Similarity Solution of Overland Flow on Pervious Surface

Abstract

Similarity solutions for the overland flow‐infiltration problem are obtained by use of a physically‐based mathematical model. The mathematical model is founded on the kinematic equations of overland flow and the Green‐Ampt formulation of the infiltration process. The governing equations of surface flow and infiltration are coupled and rewritten in terms of four physically‐based nondimensional parameters. Constant values of these parameters imply hydraulic similarity of an infinite number of different overland flow‐infiltration situations. An implicit finite difference technique is employed to solve the governing equations. The similarity approach is verified by comparisons of similarity solutions with the results of a theoretically sophisticated mathematical model for the cases of Columbia sandy loam, Yolo light clay, and Guelph loam. Also, a group of peak discharge prediction charts are developed based on the similar solutions of the overland flow‐infiltration problem and presented to emphasize the feasibility of the similarity approach. The use of these charts is illustrated by a practical application section included in the paper.