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Infiltration from a Trickle Source: I. Mathematical Models¹

ABSTRACT

Theoretical considerations and mathematical tools to analyze multidimensional transient infiltration from a trickle source have been developed. Two mathematical models were considered: (i) a plane flow model involving the Cartesian coordinates x and z; and (ii) a cylindrical flow model described by the cylindrical coordinates r and z. The diffusion- type water flow equation in unsaturated soil was solved numerically by an approach that combines the noniterative ADI difference procedure with Newton's iterative method. The numerical results have been compared with Wooding's solution for steady infiltration from a circular pond and with a simple one-dimensional solution. These comparisons indicate that the method is reliable and can be used with confidence. Typical results are demonstrated to show the effect of trickle discharge on the water content field, the saturated water entry zone, and the water flux at the soil surface.

¹ Contribution from the Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel; The Hebrew University of Jerusalem, Rehovot, Israel; and The Volcani Institute of Agricultural Research, Bet Dagan, Israel. 1971 Series, no. 1878-E.

² Mathematician, The Weizmann Inst. of Sci.; Soil Physicist, The Volcani Inst. of Agr. Res.; Graduate Student, The Weizmann Inst. of Sci.; Graduate Student, The Hebrew Univ. of Jerusalem; Soil Physicist, the Volcani Inst. of Agr. Res.; and Professor of Irrigation, the Hebrew Univ. of Jerusalem.

Received for publication January 6, 1971. Accepted for publication April 30, 1971.