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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 and
F. Viera
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.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 4 , April 1998, pp. 557 - 576
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 products” Gazette Aust. Math. Soc. 21 (1994) 39–40.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) 49–64.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) 177–204.CrossRefGoogle Scholar
[7]Philip, J. R., “Aspects of quasilinear infiltration from surface sources, especially the case α = 0.” Water Resources Res. 20 (1984) 633–635.CrossRefGoogle Scholar
[8]Philip, J. R., “Steady unsaturated seepage above a sloping impermeable base”, Water Resources Res. 24 (1988) 1192–1196.CrossRefGoogle Scholar
[9]Philip, J. R. “The scattering analog for infiltration in porous media.” Rev. Geophys. 27 (1989) 431–448.CrossRefGoogle Scholar
[10]Raats, P. A. C., “Steady infiltration from line sources and furrows” Soil Sci. Soc. Am. Proc. 34 (1970) 709–714.CrossRefGoogle Scholar
[11]Waechter, R. T. and Philip, J. R., “Steady two and three dimensional flows in unsaturated soil: the scattering analog” Water Resources Res. 21 (1985) 1875–1887.CrossRefGoogle Scholar
[12]Weir, G. J., “Linearised evaporation about a shallow half-plane pond”, J. Aust. Math. Soc. Ser. B, 34 (1993) 355–367.CrossRefGoogle Scholar
[13]Whittaker, E. T. and Watson, G. N., A course of modern analysis, (Cambridge Univ. Press, Cambridge, 1963).Google Scholar