Spatiotemporal behavior of convective Turing patterns in porous media

We investigate the effects of convection on Turing patterns in porous media. We show that convectionless patterns can only exist confined to small domains. These patterns are unstable to convection if the density gradients are large enough. The numerical solution of the Schnackenberg model coupled to Darcy's law shows that the convective pattern is either steady, oscillatory, or reverses direction, depending on the density gradient. In larger domains, we find that convection leads to an oscillatory state which becomes steady for large density gradients.