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

Stanley B. Grant; Jesus D. Gomez-Velez; Marco Ghisalberti; Ian Guymer; Fulvio Boano; Kevin Roche; Judson Harvey

doi:10.1029/2019WR026822

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

Stanley B. Grant, Jesus D. Gomez-Velez, Marco Ghisalberti, Ian Guymer, Fulvio Boano, Kevin Roche, Judson Harvey

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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.

Original language	English
Article number	e2019WR026822
Journal	Water Resources Research
Volume	56
Issue number	12
DOIs	https://doi.org/10.1029/2019WR026822
State	Published - Dec 2020
Externally published	Yes

Funding

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. 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.

Funders	Funder number
Fulbright program
SBR Scientific Focus Area
U.S. Government
UC Office of the President Multicampus Research Program Initiative	MRP‐17‐455083, EAR 1830172
National Science Foundation	2021015, 1840504
U.S. Department of Energy
U.S. Geological Survey
Biological and Environmental Research
Pacific Northwest National Laboratory
Southern Finance Association
Engineering and Physical Sciences Research Council	EP/P012027/1
Australian Research Council	DP120102500

Keywords

hyporheic
nutrient cycling
pollution
stream
streambed
turbulence

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10.1029/2019WR026822

Cite this

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

abstract = "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.",

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author = "Grant, {Stanley B.} and Gomez-Velez, {Jesus D.} and Marco Ghisalberti and Ian Guymer and Fulvio Boano and Kevin Roche and Judson Harvey",

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AU - Ghisalberti, Marco

AU - Guymer, Ian

AU - Boano, Fulvio

AU - Roche, Kevin

AU - Harvey, Judson

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N2 - 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.

AB - 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.

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KW - streambed

KW - turbulence

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

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