Ultimate Regime of High Rayleigh Number Convection in a Porous Medium

Well-resolved direct numerical simulations of 2D Rayleigh-Bénard convection in a porous medium are presented for Rayleigh numbers Ra≤4×104 which reveal that, contrary to previous indications, the linear classical scaling for the Nusselt number, Nu∼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→∞ 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∼Ra0.4