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Two-Dimensional Similarity Solution: Theory and Application to the Determination of Soil-Water Diffusivity¹

ABSTRACT

The Bruce and Klute methods (1956) to measure the soil-water diffusivity (D) relies on the existence of a similarity solution for the one-dimensional movement of water when the soil-water potential is maintained constant at one end of a horizontal column of soil. If the flux is kept constant along a line-source, a similarity solution exists also in two-dimensions and an exact equation for this case is derived:

where _o is the initial moisture content, is the moisture content after time, t, and is the similarity variable.

The application of this equation in measuring the soil-water diffusivity of a sandy soil is shown.

¹ Contribution from the Dept. of Ecology and Climatology, The Connecticut Agric. Exp. Sta., New Haven 06504.

² Associate Scientist and Mathematician, respectively. Present address of first author: CSIRO Division of Plant Industry, P.O. Box 1600, Canberra City, A.C.T., 2601. Australia.

Received for publication June 6, 1974. Accepted for publication January 14, 1975.