A Novel Modeling Framework to Represent Turbulent Mixing in the Benthic Biolayer of Streams

Many of the most important ecosystem services performed by streams occur in the benthic biolayer, the biologically active upper layer of the streambed. Here we develop and test a rigorous modeling framework for the unsteady one-dimensional transport and mixing of a solute in the benthic biolayer of a turbulent stream. Our framework allows for depth-varying diffusivity profiles, accounts for the change in porosity across the sediment-water interface and captures the two-way feedback 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 data, 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 and enhanced mixing profiles are superior and their reference diffusivities scale with a dimensionless measure of stream turbulence and streambed permeability called the Permeability Reynolds Number, Re_K. The dependence on Re_K changes abruptly at Re_K = 1, reflecting different modes of mixing below (dispersion) and above (turbulent diffusion) this threshold value. Because our modeling framework can be applied to open systems, it should inform the prediction and management of pollutant migration through a diverse array of aquatic ecosystems.