Shear Flows Accelerate Mixing Dynamics in Hyporheic Zones and Hilslopes

Topographic relief and river bedforms generate nested streamline patterns, which drive the propagation and mixing at depth of changes in surface water concentration or temperature. While concentration distributions and biogeochemical reactions in such flow cells are often studied under steady state transport conditions, there is increasing evidence that transient mixing processes may have a significant contribution to effective mixing and reaction rates. Here we show that these streamline patterns act as shear flows, which significantly accelerate mixing dynamics within flow cells and can lead to the formation of transient mixing hot spots at depth. We provide analytical solutions that quantify the dynamics of mixing in a flow cell for a pulse and a front initial solute distribution, which represent two idealized end-members of more complex solute distributions in natural systems. These results provide new insights into the patterns and dynamics of mixing at hyporheic zone, hillslope, and catchment scales. Plain Language Summary As surface water infiltrates in the subsurface in riverbeds or hillslopes, it mixes with the resident groundwater, which leads to changes in the concentration of transported dissolved chemical species. Such transient mixing processes play a key role in contaminant transport and biogeochemical reactions. Here we demonstrate that flow patterns that are generated by topography gradients at different scales act effectively as shear flows due to the differential velocity of neighboring streamlines. We show that such shear flows strongly enhance transient mixing rates and may lead to the formation mixing hot spots where mixing rates are orders of magnitude larger than the background. These results will likely contribute to the understanding and modeling of solute transport and reaction in the context of surface water-groundwater interactions.