Relaxed energy stability analysis on the onset of buoyancy-driven instability in the horizontal porous layer

Abstract

The onset of buoyancy-driven instability in an initially quiescent, isotropic fluid-saturated porous layer is analyzed theoretically. Darcy’s law is employed to examine characteristics of fluid motion under the Boussinesq approximation. The critical condition to mark the onset of convective instability is analyzed based on the relaxed energy method. The predicted critical conditions are compared with the various results based on the conventional energy method and the linear stability theory.