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  • Scope for further analytical solutions for constant flux Infiltration into a semi-Infinite soil profile or redistribution in a finite soil profile

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    Author(s)
    Barry, DA
    Parlange, JY
    Lisle, IG
    Li, L
    Jeng, DS
    Stagnitti, F
    Sander, GC
    Griffith University Author(s)
    Jeng, Dong-Sheng
    Sander, Graham C.
    Year published
    2002
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    Abstract
    We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, ...
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    We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.
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    Journal Title
    Water Resources Research
    Volume
    38
    Issue
    12
    DOI
    https://doi.org/10.1029/2001WR000611
    Copyright Statement
    © 2002 American Geophysical Union. The attached file is reproduced here in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
    Subject
    Physical Geography and Environmental Geoscience
    Civil Engineering
    Environmental Engineering
    Publication URI
    http://hdl.handle.net/10072/6656
    Collection
    • Journal articles

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