Stability of a fluid interface under tangential vibrations

The stability of the interface between two immiscible fluids of different density which occupy a plane horizontal layer performing harmonic horizontal oscillations is considered. Within the framework of the ideal fluid model a transformation reducing the problem of small plane perturbations to the Mathieu equation is found. Resonance instability domains associated with the formation of capillary-gravitational waves are investigated. A model which takes into account dissipation processes due to the presence of viscous friction is constructed. The role of the viscous dissipation in suppressing resonance instability is discussed. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–31, May–June, 1998. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 95-01-00386).     

Quasi-steady-state flows in a liquid film in a gas: Comparison of two methods of describing waves

The motion of thin films of a viscous incompressible liquid in a gas under the action of capillary forces is studied. The surface tension depends on the surfactant concentration, and the liquid is nonvolatile. The motion is described by the well-known model of quasi-steady-state viscous film flow. The linear-wave solutions are compared with the solution using the Navier-Stokes equations. Situations are studied where a solution close to the inviscid two-dimensional solutions exists and in the case of long wavelength, the occurrence of sound waves in the film due to the Gibbs surface elasticity is possible. The behavior of the exact solutions near the region of applicability of asymptotic equations is studied, and nonmonotonic dependences of the wave characteristics on wavenumber are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 103–111, May–June, 2007.     

Steady-state conditions of a nonisothermal film with a heat-insulated free boundary

The equilibrium shapes of a nonisothermal liquid film with a heat-insulated free surface for large Marangoni numbers are investigated in the long-wave approximation using a combination of analytical and numerical methods. It is proved that the two-dimensional problem of the equilibrium of a strip-shaped film has a steady-state solution for an arbitrary large temperature gradient on the boundaries of the strip. An increase in this gradient leads to an abrupt thinning of the film near the heated boundary, which can result in instability and rupture of the film. In the equilibrium problem for a film fixed on a circular contour, the nonuniform distribution of the heat flux on the contour was found to have a significant influence on the free-surface shape. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 59–73, July–August, 2008.     

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).     

Thermocapillary instability of a liquid layer with allowance for the soret effect

The effect of thermodiffusion on the onset of thermocapillary instability in the presence of a surfactant is investigated with reference to a plane liquid layer. It is shown that taking the Soret effect into account leads to destabilization in the case of heating of both the rigid surface and the free boundary. Krasnoyarsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 2000.     

An analog of the Bernoulli and Cauchy-Lagrange integrals for a time-dependent vortex flow of an ideal incompressible fluid

An expression with a constant value over all space (including multiply connected domains) relating the pressure function to the square of the velocity and the characteristics of the traveling vortices is derived for a time-dependent ideal incompressible fluid flow with nonzero vorticity. When there are bodies in the flow, they must also be represented in the form of traveling vortices. For steady-state flow the formula obtained goes over into the Bernoulli integral and for time-dependent irrotational flow into the Cauchy-Lagrange integral. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–41, January–February, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00156 and project No. 96-15-9603 for the support of leading science schools).     

Subsonic compressible cavitation flow past a plate at small cavitation numbers

A solution of the problem of symmetric inviscid compressible cavitation flow past a plate at small cavitation numbers is presented. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–104, July–August, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00111).     

Initiation and development of separated flow behind a circular cylinder in a supersonic stream

On the basis of the two-dimensional Navier-Stokes equations, the initiation and development of the separated flow behind a thermally insulated circular cylinder in a supersonic perfect-gas stream is investigated in relation to the Reynolds number. It is shown that the entire Re-range can be subdivided into a number of intervals with their own characteristic features. In particular, the conditions for the generation and development of global separation are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 27–36, November–December, 1998. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 95-01-01129a).     

Gas injection from the surface of a triangular plate in a hypersonic flow

The flow formed as a result of gas injection through the permeable surface of a triangular plate is investigated in the regime of strong viscous-inviscid interaction between the hypersonic flow and the laminar boundary layer. The features of the flow past strongly cooled surfaces with the formation of supercritical and subcritical flow regions in the boundary layer are studied. The injected gas distribution ensuring the existence of self-similar solutions in the supercritical flow regions is obtained. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 125–133, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-01391).     

