Convective instability in a gravity modulated anisotropic thermally stable porous medium

The effect of gravity modulation on the onset of convection in a horizontal fluid saturated porous layer in which the applied temperature gradient is opposite to that of gravity is investigated. The flow through the porous layer is governed by an extended form of Darcy's law incorporating Brinkman's boundary layer correction. The permeability and thermal conductivity of the medium are assumed to be transversely anisotropic. A stability analysis based on the method of small perturbations is performed using normal mode assumption. The study is focussed on low amplitude gravity modulation and the thresholds are found using Mathieu's functions. The emergence of instability via the synchronous and subharmonic modes and the transition between them are discussed as a function of the physical parameters of interest.