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Linearised evaporation from a soil of finite depth above a water table

Published online by Cambridge University Press:  17 February 2009

V. T. Buchwald
Affiliation:
Department of Mathematics and Computing Science, The University of the South Pacific, Suva, Fiji, Current address: School of Mathematics, University of New South Wales, Sydney 2052, Australia.
F. Viera
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006.
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Abstract

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The quasi-linear infiltration problem of flow from a semi-infinite wetted region on a soil of finite depth above a horizontal water table is considered in the presence of linearised evaporative loss away from the region. The resulting equations are solved by the Wiener-Hopf technique in terms of certain infinite products. Expressions for the porosity and stream function are derived, and appropriately plotted throughout the layer.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Abramowitz, M. and Stegun, I. A. (eds). Handbook of mathematical Junctions, (Dover, New York, 1970).Google Scholar
[2]Buchwald, V. T., “The value of certain infinite productsGazette Aust. Math. Soc. 21 (1994) 3940.Google Scholar
[3]Buchwald, V. T. and Viera, F., “Linearised evaporation from a soil of finite depth near a wetted region,” Quart. J. Mech. App. Math. 49 (1996) 4964.CrossRefGoogle Scholar
[4]Lighthill, M. J., “Introduction to Fourier analysis and generalised functions,” (Cambridge Univ.Press, Cambridge, 1960).Google Scholar
[5]Noble, B., Methods based on the Wiener-Hopf technique (Pergamon Press, London, 1958, Example 3.4).Google Scholar
[6]Philip, J. R., “Flow in porous media”, Annual Rev. Fluid Mech. 2 (1970) 177204.CrossRefGoogle Scholar
[7]Philip, J. R., “Aspects of quasilinear infiltration from surface sources, especially the case α = 0.Water Resources Res. 20 (1984) 633635.CrossRefGoogle Scholar
[8]Philip, J. R., “Steady unsaturated seepage above a sloping impermeable base”, Water Resources Res. 24 (1988) 11921196.CrossRefGoogle Scholar
[9]Philip, J. R.The scattering analog for infiltration in porous media.Rev. Geophys. 27 (1989) 431448.CrossRefGoogle Scholar
[10]Raats, P. A. C., “Steady infiltration from line sources and furrowsSoil Sci. Soc. Am. Proc. 34 (1970) 709714.CrossRefGoogle Scholar
[11]Waechter, R. T. and Philip, J. R., “Steady two and three dimensional flows in unsaturated soil: the scattering analogWater Resources Res. 21 (1985) 18751887.CrossRefGoogle Scholar
[12]Weir, G. J., “Linearised evaporation about a shallow half-plane pond”, J. Aust. Math. Soc. Ser. B, 34 (1993) 355367.CrossRefGoogle Scholar
[13]Whittaker, E. T. and Watson, G. N., A course of modern analysis, (Cambridge Univ. Press, Cambridge, 1963).Google Scholar