Abstract
The influence of a water-ice phase change on the onset of natural convection is examined for a saturated porous layer overlying a frozen region. Darcy's law is used and a parabolic equation of state is assumed for water. From a linear instability analysis we obtain predictions for the onset of convection in the melted region and the corresponding criticial wavenumber. The critical numbers are calculated by employing finite differences and solving the associated generalized eigenvalue problem. We study the effect varying thermal conductivities and boundary conditions have on these predictions. The analysis is applied to the formation of patterned ground, a geophysical phenomenon of stone borders forming regular hexagonal patterns. The theoretical model for patterned ground is based on natural convection in saturated soil below which is a cold permafrost layer.
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McKay, G. Patterned ground formation and convection in porous media with a phase change. Continuum Mech. Thermodyn 8, 189–199 (1996). https://doi.org/10.1007/BF01181855
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DOI: https://doi.org/10.1007/BF01181855