Hostname: page-component-669899f699-tzmfd Total loading time: 0 Render date: 2025-04-24T11:21:57.274Z Has data issue: false hasContentIssue false
  • English
  • Français

Linearised evaporation about a shallow half-plane pond

Published online by Cambridge University Press:  17 February 2009

G. J. Weir
G. J. Weir
Affiliation:
Appl. Math. Group, Dept. of Scientific and Industrial Res., P.O. Box 1335, Wellington, N.Z.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Wiener-Hopf technique is applied to the quasi-linear infiltration problem of flow from a shallow half-plane pond. Fully-saturated conditions hold immediately under the pond, while on the surface away from the pond the linearised evaporative loss is assumed to be proportional to the local relative permeability.

Evaporation from the non-wetted region increases the water flow from the pond into the soil, thereby coupling to the effects from capillarity. Linearised evaporation introduces an additional length scale and additional logarithmic expressions to those derived previously. The total rate of volumetric flow into the soil from the pond per unit length of perimeter, in addition to the usual gravity flow, increases somewhat slowly as evaporation increases. The most extreme case considered in this paper yielded an additional flow rate 63% greater than that obtained in the absence of evaporation.

The interaction between evaporation and capillarity is enhanced in poorlydraining soils, where the reduced ability to transmit liquid water need not be compensated by a corresponding reduction in evaporative losses. However, in freelydraining soils the interaction between evaporation and capillarity is probably small.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 3 , January 1993 , pp. 355 - 367
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Carrier, G. F., Krook, M. and Pearson, C. E., Functions of a complex variable (McGraw-Hill Book Co., New York, 1966).Google Scholar
[2]Hillel, D., Soil and water, physical principles and processes (Academic Press, New York, 1971).Google Scholar
[3]Noble, B., Methods based on the Wiener-Hopf technique, (Pergamon Press, London, 1958).Google Scholar
[4]Philip, J. R., “Steady infiltration from buried point sources and spherical cavities”, Water Resour. Res. (4) (1968) 1039–1047.CrossRefGoogle Scholar
[5]Philip, J. R., “Evaporation, and moisture and heat fields in the soil”, J. Meteorol. 14 (1975) 354–366.2.0.CO;2>CrossRefGoogle Scholar
[6]Pruess, K., TOUGH Users Guide, Lawrence Berkeley Laboratory, report for the US Department of Energy, 1986.Google Scholar
[7]Waechter, R. T. and Philip, J. R., “Steady two- and three-dimensional flows in unsaturated soil: the scattering analog”, Water Resour. Res. (21) (1985) 1875–1887.Google Scholar
[8]Weir, G. J., “Steady infiltration from large shallow ponds”, Water Resour. Res. (22) (1986) 1462–1468.Google Scholar