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Abstract
Abstract
Highlights
This study of convection in a porous medium is motivated by the patterns shown in figure 1
Dry lakes covered with a salt crust organised into beautifully patterned networks of narrow ridges are common in arid regions
We have presented a linear stability analysis and subsequent numerical study of buoyancy-driven convection in a fluid-saturated porous medium with surface evaporation and where fluid is replenished from a distant reservoir
Summary
This study of convection in a porous medium is motivated by the patterns shown in figure 1. In the slightly different case of a constant pressure boundary condition at the surface, a situation that resembles an evaporating salt lake covered with brine, the critical values of Rac ≈ 6.95 and kc ≈ 0.43 are smaller and the system is unstable for a greater range of parameters (Wooding 1960). We are able to complement the existing analysis by determining the most unstable mode for both constant pressure and constant throughflow boundary conditions, as well as solving for the growth rate of an arbitrary mode This is followed by a numerical study of the ultimate fate of this instability, including a discussion of how the resulting convection coarsens and scales in the highly nonlinear regime
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