Connective instability of a two-layer system with thermally insulated boundaries

The investigation of the convective stability of mechanical equilibrium of two horizontal layers of immiscible fluids has revealed the characteristics of such systems [1–3]. In particular, it has been found that, as distinct from a homogeneous horizontal layer, under certain conditions two-layer systems experience convective instability when uniformly heated from above and, moreover, oscillatory instability when heated from below. In [1–3] the problem was solved for a system with isothermal outer boundaries. In this paper the stability of equilibrium of two-layer systems is investigated for thermally insulated outer boundaries. Special attention is given to the study of the long wave instability mode.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 22–28, March–April, 1986.The authors wish to thank O. V. Kustova for assisting with the computations.     

Parametric instability of a nonuniformly heated horizontal layer of liquid dielectric in a variable electric field

The parametric instability of a nonuniformly heated horizontal layer of liquid dielectric with free isothermal boundaries in a transverse electric field is studied analytically. An instability map is obtained. It is shown that instability can develop at some critical electric field strength which depends on the frequency and is several times greater than the critical strength of the constant electric field.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 184–186, September–October, 1993.     

Propagation of magnetohydrodynamic shock waves in a medium of decreasing density

It is explained under what condition instability develops in the wave front when a shock wave travels in a medium whose density is decreasing. It is shown that under laboratory conditions the buildup of such an instability may be suppressed by a diffusion of wave front segments into the walls of the system. Such an instability can occur, for example, in certain astrophysical bodies.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 24–27, May–June, 1972.     

Development of thermogravitation convection in a two-layer system in the presence of a surface-active material on the boundary

Convective instability of equilibrium in a system of two horizontal layers of immiscible liquids, caused by the Rayleigh instability mechanism, has been studied within the framework of the linear theory in [1–5]. The present study will investigate the effect of a surface-active material (SAM), deposited on the boundary between the liquids, on the development of thermogravitation convection. Calculations were performed for two types of systems, which in the absence of a SAM show instability of a monotonic or an oscillatory character. A new type of oscillatory equilibrium instability was observed, produced by the effect of the SAM. In some region of parameter values the oscillatory instability may prove to be the more dangerous one. The action of the Marangoni effect on thermogravitation oscillations is considered.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 76–81, September–October, 1986.In conclusion, the authors express their gratitude to E. M. Zhukhovitskii for his helpful evaluation.     

Three-dimensional instability of an elliptic Kirchhoff vortex

The instability of a Kirchhoff vortex [1–3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4–6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4–9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 40–45, May–June, 1988.     

Convection in a two-layer system due to the combined action of the Rayleigh and thermocapillary instability mechanisms

In a two-layer system loss of stability may be monotonic or oscillatory in character. Increasing oscillatory perturbations have been detected in the case of both Rayleigh [1, 2] and thermocapillary convection [3–5]; however, for many systems the minimum of the neutral curve corresponds to monotonic perturbations. In [5] an example was given of a system for which oscillatory instability is most dangerous when the thermogravitational and thermocapillary instability mechanisms are simultaneously operative. In this paper the occurrence of convection in a two-layer system due to the combined action of the Rayleigh (volume) and thermocapillary (surface) instability mechanisms is systematically investigated. It is shown that when the Rayleigh mechanism operates primarily in the upper layer of fluid, in the presence of a thermocapillary effect oscillatory instability may be the more dangerous. If thermogravitational convection is excited in the lower layer of fluid, the instability will be monotonic.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–170, January–February, 1987.     

“Inviscid Finger” Instability in Regular Models of a Porous Medium

Displacement of a fluid from a porous medium is considered. The flow is assumed to be fast enough, i.e., the Reynolds number based on the characteristic pore size is large. If he driving fluid is less dense (for example, a gas), the interface is unstable. This instability is similar to the well–known viscous finger instability but the governing parameter is density instead of viscosity. The instability is demonstrated experimentally using two–dimensional models. In square lattices of perpendicular channels, noticeable branching of fingers is not observed, which is attributed to the anisotropy of such an artificial porous medium. A more ordinary pattern with finger branching is obtained in a two–dimensional layer of spheres, which appears to be more isotropic. A simple model describing flow in a square lattice is proposed. The initial stage of growth is considered, and the instability increment is estimated. A qualitative analysis of the nonlinear stage is performed.     

Absolute instability of a weakly conducting jet with current

The influence of current on the absolute instability of a capillary jet of nonviscous weakly conducting fluid is considered. A relation between the Weber and Alfven numbers that sets off regions of absolute and convective instability is obtained.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 179–182, July–August, 1995.     

Thermocapillary convection in two-layer systems in the presence of a surface active agent at the interface

Convective instability in a layered system due to the thermocapillary effect was investigated in [1–5]. In these studies it was shown that the perturbations responsible for equilibrium crisis may build up either monotonically or in an oscillatory fashion. In [6] the stabilizing effect of a surface active agent (SAA) on thermocapillary instability was established for a layer with a free surface. For layers of infinite thickness the effect of SAA on thermocapillary convection was studied in [7–9]. The present investigation is concerned with thermocapillary convection in a system of two layers of finite thickness in the presence of an SAA. Convection due to the lift force is not considered. It is established that the principal result of the action of the SAA is not the stabilizing effect on the monotonic mode but the appearance of a new type of oscillatory instability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2 pp. 3–8, March–April, 1986.In conclusion the authors wish to thank E. M. Zhukhovitskii for discussind the results.     

