High-Rayleigh-number convection of a reactive solute in a porous medium

We consider two-dimensional one-sided convection of a solute in a fluid-saturated porous medium, where the solute decays via a first-order reaction. Fully nonlinear convection is investigated using high-resolution numerical simulations and a low-order model that couples the dynamic boundary layer immediately beneath the distributed solute source to the slender vertical plumes that form beneath. A transient-growth analysis of the boundary layer is used to characterise its excitability. Three asymptotic regimes are investigated in the limit of high Rayleigh number Ra, in which the domain is considered deep, shallow or of intermediate depth, and for which the Damkohler number Da is respectively large, small or of order unity. Scaling properties of the flow are identified numerically and rationalised via the analytic model. For fully established high-Ra convection, analysis and simulation suggest that the time-averaged solute transfer rate scales with Ra and the plume horizontal wavenumber with Ra-1/2, with coefficients modulated by Da in each case. For large Da, the rapid reaction rate limits the plume depth and the boundary layer restricts the rate of solute transfer to the bulk, whereas for small Da the average solute transfer rate is ultimately limited by the domain depth and the convection is correspondingly weaker.