SERIES SOLUTIONS FOR STEADY UNSATURATED FLOW IN IRREGULAR POROUS DOMAINS

For the most part, analytical solutions for steady unsaturated infiltr ation have been restricted to infinite and semi-infinite seepage geome tries, using the quasi-linear approximation for the hydraulic conducti vity. We provide analytical series methods to solve the steady quasi-l inear flow equations, in finite irregular seepage geometries. Unlike t he classical approach, the series method has been modified, to cater f or arbitrary boundary geometry and surface recharge distributions. The matrix flux potential and the stream function both satisfy the same g overning partial differential equation, and the stream function formul ation is used to estimate the series coefficients. For a finite vadose zone, the stream function solution does not uniquely determine the ma trix flux potential, when flux boundary conditions are used. Consequen tly, the stream function solution applies to a range of moisture distr ibutions, for given infiltration and evapotranspiration rates through the surface.