Solution of Unsteady Flow in a Confined Aquifer Interacting with a Stream with Exponentially Decreasing Stream Stage

Abstract

The solution of interactions between groundwater and surface water provides good insight into the mechanism of these water resources. Considering groundwater as a significant source of irrigation and a main freshwater supply for agricultural purposes, a stream–aquifer system is studied to investigate the groundwater level and flow direction. The solution is obtained and applicable for streams fully penetrating the aquifer. The system is solved and a set of expressions for computing level and exchange in the aquifer are derived by means of the Laplace transformation technique, wherein the right end of the aquifer is a constant head boundary and the stream stage at the left boundary decreases exponentially with time. A broad range of sensitivity analysis is carried out to investigate the effects of variations in aquifer parameters on groundwater head. Aquifer response for exponential and sudden drops in stream stage is investigated. A useful expression describing the relation of stream stage variation rate and volumetric exchange is found, which clarifies whether the final volumetric exchange is negative, zero, or positive. For a sudden drop in stream stage, a water divide takes place in the aquifer and therefore flow reversal occurs at the water divide position. It is shown that how and how much the position of the water divide changes depends on changes in aquifer parameters. In addition, it is observed that groundwater level stabilization occurs relatively faster in aquifers with a greater hydraulic conductivity, smaller specific storage, or smaller length.