The steady distribution of moisture beneath a two‐dimensional surface source

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Abstract
The steady distribution of moisture beneath a two‐dimensional strip source is analyzed by applying the quasi‐linear approximation. The source is described by specifying either the moisture content or the infiltration rate. A water table is specified at some depthDbelow the surface, the depth varying from shallow to semi‐infinite. Numerical solutions are determined, via the boundary integral equation method, as a function of the material inverse sorptive length α, the width of the strip source 2L, and the depth to the water table. The moisture introduced at the source is broadly spread below the surface when αL≪ 1, for which absorption by capillary forces is dominant over gravity‐induced flow. Conversely, the distribution becomes fingerlike along the vertical when αL≫ 1, where gravity is dominant over absorption. For a source described by specifying the moisture content, the presence of a water table at finite depth influences the infiltration through the source when αDis less than about 4; infiltration rates obtained assuming the water table depth is semi‐infinite are of sufficient accuracy for greater values of αD. When the source is described by a specified infiltration flux, the maximum allowable value of this flux for which the material beneath the source remains unsaturated is determined as a function of nondimensional sorptive number and depth to the water table.

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