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

  • T. J. Ward (a1), O. E. Jensen (a2), H. Power (a3) and D. S. Riley (a1)

Abstract

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.

Copyright

Corresponding author

Email address for correspondence: Oliver.Jensen@manchester.ac.uk

References

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JFM classification

Type Description Title
VIDEO
Movie

Ward et al. supplementary movie
Concentration (left) and streamfunction (right) for fully established convection in a deep domain for parameters as given in figure 2 of the main paper.

 Video (10.1 MB)
10.1 MB
VIDEO
Movie

Ward et al. supplementary movie
Concentration (left) and streamfunction (right) for fully established convection in a deep domain for parameters as given in figure 2 of the main paper.

 Video (6.0 MB)
6.0 MB

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

  • T. J. Ward (a1), O. E. Jensen (a2), H. Power (a3) and D. S. Riley (a1)

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