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Quantifying a significance of sediment particle size to hyporheic sedimentary oxygen demand with a permeable stream bed

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Abstract

A mechanistic model of sedimentary oxygen demand (SOD) for hyporheic flow is presented. The permeable sediment bed, e.g. sand or fine gravel, is considered with hydraulic conductivity in the range \(0.1 < K < 20\) cm/s. Hyporheic pore water flow is induced by pressure fluctuations at the sediment/water interface due to near-bed turbulent coherent motions. A 2-D advection–diffusion equation is linked to the pore water flow model to simulate the effect of advection–dispersion driven by interstitial flow on oxygen transfer through the permeable sediment. Microbial oxygen uptake in the sediment is expressed as a function of the microbial growth rate, and is related to the sediment properties, i.e. the grain diameter \((d_{s})\) and porosity \((\phi )\). The model describes the significance of sediment particle size to oxygen transfer through the sediment and microbial oxygen uptake: With increasing grain diameter \((d_{s})\), the hydraulic conductivity \((K)\) increases so does the oxygen transfer rate, while particle surface area per volume (the available surface area for colonization by biofilms) decreases reducing the microbial oxygen uptake rate. Simulation results show that SOD increases as the hydraulic conductivity \((K)\) increases before a threshold has been reached. After that, SOD diminishes with the increment of the hydraulic conductivity \((K)\).

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Abbreviations

\(A\) :

Total surface area of particles in the unit volume of sediment \((\text{ cm}^{2})\)

\(C\) :

Dissolved oxygen concentration \((\text{ mg}/\text{ l})\)

\(C_{\infty }\) :

Dissolved oxygen concentration in the bulk water \((\text{ mg}/\text{ l})\)

\(D_{e}\) :

Effective diffusion coefficient for dissolved oxygen in sediment pore system \((\text{ cm}^{2}/\text{ s})\)

\(D_{m}\) :

Molecular diffusion coefficient for dissolved oxygen in water \((\text{ cm}^{2}/\text{ s})\)

\(D_{xx},D_{xy},D_{yx},D_{yy}\) :

The components of the two-dimensional dispersion coefficient tensor \((\text{ cm}^{2}/\text{ s})\)

\(d_{s}\) :

Sediment grain diameter (cm)

\(g\) :

Gravitational acceleration \((=9.8\,\text{ m}/\text{ s}^{2})\)

\(h\) :

Sediment layer thickness (cm)

\(i(=\sqrt{-1})\) :

Imaginary unit

\(K\) :

Darcy hydraulic conductivity (cm/s)

\(k_{d}\) :

First-order decay coefficient \((\text{ d}^{-1})\)

\(Ko_{2}\) :

Half saturation constant for dissolved oxygen \((\text{ mg}/\text{ l})\)

\(N\) :

Number of particles in the unit volume of sediment

SOD :

Sedimentary oxygen demand \((\text{ gm}^{-2}/\text{ d})\)

\(U_{*}\) :

Bed shear velocity \((\text{ cm}/\text{ s})\)

\(u\) :

Seepage velocity component in stream-wise direction \((\text{ cm}/\text{ s})\)

\(v\) :

Seepage velocity component in vertical direction \((\text{ cm}/\text{ s})\)

\(\left| V \right|=\sqrt{u^{2}+v^{2}}\) :

Magnitude of the seepage velocity

\(V_{s}\) :

Total volume of particles in the unit volume of sediment \((\text{ cm}^{3})\)

\(X\) :

Biomass concentration of the aerobic heterotrophs \((\text{ mg}/\text{ l})\)

\(X_{max}\) :

Maximum possible biomass concentration \((\text{ mg}/\text{ l})\)

\(x\) :

Longitudinal coordinate (cm)

\(y\) :

Vertical coordinate (cm)

\(Y_{c}\) :

Effective yield for the microbial utilization of DO \((\text{ mgXmgDO}^{-1})\)

\(\alpha \) :

Possible biomass concentration per unit area of particles \((\text{ mg}/\text{ cm}^{2})\)

\(\alpha _{L}\) :

Longitudinal dispersivity (cm)

\(\alpha _{T}\) :

Transverse dispersivity (cm)

\(\Delta t\) :

Time step

\(\upmu \) :

Maximum oxidation rate \((\text{ mgl}^{-1}\text{ d}^{-1})\)

\(\rho \) :

Fluid (water) density \((\text{ g}/\text{ cm}^{3})\)

\(\tau \) :

Bed shear stress \((\text{ N}/\text{ cm}^{2})\)

\(\upvarphi \) :

Sediment porosity and

\(\chi \) :

Wave number \((\text{ cm}^{-1})\)

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Acknowledgments

This work was supported by JSPS Grant-in-Aid for Scientific Research (22560522). Dr. Ratherford provided helpful comments on an early version of the manuscript. Dr. Packman and an anonymous reviewer suggested improvements of the final manuscript. The author is grateful to these individuals and organization for their support.

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  1. Department of Civil and Environmental Engineering, Oita National College of Technology, 1666 Maki, Oita, 870-0152, Japan

    Makoto Higashino

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  1. Makoto Higashino
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Correspondence to Makoto Higashino.

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Higashino, M. Quantifying a significance of sediment particle size to hyporheic sedimentary oxygen demand with a permeable stream bed. Environ Fluid Mech 13, 227–241 (2013). https://doi.org/10.1007/s10652-012-9262-3

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