Vertical Structure and Scaling of Turbulent Mixing in the Benthic
Biolayer of Stream and Coastal Sediments
Abstract
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.