Double diffusion in rotating porous media under general boundary conditions

In this article we study a binary fluid saturating a rotating porous medium; the fluid is modeled according to Darcy–Brinkman law and the boundary conditions are rigid or stress-free on the velocity field and of Robin type on temperature and solute concentration. We determine the threshold of linear instability and its dependence on Taylor and Darcy numbers. Using a Lyapunov function we prove analytically, under certain assumptions, the coincidence of linear and nonlinear thresholds. A second Lyapunov function allows us to prove numerically the coincidence of the two thresholds with weaker assumptions on the parameters. We show that in the particular limit case of fixed heat and solute fluxes this system has a remarkable feature: the wave number of critical cells goes to zero when the Taylor number is below a threshold. Above such threshold, the wave number is non-zero when the Darcy number belongs to a finite interval. These phenomena could perhaps be tested experimentally.