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. U.S. National Science FoundationNational Science Foundation (NSF) [1840504, 2021015, EAR 1830172]; Virginia Tech's ICTAS EFO Opportunity Seed Investment Grant; UC Office of the President Multicampus Research Program Initiative award [MRP-17-455083]; U.S. Department of Energy, Office of Biological and Environmental Research (BER), as part of BER's Subsurface Biogeochemistry Research Program (SBR)United States Department of Energy (DOE); UK EPSRC Established Career FellowshipEngineering & Physical Sciences Research Council (EPSRC) [EP/P012027/1]; Australian Research CouncilAustralian Research Council [DP120102500]; Fulbright program; U.S. Geological Survey Water Availability and Use Science Program S. B. G. was supported by the U.S. National Science Foundation (Awards 1840504 and 2021015), Virginia Tech's ICTAS EFO Opportunity Seed Investment Grant, and the UC Office of the President Multicampus Research Program Initiative award (MRP-17-455083). J. G. V. was funded by the U.S. National Science Foundation (Award EAR 1830172) and the U.S. Department of Energy, Office of Biological and Environmental Research (BER), as part of BER's Subsurface Biogeochemistry Research Program (SBR). This contribution originates from the SBR Scientific Focus Area (SFA) at the Pacific Northwest National Laboratory (PNNL). I. G. was supported by UK EPSRC Established Career Fellowship (Award EP/P012027/1). M. G. was funded by an Australian Research Council Discovery Project (DP120102500). K. R. R. was supported by the Fulbright program. J. H. was supported by the U.S. Geological Survey Water Availability and Use Science Program. Supporting Information includes tables and text. The authors thank M. Chappell, A. Monofy, three anonymous reviewers, and the Associate Editor for their insightful comments and manuscript edits. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.