Effect of gravity modulation on the onset of thermal convection in rotating fluid and porous layer

Abstract

The combined effect of gravity modulation and rotation on the onset of thermal convection in a horizontal fluid layer and a fluid-saturated porous layer is studied analytically using linear stability theory. The regular perturbation method based on small amplitude of modulation is employed to compute the critical value of Rayleigh number and wavenumber. We considered in the present paper only synchronous mode. The correction critical Rayleigh number is calculated as a function of Taylor number, Prandtl number, Darcy number, frequency of the modulation, normalized porosity, and viscosity ratio. It is shown that in general the gravity modulation produces a stabilizing effect in case of viscous fluid layer and both destabilizing and stabilizing effects in case of Brinkman porous layer while it produces a destabilizing effect in case of Darcy porous layer. The low frequency gravity modulation is found to have a significant effect on the stability of the system. It is shown that the onset of convection can be advanced or delayed by proper tuning of various governing parameters. The results of Darcy limit and viscous flow limit are derived as the degenerate cases of Brinkman model.