Unsteady seepage flow over sloping beds in response to multiple localized recharge

Abstract

New generalized solutions of linearized Boussinesq equation are derived to approximate the dynamic behavior of subsurface seepage flow induced by multiple localized time-varying recharges over sloping ditch–drain aquifer system. The mathematical model is based on extended Dupuit–Forchheimer assumption and treats the spatial location of recharge basins as additional parameter. Closed form analytic expressions for spatio-temporal variations in water head distribution and discharge rate into the drains are obtained by solving the governing flow equation using eigenvalue–eigenfunction method. Downward and zero-sloping aquifers are treated as special cases of main results. A numerical example is used for illustration of combined effects of various parameters such as spatial coordinates of the recharge basin, aquifer's bed slope, and recharge rate on the dynamic profiles of phreatic surface.