Burgers' equation: A general nonlinear solution of infiltration and redistribution

Abstract

The general one-dimensional solution of Burgers equation is developed using a series of transformations and the Green's function method. The solution gives the distribution of the reduced water content in a semi-infinite and in a finite domain for arbitrary initial moisture distributions. The boundary condition at the soil surface can be either a time-dependent flux or constant water content while the bottom boundary condition for the finite case is a constant water content value. Explicit results for a uniform, discrete, hydrostatic and steady state initial moisture profiles are derived. An analytical solution that spans the preponding to the postponding period of rainfall is also obtained. Expressions for the time to ponding and infiltration equations are presented for the various cases of initial moisture profiles and a shallow water table. These results allowed the quantification of the error in the various approximations to the time to ponding and the cumulative infiltration in the postponding period.