Convective flows in a cylindrical fluid zone in a high-frequency vibration field

Convective flows of a nonuniformly heated fluid in a cylindrical fluid zone in a high-frequency longitudinal vibration field are studied. Vibration frequencies which are high as compared with dissipative decrements and capillary frequencies, but small as compared with acoustic frequencies are considered. The general method formulated earlier for describing the behavior of inhomogeneous fluids under the influence of high-frequency vibrations is used. The interaction between the vibrational flow mechanisms and thermocapillary effects on a free surface is analyzed.Perm'. Marseilles (France). Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 53–61, September–October, 1994.     

Average stationary binary-mixture convection in connected channels in the presence of high-frequency vibration

The effect of vertical high-frequency vibration on steady-state binary-mixture flows in connected channels is studied theoretically. Mixtures with both positive and negative thermal diffusion are considered. It is shown that the convection excitation mode changes with the sign of the thermal diffusion. The dependence of the flow amplitude on the supercriticality is analytically obtained for various vibrational Rayleigh numbers.     

Vibrational thermal convection in a cavity executing high-frequency rocking motions

The vibrational thermal convection in a cavity executing high-frequency rocking motions is investigated. The equations of vibrational convection are obtained by the method of averaging. It is shown that rocking motions lead to some new and distinctive effects. The convective stability in a plane layer in the presence of such vibrations is investigated on the basis of the obtained equations. A comparison with known experimental data is made. The results of experiments confirm the theoretical conclusions drawn on the basis of the averaged equations of vibrational convection.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 138–144, May–June, 1988.I thank E. M. Zhukhovitskii for helpful discussion.     

Effectofhigh-frequency vibration on filtration convection

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 83–88, September–October, 1992.     

Instability of a liquid jet in a high-frequency alternating electric field

Stability of a liquid (electrolyte) jet in a tangential electric field harmonically oscillating with a high frequency is considered under an assumption of an ideal liquid. It is demonstrated that it is possible to solve the electrodynamic and hydrodynamic parts of the problem inside the jet separately if the Peclet number based on the Debye layer thickness is small. Linear stability of the trivial solution of the problem is studied. A dispersion relation is derived, which is used to study the effect of the amplitude and frequency of electric field oscillations on jet stability. An increase in the amplitude of oscillations is demonstrated to exert a stabilizing effect, whereas an increase in frequency leads to insignificant destabilization of the jet.     

Filtration convection in an annular domain and branching of a family of steady-state regimes

A plane problem of convection of incompressible fluid saturating a porous annular domain is considered. Using the Darcy model and a finite-differencemethod, which retains the cosymmetry of the original problem, we investigate the branching of a family of steady-state regimes from the mechanical equilibrium. The evolution of convective motions with increase in the Rayleigh number is studied and the onset of instability on the family of steady-state regimes is analyzed. For narrow annular domains, the cosymmetric effect of a delay in the branching of a secondary self-oscillation mode from the family is detected, while for domains of moderate thickness and sectors the monotonic instability is typical.     

Laboratory observations of double-diffusive convection using high-frequency broadband acoustics

High-frequency broadband (200–300 kHz) acoustic scattering techniques have been used to observe the diffusive regime of double-diffusive convection in the laboratory. Pulse compression signal processing techniques allow (1) centimetre-scale interface thickness to be rapidly, remotely, and continuously measured, (2) the evolution, and ultimate merging, of multiple interfaces to be observed at high-resolution, and (3) convection cells within the surrounding mixed layers to be observed. The acoustically measured interface thickness, combined with knowledge of the slowly varying temperatures within the surrounding layers, in turn allows the direct estimation of double-diffusive heat and buoyancy fluxes. The acoustically derived interface thickness, interfacial fluxes and migration rates are shown to support established theory. Acoustic techniques complement traditional laboratory sampling methods and provide enhanced capabilities for observing the diffusive regime of double-diffusion in the ocean.     

Stability of a viscous liquid jet in a high-frequency alternating electric field

The stability of a liquid electrolyte placed in a tangential electric field oscillating harmonically at high frequency is considered assuming that the liquid is viscous and Newtonian. It is shown that, if the Peclet number calculated from the thickness of the Debye layer is small, the problem can be solved separately for the electrodynamic part of the problem in the Debye layer and for the hydrodynamic part of the problem in the jet. The linear stability of the trivial solution of the problem is investigated. A dispersion relation is derived and used to study the effect of the amplitude and frequency of electric field oscillations on the stability of the jet. It is shown that the presence of the external oscillating field has a stabilizing effect on the jet. The basic stability regimes as functions of the control parameters of the problem and bifurcation changes in the regimes are investigated.     