Properties of the nonequilibrium high-velocity “Tails” of the molecular distribution function in plane couette flow of a compressible gas

The results of an analytic and numerical investigation of the properties of the high-velocity “tails” of the distribution function are given for the solution of the BGK model of the kinetic Boltzmann equation for plane Couette flow of a compressible gas. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 183–190, July–August, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00573; grant in support of leading science schools No. 96-15-9603).     

Two-dimensional instability of a tangential discontinuity in dispersive media

The instability of a tangential discontinuity in a compressible dispersive medium with respect to small two-dimensional perturbations is demonstrated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–23, January–February, 1997. The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 96-01-01340).     

Rarefied flow in a channel and a periodic system of channels

the steady two-dimensional isothermal rarefied flow in a channel formed by two parallel flat plates of finite length is studied on the basis of the numerical solution of a linearized kinetic problem. The channel may either be isolated or constitute a cell of a periodic cascade consisting of zero-thickness plates arranged one above the other. As the channel length increases, the flow in it approaches the asymptotic one-dimensional Poiseuille flow. It is shown that the asymptotic dependence of the gas flow rate on the low Knudsen number corresponding to an infinitely long channel is already attained for a channel of length equal to several channel widths, if the flow rate is referred to the pressure gradient at the middle of the channel rather than to the mean pressure difference at the channel ends. The effect of the boundary conditions imposed on the channel entrance is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–175, May–June, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00443).     

Convective instability of a plane horizontal layer of weakly conducting fluid in alternating and modulated electric fields

The electrothermoconvective instability of a plane horizontal layer of weakly conducting fluid in a modulated vertical electric field is investigated. The analysis is based on the electrohydrodynamic approximation. The stability threshold in the linear approximation is found using Floquet’s theory. The effect of periodic modulation on the fluid behavior is studied in both the presence and the absence of the constant component of the electric field. It is shown that modulation can stabilize the unstable ground state or destabilize fluid equilibrium, depending on the amplitude and frequency. In addition to a synchronous or subharmonic response to an external forcing, the instability may be associated with two-frequency (quasiperiodic) perturbations. The cases of weightlessness and a transversely stratified fluid in a static gravity field are considered. Madrid, Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 31–38, May–June, 2000. The investigations whose results are presented in this paper were supported by the Russian Foundation for Basic Research (project No. 98-01-00507).     

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

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

Aerosol aspiration into a tube from a calm medium

The problem of aerosol aspiration into a thin-walled tube from a calm medium is solved. The dependence of the aspiration coefficient on the Stokes number and the steady-state settling velocity is investigated. The results obtained are compared with the calculations [1, 2] and the experimental formula [3]. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 104–109, March–April, 2000. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-00111).     

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).     

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).     

Weakly nonlinear stability analysis of a falling film with countercurrent gas flow

Weakly nonlinear stability analysis of a falling film with countercurrent gas–liquid flow has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear and nonlinear stability solutions for the film flow system. The results show that both supercritical stability and subcritical instability are possible for a film flow system when the gas flows in the countercurrent direction. The stability characteristics of the film flow system are strongly influenced by the effects of interfacial shear stress when the gas flows in the countercurrent direction. The effect of countercurrent gas flow in a falling film is to stabilize the film flow system.     

On local perturbations of a boundary layer with small skin friction

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

Two-parameter model of a turbulent flow with a dispersed-particle admixture

Using a two-point probability density function for the particle distribution over velocities and coordinates, a closed model of the particle effect on the turbulent flow characteristics is formulated. The processes of turbulent dissipation and turbulent energy transfer across the spectrum are studied. Different models of two-phase turbulence are compared. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 40–56, July–August, 1998. The work received financial support from INTAS (grant No. 94-4348) and the Russian Foundation for Basic Research (project No. 98-01-00-353).