Abstract: Motivated loosely by the problem of carbon sequestration in underground aquifers, I will describe computations and analysis of one-sided two-dimensional convection of a solute in a fluid-saturated porous medium, focusing on the case in which the solute decays via a chemical reaction. Scaling properties of the flow at high Rayleigh number are established and rationalized through an asymptotic model, that addresses the transient stability of a near-surface boundary layer and the structure of slender plumes that form beneath. The boundary layer is shown to restrict the rate of solute transport to deep domains. Knowledge of the plume structure enables slow erosion of the substrate of the reaction to be described in terms of a simplified free boundary problem.
Co-authors: KA Cliffe, H Power, DS Riley, TJ Ward
- Industrial and Applied Mathematics Seminar