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Published online by Cambridge University Press: 04 November 2014
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 $\mathit{Ra}$, in which the domain is considered deep, shallow or of intermediate depth, and for which the Damköhler number
$\mathit{Da}$ 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-
$\mathit{Ra}$ convection, analysis and simulation suggest that the time-averaged solute transfer rate scales with
$\mathit{Ra}$ and the plume horizontal wavenumber with
$\mathit{Ra}^{1/2}$, with coefficients modulated by
$\mathit{Da}$ in each case. For large
$\mathit{Da}$, the rapid reaction rate limits the plume depth and the boundary layer restricts the rate of solute transfer to the bulk, whereas for small
$\mathit{Da}$ the average solute transfer rate is ultimately limited by the domain depth and the convection is correspondingly weaker.