In this paper we develop and test a rigorous modeling framework, based on Duhamel’s Theorem, for the unsteady one-dimensional transport and mixing of a solute across a flat sediment-water interface (SWI) and through the benthic biolayer of a turbulent stream. The modeling framework is novel in that it allows for depth-varying diffusivity profiles, accounts for the change in porosity across the SWI and captures the two-way coupling between evolving solute concentrations in both the overlying water column and interstitial fluids of the sediment bed. We apply this new modeling framework to an extensive set of previously published laboratory measurements of turbulent mixing across a flat sediment bed, with the goal of evaluating four diffusivity profiles (constant, exponentially declining, and two hybrid models that account for molecular diffusion and enhanced turbulent mixing in the surficial portion of the bed). The exponentially declining profile is superior (based on RMSE, coefficient of determination, AICc, and model parsimony) and its reference diffusivity scales with a dimensionless measure of stream turbulence and streambed permeability called the Permeability Reynolds Number, . The diffusivity’s dependence on changes abruptly at , reflecting different modes of mixing below (dispersion) and above (turbulent diffusion) this threshold value. The depth-scale over which the diffusivity exponentially decays is about equal to the thickness of the benthic biolayer (2 to 5 cm), implying that turbulent mixing, and specifically turbulent pumping, may play an outsized role in the biogeochemical processing of nutrients and other contaminants in stream and coastal sediments.

Many water quality and ecosystem functions performed by streams occur in the benthic biolayer, the biologically active upper (~5 cm) layer of the streambed. Solute transport through the benthic biolayer is facilitated by bedform pumping, a physical process in which dynamic and static pressure variations over the surface of stationary bedforms (e.g., ripples and dunes) drive flow across the sediment-water interface. In this paper we derive two predictive modeling frameworks, one advective and the other diffusive, for solute transport through the benthic biolayer by bedform pumping. Both frameworks closely reproduce patterns and rates of bedform pumping previously measured in the laboratory, provided that the diffusion model’s dispersion coefficient declines exponentially with depth. They are also functionally equivalent, such that parameter sets inferred from the advective model can be applied to the diffusive model, and vice versa. The functional equivalence and complementary strengths of these two models expands the range of questions that can be answered, for example by adopting the advective model to study the effects of geomorphic processes (such as bedform adjustments to land use change) on flow-dependent processes, and the diffusive model to study problems where multiple transport mechanisms combine (such as bedform pumping and turbulent diffusion). By unifying advective and diffusive descriptions of bedform pumping, our analytical results provide a straightforward and computationally efficient approach for predicting, and better understanding, solute transport in the benthic biolayer of streams and coastal sediments.