-surface ideal fluid are rearranged to a special form and used to describe discontinuous solutions. Relations at the discontinuity front are derived, and stability conditions for the discontinuity are formulated. The problem of determining the flow parameters behind the discontinuity front from known parameters before the front and specified velocity of motion of the front are investigated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 206–213, July–August, 2008.     

Effect of fluid compressibility on the linear stability of Poiseuille flow in a circular tube

The linear stability of a barotropic fluid flow in a circular absolutely rigid tube is considered. The behavior of perturbations in the form of monoharmonic waves resulting from the viscosity as well as the compressibility of the fluid is investigated. It is shown that the compressibility of the fluid affects the first type of perturbations only slightly and the second significantly and that the latter can be more dangerous from the standpoint of initiating instability, even for weakly compressible flows. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 5–10, March–April, 1994.     

Oscillating thermocapillary convection regimes driven by a point heat source

The stability of an axisymmetric thermocapillary flow driven by a point heat source located in the neighborhood of the free surface of a fluid filling a deep tank is investigated theoretically and experimentally. It is shown that for certain values of the depth and power of the heat source thermocapillary convection becomes unstable with respect to oscillating perturbations of the surface shape. Perm’, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 92–103, March–April, 2000.     

Dissipative instability of fluid flows with piecewise linear velocity profiles

The viscous dissipative instability of two flows with continuous spectrum of neutrally-stable perturbations in the absence of dissipation is investigated. Ranges of wave numbers in which viscosity leads to flow destabilization are determined for a shear discontinuity in a smoothly-stratified fluid. A shear flow with a velocity in the transition layer that depends linearly on the coordinate has a continuum of neutral modes even in the case of an unstratified fluid. When viscosity is present in one of the layers with constant velocity, one of the branches of the spectrum becomes unstable. When the viscosity is the same above and below the shear layer, dissipation only leads to the damping of the perturbations. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 14–19, November–December, 1986.     

Azimuthal wave motions on the surface of a rotating fluid cylinder

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

Stability of a compressible swirling flow in a circular pipe

The stability of an axisymmetric flow of viscous gas in a circular pipe, which models the Burgers vortex in the pipe axis neighborhood, is studied within the linear theory framework. Neutral curves for the most unstable disturbances are calculated. The influence of the characteristic Mach number on the flow stability is investigated. It is shown that for a given model velocity distribution the Mach number affects only the temperature and pressure profiles of the main undisturbed flow. In this case, for the disturbance types considered, as the Mach number increases, the critical Reynolds number corresponding to loss of stability decreases. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 35–41, January–February, 1999. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-00586).     

Ideal incompressible flow around a wedge tip

A planar analog of conical flows is considered: an inviscid incompressible fluid flow around a wedge tip. A class of conical flows is found where vorticity is transported along streamlines by the potential component of velocity. Problems of a wave “locked” in the corner region and of a flow accelerating along the rib of a dihedral angle are considered. By analogy with an axisymmetric quasi-conical flow, a planar quasi-conical flow of the fluid is determined, namely, the flow inside and outside the region bounded by tangent curves described by a power law. Conditions are found where vorticity and swirl produce a significant effect. An approximate solution of the problem of the fluid flow inside a “zero” angle is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 57–65, March–April, 2007.     

Influence of a sureactant on the instability of a falling liquid film

The hydrodynamic instability of a film flow of a weak solution containing a soluble volatile surfactant is investigated. Diffusion of the surfactant in the liquid, its evaporation into the boundary gas medium, and the adsorption and desorption processes in the near-surface layer are taken into account. A system of evolutionary equations is derived and a steady-state solution film flow along a vertical surface and the stability of this flow are investigated for the simultaneous action of body and capillary forces and the Marangoni effect. Hydrodynamic and diffusion instability modes are detected and their properties are investigated for constant and variable surfactant concentration in the adsorbed sublayer. Moscow, Madrid. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 56–67, July–August, 2000. The work was carried out with support from the Russian Foundation for Basic Research (project No. 97-01-00153) and the Spanish Ministry of Higher Education (program DGICYT (Spain), project No. PB 96-599).     

Convective instability of a fluid in two-layer saturated strata

The problem of convective instability of a fluid in a system consisting of two horizontal porous strata with different permeabilities and a permeable common boundary is considered. The problem is investigated in parametric form as a function of the stratum thickness ratio and stratum permeabilities. As distinct from a uniform stratum, in this case the neutral curve can have one or two minima depending on the relationship between the parameters. The case of two minima is characterized by the condition of loss of stability of the fluid in the system as a whole and in the thinner stratum with greater permeability. These minima correspond to significantly different wave numbers. Makhachkala. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 165–169, January–February, 1999.     

