ANALYTICAL SOLUTION FOR ONE-DIMENSIONAL DRAINAGE - BURGERS AND SIMPLIFIED FORMS

Solutions are developed for Burgers' equation and for the surface wate r content subject to one-dimensional drainage. These are found as limi ting cases of Richards' equation using diffusivity and conductivity fu nctions from Fujita as extended by Broadbridge and White. The solution from Burgers' equation can generally be expressed as a function of on ly a dimensionless time, depth, and initial reduced water content. For the more strongly nonlinear case, initially the surface water content decreases in proportion to the square root of time. For large times, the surface water content approaches the residual water content invers ely with the square root of time.