HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Lockington, D. Articles by Surin, A. Search for Related Content PubMed Articles by Lockington, D. Articles by Surin, A. Agricola Articles by Lockington, D. Articles by Surin, A.

Optimal Prediction of Saturation and Wetting Fronts during Trickle Irrigation¹

ABSTRACT

The nonlinear diffusion equation in spherical geometry describes water movement from a point source into a porous medium. This situation occurs, for example, in the early stages of trickle irrigation. Prediction of the saturation and wetting front positions during irrigation is of obvious practical importance. In the present paper, a general formula which predicts the positions of the two fronts is found by optimization. For particular soil properties the exact numerical solution of the diffusion equation can be easily found and is used to check the accuracy of the optimization formula. This formula proves to be extremely accurate. A simple asymptotic solution is also obtained which compares favorably with the above results in the long-time limit. The maximum error associated with neglecting gravity is quantified using this solution and proves to be quite acceptable for most practical applications. In those few cases when this error is too large to be neglected and gravity needs to be included in the theory, other effects, e.g., instability, should also be considered.

¹ Contribution from the School of Australian Environmental Studies, Griffith University, Brisbane, Queensland, Australia, 4111.

² Postgraduate Student and Professor, Griffith University, respectively.

³ Professor, Dep. of Mathematics, University of Rouen, France.

Received for publication March 9, 1983. Accepted for publication December 8, 1983.