Ultimate Regime of High Rayleigh Number Convection in a Porous Medium

Well-resolved direct numerical simulations of 2D Rayleigh-Benard convection in a porous medium are presented for Rayleigh numbers Ra <= 4 x 10(4) which reveal that, contrary to previous indications, the linear classical scaling for the Nusselt number, Nu similar to Ra, is attained asymptotically. The flow dynamics are analyzed, and the interior of the vigorously convecting system is shown to be increasingly well described as Ra -> infinity by a simple columnar heat-exchanger model with a single horizontal wave number k and a linear background temperature field. The numerical results are approximately fitted by k similar to Ra-0.4.