Using the level set method to study the effects of heterogeneity and anisotropy on hyporheic exchange

The level set method was used to simulate the interface movement when a conservative solute migrated from stream water to subsurface water, and study the effects of streambed heterogeneity and anisotropy on solute penetration. The level set method is a numerical technique for tracking moving interfaces based on the idea that the interface is a level set curve of a higher‐dimensional function. Numerical simulations were compared to experiments conducted in a recirculating flume. Streambed heterogeneity led to water exchange between multiple bed forms, while in homogeneous streambeds the water exchange was restricted within a single bed form. A thin layer of homogeneous sediments at the top of the heterogeneous streambeds significantly increased the interfacial water influx, resulting in faster solute penetration and stream concentration decrease. Streambed heterogeneity generated horizontal preferential flow paths in the upper part of the bed while decreasing pore water velocities deeper in the bed, which hindered vertical penetration and consequently led to slower stream concentration decrease. Decreasing vertical permeability or increasing horizontal permeability led to slower vertical penetration and stream concentration decrease. Decreasing vertical permeability had a much more significant impact on solute penetration than increasing horizontal permeability, because mass transfer in hyporheic exchange is greatly dominated by vertical advection which depends primarily on the vertical permeability. This study was the first to apply the level set method in the study of hyporheic exchange. The theoretical and numerical methods have important applications in subsurface flow and transport processes. Key Points: Application of the level set method in hyporheic exchange Study of the effects of streambed heterogeneity and anisotropy Significant hydrological and environmental implications