W. Read et P. Broadbridge, SERIES SOLUTIONS FOR STEADY UNSATURATED FLOW IN IRREGULAR POROUS DOMAINS, Transport in porous media, 22(2), 1996, pp. 195-214
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.