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Mathematical Physics of Infiltration on Flat and Sloping Topography

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Environmental Studies

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 79))

Abstract

We review the modern mathematical-physical analysis of water movement in unsaturated soils, which is central to understanding of the terrestrial segment of the hydrologie cycle. The relevant flow equation is a strongly nonlinear Fokker-Planck (convection-diffusion) equation. The theory of infiltration (the penetration into a soil mass of water made available at its surface) is described. Solutions fire developed for hillslope topographies. We deal primarily with ponded infiltration, but constant-rainfall infiltration is discussed also. The emphasis is on quasi-analytic and analytic solutions. Fully nonlinear solutions are developed, together with linearized solutions of certain problems. The nonlinear solutions involve either usefully convergent series or travelling waves. The linearizations use product solutions.

The work was initiated during a visit to the Centre for Industrial and Applied Mathematics, University of Oxford, England.

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Authors and Affiliations

  1. CSIRO Centre for Environmental Mechanics, Canberra, 2601, Australia

    J. R. Philip

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  1. J. R. Philip
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Editor information

Editors and Affiliations

  1. Rice University, P.O. Box 1892, Houston, TX, 77843, USA

    Mary Fanett Wheeler

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© 1996 Springer-Verlag New York, Inc.

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Philip, J.R. (1996). Mathematical Physics of Infiltration on Flat and Sloping Topography. In: Wheeler, M.F. (eds) Environmental Studies. The IMA Volumes in Mathematics and its Applications, vol 79. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8492-2_16

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  • DOI: https://doi.org/10.1007/978-1-4613-8492-2_16

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8494-6

  • Online ISBN: 978-1-4613-8492-2

  • eBook Packages: Springer Book Archive

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