A One-Dimensional Model for Turbulent Mixing in the Benthic Biolayer of Stream and Coastal Sediments

In this paper, we develop and validate a rigorous modeling framework, based on Duhamel's Theorem, for the unsteady one-dimensional vertical transport 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 capturing the two-way coupling between evolving solute concentrations above and below the SWI and in allowing for a depth-varying diffusivity. Three diffusivity profiles within the sediment (constant, exponentially decaying, and a hybrid model) are evaluated against an extensive set of previously published laboratory measurements of turbulent mass transfer across the SWI. The exponential diffusivity profile best represents experimental observations and its reference diffusivity scales with the permeability Reynolds number, a dimensionless measure of turbulence at the SWI. The depth over which turbulence-enhanced diffusivity decays is of the order of centimeters and comparable to the thickness of the benthic biolayer. Thus, turbulent mixing across the SWI may serve as a universal transport mechanism, supplying the nutrient and energy fluxes needed to sustain microbial growth, and nutrient processing, in the benthic biolayer of stream and coastal sediments.