A short review on porous media convection

Abstract

We briefly review the investigations of pattern formation and transport properties of RayleighDarcy convection (or the Elder Problem), including laboratory experiments, theoretical analysis and numerical simulations. It is shown that the flow exhibits power-law-scaling characteristics at large Rayleigh-Darcy number Ra, a dimensionless parameter representing the ratio of the driving buoyancy forces to the diffusive forces. Namely, the mean spacing between neighboring interior plumes shrinks as Ra −α with the scaling exponent α ≤ 1/2 and the convective flux increases linearly with Ra. However, more laboratory experiments are needed to validate these scalings. Additionally, many conditions, e.g. the inclination of the layer and hydrodynamic dispersion, etc., may lead to a large uncertainty in the flow pattern and transport efficiency.