Transient solution for stream–unconfined aquifer interaction due to time varying stream head and in the presence of leakage

This paper presents new analytical solutions of a linearized Boussinesq equation characterizing groundwater flow in a stream–unconfined aquifer system due to transient seepage. The aquifer is underlain by a horizontal leaky bed, and interacts with an adjoining stream of varying water level through a semipervious vertical stream bank. Close form analytical expressions are derived to predict water head distribution, flow rate and volumetric exchange of water in response to time dependent rise or drop in the stream water level. Comparison between analytical and numerical results shows satisfactory agreement. The effects of the finite and semi-infinite lengths of the domain are considered in detail. Certain asymptotic situations such as sudden rise or drop in the stream water level, no flow condition at the aquifer’s base and absence of vertical stream bank can be dealt with as limiting cases of main results. An illustration of the new analytical approach is used to quantify the accretion/recession of the bank storage due to variation in various aquifer parameters.