 Darcy-Bénard convection

Darcy-Bénard convection is thermal convection in a porous layer heated from below, with velocity governed by Darcy's law. With fixed temperatures and impermeable boundaries, a normalized two-dimensional model uses streamfunction $\psi$ and temperature $\theta$:The control parameter is a porous-medium Rayleigh number. On $0<z<1$ with temperature values $0,-1$, the conductive state is $\psi =0$, $\theta =-z$.