A sharp nonlinear stability threshold in rotating porous convection

Abstract

A nonlinear stability analysis is performed for the Darcy equations of thermal convection in a fluid‐saturated porous medium when the medium is rotating about an axis orthogonal to the layer in the direction of gravity. A best possible result is established in that we show that the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. It is important to realize that the nonlinear stability boundary holds unconditionally, i.e. for all initial data, and thus for the rotating porous convection problem governed by the Darcy equations, subcritical instabilities are not possible.