modeling of groundwater flow over sloping beds in response to constant recharge and stream of varying water level

this paper presents an analytical model characterizing unsteady groundwater flow in an unconfined aquifer resting on a sloping impervious bed. the aquifer is in contact with a constant water level at one end. the other end is connected to a stream whose level is increasing form an initial level to a final level at a known exponentially decaying function of time. moreover, the aquifer is replenished by a constant downward recharge. the linearized boussinesq equation is solved analytically using laplace transform technique to obtain the closed form expression for hydraulic head and flow rate at the stream-aquifer interface.  the expressions derived in this study can also handle the cases of upward sloping, horizontal bed conditions and sudden rise in stream water. the validity of linearization method adopted in this study is examined by solving the nonlinear equation by an explicit numerical scheme. response of an aquifer to the variations in bed slope, recharge rate and rise rate of the stream water is illustrated with a numerical example. sensitivity of the flow rate with various parameters is analyzed.