Burgers’ equation

Abstract

We present the analytical constant-flux solution to Burgers’ equation. Burgers’ equation is a minimally nonlinear Fokker-Planck diffusion equation, applicable to infiltration into soils with a constant diffusivity and quadratic conductivity-water content relationship. Field Bungendore fine sand has a near-constant diffusivity-water content relationship, and analytical solutions of Burgers’ equation are in good agreement with field profiles of water content obtained in situ with a rainfall simulator. The solutions and experimental data all relate to nonponding infiltration with fluxes less than the saturated hydraulic conductivity; however, a wide range of elapsed times and flux rates are covered. Predicted wet-front penetration is in good agreement with the field experimental data. The complete analytical solution can be evaluated using a programmable hand calculator. The simpler “profile-at-infinity” solution is shown to be surprisingly accurate over a wide range of times, giving useful results easily. An expression for the time to ponding is also presented. Show more