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

Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows

“…They seem to be first to derive a closed-form unsteady solution for the thermal convection in a differently heated vertical slot subjected to the gravity modulation. Later, a similar solution was independently found by Gershuni, Keller, and Smorodin [27] for the case of the finite-frequency vibrations applied to a non-uniformly heated fluid layer performing periodic harmonic vibrations of the low frequency along with the layer in weightlessness. Since the convective flow solution found is quite physical (in contrast to non-stationary variants of Ostroumov-Birikh's flow [14]), and the behavior of the convective system in microgravity conditions is a quite topical area for research recently, several works have appeared to study the stability of this flow by applying the Floquet theory [26][27][28][29][30][31].…”

“…It turned out that it is possible to find similar solutions for inhomogeneous media. Bratsun and Teplov [32,33] have shown that the solution [26,27] can be generalized to the case of a dusty medium (fluid with small solid particles). Since the flow is significantly non-stationary, one should take into account the effect of the non-stationary friction forces between the fluid and solid phases on the stability of the flow [34].…”

Convection in heated fluid layers subjected to time-periodic horizontal accelerations

“…x . The results for the onset of transverse roll instabilities for positive as well as negative values of R x can be compared with the corresponding results obtained in the case P = 1 by Gershuni et al (1996). Good agreement has been found.…”

“…In this work, we have presented a comprehensive analysis of a Rayleigh-Bénard convection set-up subjected to a periodic acceleration in the plane. Besides considerably extending an earlier linear analysis of Gershuni et al (1996), we have investigated the nonlinear regime for the first time. In particular, we have identified some specific secondary bifurcations that lead to complex spatio-temporal patterns.…”

“…Another special case is the horizontal fluid layer subjected to horizontal accelerations which is the issue of this paper. This problem was first considered by Gershuni, Keller & Smorodin (1996) for a fixed direction of the acceleration and for the single value P = 1 of the Prandtl number P in the linear regime. In the present paper we extend these investigations in several ways.…”