Thermocapillary instability of a plane layer with a vertical temperature gradient

The oscillating disturbances in a plane layer with a temperature gradient are analyzed. It is shown that for heating from below taking the deformability of the free surface into account leads to the appearance of short-wave oscillatory instability, which becomes the most dangerous mode. Moreover, the interaction of the capillary and thermocapillary instability mechanisms results in the appearance of oscillating disturbances of a new type, which lead to equilibrium crisis at high Marangoni numbers. It is established that when the free boundary is heated, the onset of convection is possible only with respect to oscillatory disturbances.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 19–23, May–June, 1992.     

Instability of combined convective flow in a vertical layer

In the present paper, a study is made of the stability of plane-parallel flow induced by a transverse temperature difference between the boundaries of a layer and a longitudinal pressure gradient. This problem was solved earlier by the author [3] in a purely hydrodynamic formulation without allowance for thermal factors; the results then obtained correspond to the limiting case of small Prandtl numbers. In the paper, a numerical solution to the problem with the complete formulation is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1982.I thank G. Z. Gershuni for supervising the work, and also M. A. Gol'dshtik and V. N. Shtern for a helpful discussion.     

Convective flow with uniform vorticity in a vertical layer

The free convective circulation of liquid in plane vertical slits of circular and square cross section with a longitudinal horizontal temperature gradient at the boundaries was investigated experimentally. It was found that under such heating conditions there is a uniform-vorticity flow with a region of quasirigid rotation, which has the shape of a disk in a circular slit and the shape of a cross in a square slit; in each longitudinal section of this zone the liquid moves along concentric trajectories with constant angular velocity. Dimensionless numbers for the problem were established by tests with various liquids and cavities of different dimensions. In dimensionless form, the angular velocity of the vortex and the temperature gradient in it depend linearly on the temperature difference at the boundaries of the layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 160–165, May–June, 1984.     

The analysis of two-phase flow instability in a vertical U-tube evaporator

This paper describes both the experimental and theoretical analysis of two-phase flow instability in a vertical U-tube evaporator. In the experiment investigation the effects of various parameters on flow instability are studied by using Freon-12 as working medium and the influence of flow oscillations on heat transfer deterioration is obtained. The mathematical model to describe flow oscillations occurring in the vertical U-tube with flow stagnation and upward movement of bubbles due to buoyancy in the heated downcomer is developed. The finite differential equations are solved by using a modified two-step iteration technique. The calculated results are in good agreement with the experimental data.     

Convective instability of Marangoni-Poiseuille flow under a longitudinal temperature gradient

An exact solution is obtained for the problem of steady flow in a system of two horizontal layers of immiscible fluids with a common interface. The stability of the flow is studied by a linearization method. It is shown that the occurrence of instabilities is due to the different governing parameters of the fluids (thickness, heating conditions, viscous and thermal conductivity of the fluids). It is found that under constant gravity conditions, the perturbations are monotonic, and in zero gravity, oscillatory thermocapillary instability occurs.     

Measurements of layer depth during baroclinic instability in a two-layer flow

This study investigates the baroclinic instability of a two-layer rotating fluid system. The instability is generated by releasing a cylinder of buoyant fluid at the surface of ambient fluid. The buoyant fluid is dyed so that its depth may be determined from its optical thickness. The system first adjusts until the horizontal density gradient is balanced by a flow along the front, and the adjusted state is then unstable to azimuthal waves. Contours of constant upper layer depth are examined, and the perturbation at each azimuthal wavenumber is determined. The initial wavenumber is well modelled by simple quasi-geostrophic theory. There is a clear high wavenumber cutoff, and a transfer of energy to larger scales with time.     

