High Rayleigh number porous convection

Convective flow in porous media undergoes a transition around Rayleigh number $Ra = 1300$, from predominantly large-scale (quasi-) periodic rolls to vigorous columnar exchange flow driven by unsteady plume formation in boundary layers. The dynamics of these structures determine the flux of heat or solute through the system, as described by the Nusselt number $Nu$. This is of particular interest for understanding how convection affects the rate of dissolution of sequestered CO$_2$ in a saline aquifer. High resolution 2D numerical simulations of porous media Rayleigh-Benard convection are presented, which show that, for $2000