Stability of High Rayleigh-Number Equilibrium Solutions of the Darcy--Oberbeck--Boussinesq Equations

There has been significant renewed interest in dissolution-driven convection in porous layers owing to the potential impact of this process on carbon dioxide storage in terrestrial aquifers. In this talk, we present some numerically-exact equilibrium solutions to the porous medium convection problem in small laterally-periodic domains at high Rayleigh number $Ra$. The ``uni-cellular'' equilibrium solutions first found by Corson and Chini (2011) by solving the steady Darcy--Oberbeck--Boussinesq equations are recovered and, in the interior (i.e. away from upper and lower boundary layers), are shown to have the same horizontal-mean structure as the ``heat-exchanger'' solutions identified by Hewitt et al. (2012). Secondary stability analysis of the steady solutions is performed, and implications for high-Ra porous medium convection are discussed.