Global stability for penetrative double-diffusive convection in a porous medium

Linear and nonlinear stability analyses of penetrative double-diffusive convection in a porous medium are performed. Adopting a standard energy method approach yields a nonlinear threshold which is independent of the salt field. An adaptation of a new operative method by Mulone and Straughan (ZAMM 86: 507-520, 2006) is used to construct a nonlinear threshold which is dependent on the salt field, greatly reducing the region of potential subcritical instabilities. The employment of this operative technique for problems with spatially dependent coefficients, as presented in this paper, is unexplored in the present literature.