Thermal convection in an acoustic field

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

Thermal convection in an acoustic field

Thermal vibrational convection is considered for an acoustic wavelength at the vibration frequency comparable with the dimensions of the cavity. Equations of the pulsatory and average motions of a medium that generalize the well-known equations of thermovibrational convection are obtained. Effective boundary conditions for average fields on rigid boundaries are formulated. The quasi-equilibrium stability problem for a plane horizontal layer heated from below and executing high-frequency oscillations is solved. It is shown that the compressibility effects can be significant even when the acoustic wavelength substantially exceeds the length of the layer. A destabilizing compressibility effect which can lead to instability of the layer even under conditions of weightlessness is established. Perm’, e-mail: lyubimov@psu.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 28–36, March–April, 2000. The work was carried out with partial financial support from the Program of State Support for Leading Science Schools (project No. 96-015-96084).     

Noise effect on convection generation in a modulated gravity field

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.     

Plasma in a high-frequency electric field with a reflective condition on the boundary

An analytical solution is obtained for the linearized problem of the behavior of a collisional gas plasma in a half-space in an external alternating electric field. It is assumed that the electrons are mirror-reflected from the plasma boundary. The solution is used for finding the screened field. The case of an external field frequency close to the plasma frequency is investigated separately.     

Filtration of two miscible liquids in a fractured porous medium in a gravity field

The article discusses the one-dimensional problem of the displacement of a liquid (petroleum), saturating a fractured porous medium, by another liquid miscible with it in all ratios, in a gravity field. A system of two nonlinear equations in partial derivatives, of the hyperbolic type, is obtained for the concentration of one of the liquids in fractures and blocks. The system is integrated numerically by the method of characteristics. On the basis of the results universal dependences are obtained for the distribution of the concentrations over the stratum and the yield of petroleum.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 166–168, March–April, 1973.The authors axe grateful to V. M. Entov for his evaluation of the work.     

Magnetic fluid motion driven by a high-frequency rotating magnetic field

The problem of the circulating flow of a nonisothermal magnetic fluid in a long vertical cylinder placed in a rotating magnetic field is solved in the weak vorticity approximation.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 18–22, January–February, 1996.     

Hydromagnetic convection in a rotating annulus with an azimuthal magnetic field

The problem of convection induced by radial buoyancy in an electrically conducting fluid contained by a rotating cylindrical annulus (angular frequency, ) in the presence of a homogeneous magnetic field (B) in the azimuthal direction is considered. The small gap approximation is used together with rigid cylindrical boundaries. The onset of convection occurs in the form of axial, axisymmetric or oblique rolls. The angle between the roll axis and the axis of rotation depends of the ratio between the Chandrasekhar number, QB², and the Coriolis number, . Fully three-dimensional numerical simulations as well as Galerkin representations for roll patterns including the subsequent stability analysis are used in the theoretical investigation. At finite amplitudes, secondary transitions to 3D-hexarolls and to spatio-temporal chaos are found. Overlapping regions of pattern stability exist such that the asymptotically realized state may depend on the initial conditions. PACS 47.27.-i, 47.65.+a     

Parametric convection of a low-conducting liquid in an alternating electric field

The development of parametric electroconvective instability of a low-conducting liquid in a horizontal capacitor under the action of an alternating electric field is studied. The conditions on which the free charge is generated due to autonomous unipolar injection are considered. The charge distributions over the liquid at rest are determined analytically and numerically, respectively, for low and arbitrary amplitudes of the external field. The limits of parametric electroconvective instability are found within the framework of the linear theory. It is shown that the perturbations can manifest themselves in different ways depending on the modulation amplitude and frequency of the electric field and be of the subharmonic, synchronous, or quasiperiodic type of the response. The characteristics of the resonance action, namely, the amplitudes and the frequencies necessary for the efficient generation of electroconvection, are determined.     

Natural convection in vertical concentric annuli under a radial magnetic field

Exact solutions for fully developed natural convection in open-ended vertical concentric annuli under a radial magnetic field are presented. Expressions for velocity field, temperature field, mass flow rate and skin-friction are given, under more general thermal boundary conditions. It is observed that both velocity as well as temperature of the fluid is more in case of isothermal condition compared with constant heat flux case when gap between cylinders is less or equal to radius of inner cylinder while reverse phenomena occur when the gap between cylinders is greater than radius of inner cylinder.