Influence of Depth-Dependent Brinkman Viscosity on the Onset of Convection in Ternary Porous Layers

Abstract

In the Darcy–Boussinesq–Brinkman scheme, the onset of convection in a porous horizontal layer \(\mathtt L \) with depth-dependent permeability and viscosities is investigated. The linear instability is studied and the global nonlinear stability is investigated via the auxiliary system method. By looking for symmetries and skew-symmetries hidden in the Darcy–Boussinesq–Brinkman model, a condition, in closed form, guaranteeing the global nonlinear stability is furnished. Applications to the earth’s mantle and to artificial porous materials are furnished.