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

Abstract

The stability of a horizontal fluid and fluid-saturated porous layer heated from below is examined for the case of a time-dependent buoyancy force generated by gravity modulation. A linear stability analysis is performed to show that the gravity modulation can significantly affect the stability limits of the system. A method based on small amplitude of the modulation proposed by Venezian (Journal of Fluid Mechanics, 1969, 35, 243) [1] is used to compute the critical value of Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of the modulation, Prandtl number and porous parameter. It is found that the low frequency g-jitter can have a significant effect on the stability of the system. The Darcy limit and viscous flow limit are obtained as degenerate cases of the Brinkman model. Finally, an asymptotic analysis is presented for small and large frequencies. © 1997 Elsevier Science Ltd.