Towards the ultimate regime in Rayleigh-Darcy convection

Numerical simulations are used to probe Rayleigh-Darcy convection in fluid-saturated porous media towards the ultimate regime. The present three-dimensional dataset, up to Rayleigh-Darcy number Ra=80 000,  suggests that the appropriate scaling of the Nusselt number is  Nu=0.0081Ra+0.067Ra^0.61, fitting the computed data for Ra>1000. Extrapolation of current predictions to the ultimate linear regime yields the asymptotic law Nu=0.0081Ra, about 16% less than indicated in previous studies. Upon examination of the flow structures near the boundaries, we confirm previous indications of small flow cells hierarchically nesting into supercells, and we show evidence that the supercells at the boundary are the footprints of the megaplumes that dominate the interior part of the flow. The present findings pave the way for more accurate modeling of geophysical systems, with special reference to geological CO₂ sequestration.