Wetting fronts in one-dimensional periodically layered soils

George Fennemore Jack Xin

Fluid Dynamics and Shock Waves mathscidoc:1912.43882

SIAM Journal on Applied Mathematics, 58, (2), 387-427, 1998.4
We study wetting front (traveling wave) solutions to the Richards equation that describe the vertical infiltration of water through one-dimensional periodically layered unsaturated soils. We prove the existence, uniqueness, and large time asymptotic stability of the traveling wave solutions under prescribed flux boundary conditions and certain constitutive conditions. The traveling waves are connections between two steady state solutions that form near the ground surface and towards the underground water table. We found a closed form expression of the wave speed. The speed of a traveling wave is equal to the ratio of the flux difference and the difference of the spatial averages of the two steady states. We give both analytical and numerical examples showing that the wave speeds in the periodic soils can be larger or smaller than those in the homogeneous soils which have the same mean diffusivity and conductivity
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@inproceedings{george1998wetting,
  title={Wetting fronts in one-dimensional periodically layered soils},
  author={George Fennemore, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210425724231446},
  booktitle={SIAM Journal on Applied Mathematics},
  volume={58},
  number={2},
  pages={387-427},
  year={1998},
}
George Fennemore, and Jack Xin. Wetting fronts in one-dimensional periodically layered soils. 1998. Vol. 58. In SIAM Journal on Applied Mathematics. pp.387-427. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210425724231446.
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