J Austral Math Soc Ser B 34 pp355--367, 1993.

Linearised evaporation about a shallow half-plane pond

G. J. Weir

Abstract

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 poorly-draining soils, where the reduced ability to transmit liquid water need not be compensated by a corresponding reduction in evaporative losses. However, in freely-draining soils the interaction between evaporation and capillarity is probably small.

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Author

G. J. Weir

Appl. Math. Group, Dept. of Scientific and Industrial Res., P.O. Box 1335, Wellington, N.Z.