Rayleigh–Darcy convection for the ultimate regime in three dimensions

We conduct direct numerical simulations (DNS) to reach the ultimate regime for Rayleigh-Darcy convection (RDC) in a three-dimensional domain. These simulations at large Rayleigh numbers (Ra) up to 1×10⁶ are consistent with realistic Ra encountered in CO_² sequestration in deep saline aquifers (∼ O(Ra = 10⁵ − 10⁶)). The Nusselt number (Nu) and interior wave number (k) are used to analyze the ensuing heat transfer and flow dynamics. We find that the ratio Nu/Ra approaches a constant value for Ra > 5×10⁵. Under the vigorous action of buoyancy for higher Ra, high-temperature fluid protrudes faster from the boundary and reaches the opposite boundary. These plumes further form large columnar structures which appear as bright ridges at the boundary.