Stability of convective motion in a vertical layer in the presence of longitudinal vibrations

The influence of vibrations of a cavity containing a fluid on the convective stability of the equilibrium has been investigated on a number of occasions [1]. The stability of convective flows in a modulated gravity field has not hitherto been studied systematically. There is only the paper of Baxi, Arpaci, and Vest [2], which contains fragmentary data corresponding to various values of the determining parameters of the problem. The present paper investigates the linear stability of convective flow in a vertical plane layer with walls at different temperatures in the presence of longitudinal harmonic vibrations of the cavity containing the fluid. It is assumed that the frequency of the vibrations is fairly high; the motion is described by the equations of the averaged convective motion. The stability boundaries of the flow with respect to monotonic perturbations in the region of Prandtl numbers 0 ? P ? 10 are determined. It is found that high-frequency vibrations have a destabilizing influence on the convective motion. At sufficiently large values of the vibration parameter, the flow becomes unstable at arbitrarily small values of the Grashof number, this being due to the mechanism of vibrational convection, which leads to instability even under conditions of weightlessness, when the main flow is absent [3, 4].     

Nonlinear behaviour of the instability of steady natural convection in a vertical air layer

In this paper we deal with the flow of natural convection between two vertical planes with horizontal temperature gradient. We show that periodic steady flow occur when Rayleigh number increases. Critical values are obtained numerically and a nonlinear analysis is presented according to Center manifold method.     

Stability of stationary convective flow of a mixture in a vertical porous layer

In contrast to the corresponding viscous flow, the convective flow of a homogeneous liquid in a planar vertical layer whose boundaries are maintained at different temperatures is stable [1]. When a porous layer is saturated with a binary mixture, in the presence of potentially stable stratification one must expect an instability of thermal-concentration nature to be manifested. This instability mechanism is associated with the difference between the temperature and concentration relaxation times, which leads to a buoyancy force when an element of the fluid is displaced horizontally. In viscous binary mixtures, the thermal-concentration instability is the origin of the formation of layered flows, which have been studied in detail in recent years [2–4]. The convective instability of the equilibrium of a binary mixture in a porous medium was considered earlier by the present authors in [5]. In the present paper, the stability of stationary convective flow of a binary mixture in a planar vertical porous layer is studied. It is shown that in the presence of sufficient longitudinal stratification the flow becomes unstable against thermal-concentration perturbations; the stability boundary is determined as a function of the parameters of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–157, January–February, 1980.     

Asymptotic analysis of flow instability in a compressible boundary layer on a curved surface

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 84–89, May–June, 1988.     

Longwave instability of a binary mixture flow in a vertical channel in the presence of vibration

The longwave instability of a hybrid (thermogravitational and thermovibrational) flow of a binary incompressible liquid mixture occurring in a plane vertical channel, whose boundaries are maintained at constant but different temperatures, is studied. The investigation is carried out with account for the Soret thermal-diffusion effect on the ranges of normal and anomalous values of the mixture separation coefficient. It is shown that, owing to the properties of the system, the subharmonic response to an external action is absent. The ranges on which secondary flows arise are analytically determined using the asymptotic expansion method, both under weightlessness conditions and in the presence of the gravity effect. The parameter ranges on which longwave disturbances present the greatest danger for the main flow stability are determined.     

The stability of a flow in a side-heated vertical layer with internal heat sources

The linear stability of a combined convective flow in a side-heated plane vertical layer of incompressible fluid is considered. The layer contains uniformly distributed heat sources. The steadystate flow is a superposition of the Gershuni convective flow and a flow induced by the action of the internal heat sources. The stability maps of the combined flow are constructed for different values of the Prandtl number. It is found that the internal sources damp the action of the mechanisms of the Gershuni flow crisis. The lateral heating may result in both the stabilization and the destabilization of the flow caused by the action of internal heat sources.     

Microconvection in a vertical layer

In the case of very weak gravity the classical Oberbeck-Boussinesq approximation is not valid for describing thermal gravitational convection. This was pointed out in [1] where a new model was proposed under the assumption that the fluid is isothermal and incompressible. In this model the velocity vector is no longer solenoidal. Below, on the basis of this model we analyze the convective motion in a vertical layer, on the rigid boundaries of which a heat flux that depends on time only is prescribed. It is found that the nonsolenoidal character of the velocity does not lead to considerable restructuring of the steady-state convection. At the same time, the patterns of the unsteady, in particular, periodic convective flow calculated within the framework of the classical and the new models differ significantly.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 76–84, September–October, 1994.