Stability of a surface-charged viscous jet in an electric field

The stability of a surface-charged cylindrical jet in a longitudinal uniform electric field with respect to capillary pertubations is investigated in the linear approximation. The evolution of both axisymmetric and azimuthal-periodic perturbations is analyzed. In the latter case the first two modes among the azimuthal wavenumbers — bending and Bohr — are considered. Axisymmetric and bending instabilities lead to the transverse disintegration of the jet into individual drops and the Bohr mode to the longitudinal separation of the input jet into two parts. It is found that the axisymmetric and bending instabilities, respectively, can be completely suppressed and significantly attenuated by means of an external longitudinal field. In this case the role of the Bohr mode becomes more important leading under certain conditions to longitudinal longwave jet splitting. Events which can be interpreted as manifestations of longitudinal partition of the jet (dumbbell-like cross-section, branching nodes) are observed in experiments with evaporating polymer-solution microjets. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 29–40, March–April, 1998. The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 97-01-00153).     

Effect of volume energy supply on swirled flows in a subsonic cocurrent stream

The results of a numerical investigation of the effect of thermal energy supply on a swirling viscous heat-conducting gas flow in a subsonic cocurrent stream are presented. The initial stage of development of the swirling flow in the neighborhood of the vortex axis with constant circulation in the outer flow region is considered for two different distributions of the streamwise velocity vector component which simulate a swirling jet-type flow and a wake flow with a streamwise velocity deficit. The effect of local volume energy supply in the neighborhood of the vortex axis, the circulation of the azimuthal velocity component, and the longitudinal pressure gradient in the inviscid stream on the development of the swirling flow and the process of breakdown of cocurrent vortex flows is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 47–53, November–December, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00586).     

Stability of a viscoelastic plate in fluid flow

The stability of an infinite viscoelastic plate on an elastic foundation in a viscous incompressible flow is studied. The Navier-Stokes system is linearized for an exponential velocity profile. The problem is reduced by a Fourier-Laplace transform to a system of ordinary differential equations, whose solution is found in the form of convergent series. The roots of the dispersion relation that characterize the stability of the system are found numerically. The effect of the viscosities of the fluid and the plate on the stability of the waves propagating upstream and downstream is studied. The results are compared with available data on the stability of a viscoelastic plate in an ideal fluid flow. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 66–74, July–August, 2006.     

Effect of a local stationary flow disturbance on separated boundary layer stability

The separated flow past a transverse barrier on a plate surface is modeled in a wind tunnel. The linear stability of the two-dimensional laminar flow in the separation zone is investigated in the presence of a stationary disturbance imposed on the flow and concentrated in a narrow spanwise region. It is experimentally shown that the local flow nonuniformity leads to a change in the flow stability features, such as the frequencies of the growing oscillations, their growth rate, and the dispersion characteristics. As a result, the transverse velocity gradients induced in the separation zone exert a strong destabilizing influence on the flow. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 174–178, January–February, 2000. The study was carried out with the support of the INTAS Foundation under grant No, 96-2225.     

Motion of a flexible finite-length filament in a flow of a viscous fluid

The two-dimensional problem of the configuration of a flexible filament of finite length in a deformable viscous fluid is solved. The flexuural stresses in the filament and the inertial and gravitational forces are not taken into account. The equilibrium equations are obtained. The friction force that acts on the filament surface from the side of the viscous fluid is proportional to the flow rate. The specific features of the evolution of a bent filament under the conditions of pure and simple shear of a fluid are studied numerically. Analytical solutions are obtained for the evolution of a rectilinear filament; in particular, the stretching force in the filament is found. For the indicated types of flow, the stability of a rectilinear filament against small perturbations is investigated. Volzhskii Polytechnical Institute at the Volgograd State Technical University, Volgograd 404121. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 144–153, March–April, 2000.     

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

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

Stability of a spanwise nonuniform boundary layer flow

The linear stability of a boundary layer flow with a spanwise-periodic nonuniformity in the velocity profile is investigated. This flow can be considered as a model of a streaky structure occurring in the boundary layer at a high freestream turbulence level. It is shown that for a small nonuniformity amplitude symmetric modes similar to Tollmien-Schlichting waves are the most unstable. At higher nonuniformity amplitudes, antisymmetric modes, qualitatively different from Tollmien-Schlichting waves and having a larger phase velocity, are the most amplified. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 54–63, November–December, 1998. The study was carried out with the support of the International Scientific and Technical Center (project No. 199-95) and the Russian Foundation for Basic Research (project No. 95-01-01201a).     

Observation of standing waves of large amplitude in harmonic Faraday resonance

Stationary two-dimensional gravity waves on the free surface of a homogeneous fluid in a rectangular vessel in the presence of vertical oscillations excited in harmonic Faraday resonance with identical frequencies are investigated. For the second mode, the dependence of the amplitude on the excitation frequency is found and the wave profiles are obtained. The experimental results are compared with the theoretical model. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 185–188, January–February, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 99-01-01080) and CONACYT (Mexico, Catedra Patrimonial, S. Ya. Sekerzh-Zen’kovich, Ref. 489100-2, Exp. 950060).