A linear model for the coupled surface-subsurface flow in a meandering stream

The interest about the exchange of water between streams and aquifers has been increasing among the hydrologic community because of the implications of the exchange of heat, solutes, and colloids for the water quality of aquatic environments. Unfortunately, our understanding of the relevance of the exchange processes is limited by the great number of coupled hydrological and geomorphological factors that interact to generate the complex spatial patterns of exchange. In this context, the present work presents a mathematical model for the surface-subsurface exchange through the streambed of a meandering stream. The model is based on the linearization of the equations that govern the hydrodynamics and the morphodynamics of the system, and it provides a first-order analytical solution of the coupled flow field of both the surface and the subsurface flows. The results show that stream curvature determines a characteristic spatial pattern of hyporheic exchange, with water upwelling and downwelling concentrated near the stream banks. The exchange can drive surface water deep into the sediments, thus keeping deep alluvium regions connected with the stream. The relationships between hyporheic exchange flux and the geometrical and hydrodynamical properties of the stream-aquifer system are also investigated.