Onset of buoyancy-driven convection in isotropic porous media heated from below

A theoretical analysis of buoyancy-driven instability under transient basic fields is conducted in an initially quiescent, fluid-saturated, horizontal, isotropic porous layer. Darcy's law is employed to explain characteristics of fluid motion, and Boussinesq approximation is used to consider the density variation. Under the principle of exchange of stabilities, a stability analysis is conducted based on the linear stability analysis and energy method and their modifications. The critical condition of onset of buoyancy-driven convection is obtained as a function of the Darcy-Rayleigh number. The propagation theory and the modified energy method under the self-similar coordinate suggest reasonable stability criteria and support each other. The former one based on the linear stability theory predicts more stable results than the latter based on the energy method. The growth period for disturbances to grow seems to be required until the instabilities are detected experimentally.