Strong Rayleigh–Darcy convection regime in three-dimensional porous media

We perform large-scale numerical simulations to study Rayleigh–Darcy convection in three-dimensional fluid-saturated porous media up number $Ra=8\times 10^4$ . At these large values of $Ra$ , the flow is dominated by columnar structures – called megaplumes which span entire height domain. Near boundaries, hierarchically organized, with fine-scale interacting and nesting form larger-scale supercells. observe that correlation between structure core domain at boundaries decreases only slightly for increasing remains rather high even largest considered here. This confirms supercells are boundary footprint dominating In agreement available literature predictions, we show thickness thermal layer scales very well Nusselt as $\delta \sim 1/ Nu$ Measurements mean wavenumber inverse length scale support scaling $\bar {k} Ra^{0.49}$ good theoretical predictions. Interestingly, behaviour near Ra^{0.81}$ distinguishably different from presumed linear behaviour. hypothesize a can be observed ultimate regime, argue set excess $5\times 10^5$ whereas sublinear recovered more modest The present results expected help development long desired reliable models predict large- high- regime typically encountered geophysical processes, such instance geological carbon dioxide sequestration.