Quantifying the Effects of Bed Roughness on Transit Time Distributions via Direct Numerical Simulations of Turbulent Hyporheic Exchange

We report direct numerical simulation (DNS) results of hyporheic exchange for a flat river bed with two different particle roughness textures, at a surface flow friction Reynolds number of 395 and a bed permeability Reynolds number of 2.6. Transit time distributions (TTDs), subsurface flow patterns, and the interfacial volumetric fluxes are discussed. The transit time was quantified using a forward particle tracking method based on pure advection by three‐dimensional, pore‐resolved, time‐mean velocities. Results show that bed roughness induces deep subsurface flow paths that yield a TTD with a power‐law tail. Roughness obstructs the surface flow, creating interfacial pressure variations which induce subsurface flow. Next, the molecular diffusion is accounted for based on a random walk method and is shown to increase transit times regardless of roughness texture. This work demonstrates that particle roughness on a macroscopically flat sediment bed can induce significant hyporheic exchange that is fundamentally similar to that induced by bedforms. Plain Language Summary Riverine flows are turbulent flows with wide range of scales of motion in both space and time. Driven and modified by natural and anthropogenic factors, channel flows interact with local features (e.g., bars, ripples, and dunes), and smaller features down to the scale of individual sediment grains. The magnitude of exchange of water with bed sediment (hyporheic exchange) and the time water molecules spend within the bed before reentering the channel are key details that control water quality in streams, as they determine the nature of biogeochemical processes. The role played by processes at the scale of individual grains and grain clusters (collectively referred to as bed roughness) have not been understood. We use direct simulation of turbulent flows and consider two “flat bed” scenarios with regular or random roughness at the sediment‐water interface. We show that bed roughness induces deep flow paths and long transit times similar to those produced by local features and that the roughness texture plays an important role. The results offer novel insights into small‐scale hyporheic flows and provide quantitative estimates of the inherent uncertainty that can be expected in estimates of hyporheic exchange due to changes at larger scales. Key Points Transit times calculated with particle tracking using pore‐resolved velocities from direct numerical simulation (DNS) of turbulent surface‐subsur