WATER TABLE FLUCTUATIONS IN A SLOPING AQUIFER: ANALYTICAL EXPRESSIONS FOR WATER EXCHANGE BETWEEN STREAM AND GROUND-WATER WITH SURFACE INFILTRATION

Abstract

This paper presents an analytical solution of a linearized Boussinesq’s equation to obtain exact expressions for hydraulic head and flow rate in an unconfined downward sloping aquifer. The aquifer is in contact with a constant piezometric head at the left boundary and a stream at the right boundary whose water level is rising at a constant rate. The aquifer also receives a constant vertical recharge from the land surface due to rain infiltration. The governing equation is solved analytically using the Laplace transform to obtain the expressions for hydraulic head and flow rate. The proposed analytical solutions are verified with an earlier known solution for a horizontal aquifer with zero surface infiltration and found to be in complete agreement. The combined effect of slope and recharge on water table fluctuation and flow rate is studied by considering a numerical example. Model results establish the dependence of the water table fluctuations and flow rate on bed slope and surface recharge rate. The analytical expressions derived here can also represent an asymptotic scenario of either sudden rise or very slow rise in the stream water.