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Abstract

Dry lakes covered with a salt crust organised into beautifully patterned networks of narrow
ridges are common in arid regions. Here, we consider the initial instability and the ultimate
fate of buoyancy-driven convection that could lead to such patterns. Specifically, we look
at convection in a deep porous medium with a constant throughflow boundary condition
on a horizontal surface, which resembles the situation found below an evaporating salt
lake. The system is scaled to have only one free parameter, the Rayleigh number, which
characterises the relative driving force for convection. We then solve the resulting linear
stability problem for the onset of convection. Further exploring the nonlinear regime of this
model with pseudo-spectral numerical methods, we demonstrate how the growth of small
downwelling plumes is itself unstable to coarsening, as the system develops into a dynamic
steady state. In this mature state we show how the typical speeds and length scales of the
convective plumes scale with forcing conditions, and the Rayleigh number. Interestingly, a
robust length scale emerges for the pattern wavelength, which is largely independent of the
driving parameters. Finally, we introduce a spatially inhomogeneous boundary condition
– a modulated evaporation rate – to mimic any feedback between a growing salt crust and
the evaporation over the dry salt lake. We show how this boundary condition can introduce
phase locking of the downwelling plumes below sites of low evaporation, such as at the
ridges of salt polygons.