Onset of thermal convection in a superposed fluid-porous layer subjected to high-frequency longitudinal vibration in weightlessness

Abstract

The onset of thermal vibrational convection in a fluid layer overlaying a fluid-saturated porous layer is studied in zero gravity. A thermal gradient is imposed transverse to the layers. The two-layer system performs high-frequency small-amplitude oscillations perpendicular to the thermal gradient. We solve a linear stability problem with respect to the fluid quasi-equilibrium state. The basic closed-looped oscillatory flow with zero average velocity characterizes the quasi-equilibrium state. The average roll convection is generated if the Rayleigh number exceeds its threshold value. The bimodal marginal stability curves are revealed at different ratios of the fluid layer thickness to that of the porous layer. They are somewhat similar to the curves first obtained by Chen and Chen for the onset of thermal convection in a superposed fluid-porous layer in a gravity field. We find that short-wave convection replaces the long-wave one with an increase in the ratio of layer thicknesses. The transition is accompanied by a jump-wise increase in the wave number of the most dangerous convective rolls. However, the critical wave number of the vibrational convection rolls can change by several orders of magnitude in contrast to that of the gravitational convection rolls. So, one can have super short-wave convection in zero gravity. A value of the instability threshold varies non-monotonically. The convection onset delays rather weakly at small thickness ratios. On the contrary, sufficiently high thickness ratios make the convection onset speed up strongly.