Scaling of the Richards Equation Under Invariant Flux Boundary Conditions

Abstract

Richards' equation of the unsaturated flow has been scaled in an invariant form with regard to the variation of boundary conditions within a defined class of flow problems. Two classes of problems were examined: (1) vertical infiltration into a homogeneous soil with a constant surface boundary flux, and (2) vertical infiltration into a soil topped by a seal layer of negligible thickness and with a given positive pressure head above the seal layer. The solution of the problem when plotted as function of scaled variables is unchanged for any variation at the boundary, i.e., variation of the flux in the first class and variation of the seal in the second class.