Patterned ground formation and solar radiation ground heating
A mathematical analysis is presented for the onset of cellular convection in a saturated horizontal porous layer which is subject to a time-periodic boundary condition. Darcy’s law is used but variable permeability is allowed for and a parabolic equation of state is assumed. The modulated boundary c...
| Published in: | Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences |
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| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
The Royal Society
1992
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1098/rspa.1992.0105 https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1992.0105 |
| Summary: | A mathematical analysis is presented for the onset of cellular convection in a saturated horizontal porous layer which is subject to a time-periodic boundary condition. Darcy’s law is used but variable permeability is allowed for and a parabolic equation of state is assumed. The modulated boundary condition produces a time-periodic temperature gradient in the layer. To obtain predictions for the onset of convection and the critical wavenumber from the linear system, we use the Galerkin method and Floquet theory. Similar predictions are obtained from the nonlinear system via the energy method. We study the effect varying frequency and modulation amplitude have on these predictions. To illustrate this we apply our analysis to the formation of polygonal ground, a geological phenomenon consisting of stone borders forming regular hexagons and soil centres. The theoretical model for patterned ground is based on the onset of convection in a saturated soil below which is a cold permafrost layer. |
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