Porous Media and the Bénard–Marangoni Problem

The Rayleigh–Bénard instability for a clear fluid has its equivalent for a liquid saturated porous matrix. The phenomenological Darcy momentum law cannot give rise by itself to an instability analogous to that of Bénard–Marangoni, but the Brinkman model at least allows it. A critical Marangoni number exists leading to cellullar patterns and, for realistic values of the permeability, it is proportional to the inverse of this last parameter.     

Occurrence of thermocapillary convection in a two-layer system in the presence of a soluble surfactant

The present study considers the effect of the solubility of a surfactant on monotonic oscillatory thermocapillary instability of equilibrium in a two-layer system. It is established that with increase in the parameter which characterizes the solubility of the surfactant a reduction takes place in the threshold of the monotonic instability; finally the monotonic perturbations become most dangerous.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–175, March–April, 1988.     

Development and instability of steady convective flows in a square cavity heated from below and a field of vertically directed vibrational forces

The present paper is devoted to numerical investigation of the spatial structure and stability of secondary vibrational convective flows resulting from instability of the equilibrium of a fluid heated from below. Vibrations parallel to the vector of the gravitational force (vertical vibrations) are considered. As in earlier work [7–9], a region of finite size is used — a square cavity heated from below. It is shown that enhancement of the vibrational disturbance of the natural convective flow may either stabilize or destabilize flows with different spatial structures; it may also stabilize certain solutions of the system of convection equations that are unstable in the absence of vibrational forces. In addition, increase of the vibrational Rayleigh number can lead to a change of the mechanisms responsible for equilibrium instability and oscillatory instability of the secondary steady flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 9–18, March–April, 1991.I thank G. Z. Gershuni for assistance and extremely fruitful discussions of the results of the paper.     

Motion of the surface separating two liquids of finite depth under the influence of variable force fields

We consider the motion of the surface separating two liquids in a nonstationary gravitational field or, equivalently, under the action of a variable acceleration (an overload) perpendicular to the surface. Conditions are derived for the instability of the surface separating two liquids of finite depth in periodic, constant, and impulsive force fields; the physical mechanism acting during the development of instability is studied, and some features of the onset of instability are investigated for the case in which the space is bounded.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 55–62, September–October, 1970.     

Capillary instabilities of charged drops and electrical dispersion of liquids

The phenomenology of the instability of charged and uncharged drops and liquid menisci at the end of a capillary through which liquid is fed in constant and variable external electric fields, both uniform and nonuniform, is considered. Methods of investigating such instability are described. The steady-state deformation of drops in electric fields, the critical conditions under which their charged surface loses stability, and the laws of electrical dispersion of liquids in the final stage of instability are discussed.Yaroslavl'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 3–22, May–June, 1994.     

Stability of a homogeneous plasma confined between two parallel planes

A study is made of the conditions of global instability of a collisionless plasma with a given distribution function.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 26–28, September–October, 1970.     

Oscillatory thermocapillary instability of a liquid layer in the presence of a surfactant

The effect of capillarity and a surfactant on the stability of a liquid layer in the presence of a vertical temperature gradient is investigated. It is found that the surfactant leads to the appearance of both monotonic and oscillatory instability, the presence of a surface concentration destabilizing the equilibrium in the case of heating from below. When the free surface is heated, the surfactant stabilizes the capillary instability.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 6–10, January–February, 1993.     

Vibrational and convective instability of a plane horizontal fluid layer at finite vibration frequencies

The vibrational-convective instability of a plane horizontal fluid layer subject to longitudinal harmonic vibrations of finite frequency and transverse stratification in a static gravity field is studied. The analysis is based on the complete convection equations in the Boussinesq approximation. It is demonstrated that in the limiting case of high-frequency vibrations the results thus obtained coincide with those obtained earlier on the basis of the averaged equations. In the limiting low-frequency case the nature of the instability is quite different being due to the instability of oscillating counterstreams.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 44–51, September–October, 1996.     

Development of two- and three-dimensional perturbations in the case of an ionization instability in a channel with nonconducting walls

An lonization instability of a plasma bounded by nonconducting walls is investigated taking into account electron thermal conduction. The wave vector is considered directed at some angle to the magnetic field direction. Perturbations with a wave vector orthogonal to the magnetic field induction vector turn out to be most unstable. A relatively simple formula to compute the neutral curve separating the stability and instability domains is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 119–123, May–June, 1976.     

Stability of the motion of a rigid body in an unsteady flow

The problem of rigid-body motion in an unsteady gas flow is considered using a flow model [1] in which the motion of the body is described by a system of integrodifferential equations. The case in which among the characteristic exponents of the fundamental system of solutions of the linearized equations there are not only negative but also one zero exponent is analyzed. The instability conditions established with respect to the second-order terms on the right sides of the equations are noted. The problem may be regarded as a generalization of the problem of the lateral instability of an airplane in the critical case solved by Chetaev [2], pp. 407–408.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 18–22, May–June, 1989.     

Superheating instability in a pulsed xenon discharge

It is shown that previously obtained conditions for superheating instability substantially vary if we take into account secondary xenon ionization. Instability completely vanishes if the density of heavy particles in the discharge is kept constant and whenever a discontinuous time variation of temperature T in a restricted region between 15 · 10³ ° K and 20 · 10³ ° K is possible for a constant effective pressure. The development of instability is studied numerically by a ranging method. Stationary temperature distributions possessing a high contrast as a local temperature passes through a given range of instability with constant pressure are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 27–30, January–February, 1976.