SpringerLink
Log in

Transport of dissolved oxygen at the sediment-water interface in the spanwise oscillating flow

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The distribution and concentration of dissolved oxygen (DO) play important roles in aerobic heterotroph activities and some slow chemical reactions, and can affect the water quality, biological communities, and ecosystem functions of rivers and lakes. In this work, the transport of high Schmidt number DO at the sediment-water interface of spanwise oscillating flow is investigated. The volume-averaged Navier-Stokes (VANS) equations and Monod equation are used to describe the flow in the sediment layer and the sediment oxygen demand of microorganisms. The phase-averaged velocities and concentrations of different amplitudes and periods are studied. The dependence of DO transfer on the amplitude and period is analyzed by means of phase-average statistical quantities. It is shown that the concentration in the sediment layer is positively correlated with the turbulence intensity, and the DO concentration and penetration depth in the sediment layer increases when the period and amplitude of the oscillating flow increase. Moreover, in the presence of oscillating flow, a specific scaling relationship exists between the Sherwood number/oxygen consumption of aerobic heterotrophs and the Reynolds number.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. DIAZ, R. J. and ROSENBERG, R. Spreading dead zones and consequences for marine ecosystems. Science, 321, 926–929 (2008)

    Article  Google Scholar 

  2. RABALAIS, N. N., DÍAZ, R. J., LEVIN, L. A., TURNER, R. E., GILBERT, D., and ZHANG, J. Dynamics and distribution of natural and human-caused hypoxia. Biogeosciences Discuss, 6, 585–619 (2009)

    Article  Google Scholar 

  3. HONDZO, M., FEYAERTS, T., DONOVAN, R., and O’CONNOR, B. L. Universal scaling of dissolved oxygen distribution at the sediment-water interface: a power law. Limnology and Oceanography, 50, 1667–1676 (2005)

    Article  Google Scholar 

  4. O’CONNOR, B. L. and HONDZO, M. Enhancement and inhibition of denitrification by fluid-flow and dissolved oxygen flux to stream sediments. Environmental Science and Technology, 42, 119–125 (2007)

    Article  Google Scholar 

  5. O’CONNOR, B. L. and HONDZO, M. Dissolved oxygen transfer to sediments by sweep and eject motions in aquatic environments. Limnology and Oceanography, 53, 566–578 (2008)

    Article  Google Scholar 

  6. BOUDREAU, B. and JØRGENSEN, B. The Benthic Boundary Layer: Transport Processes and Biogeochemistry, Oxford University Press, New York (2001)

    Google Scholar 

  7. WALKER, R. R. and SNODGRASS, W. J. Model for sediment oxygen demand in lakes. Journal of Environmental Engineering, 112, 25–43 (1986)

    Article  Google Scholar 

  8. HIGASHINO, M., GANTZER, C. J., and STEFAN, H. G. Unsteady diffusional mass transfer at the sediment/water interface: theory and significance for SOD measurement. Water Resources Research, 38, 1–12 (2004)

    Article  Google Scholar 

  9. HIGASHINO, M., O’CONNOR, B. L., HONDZO, M., and STEFAN, H. G. Oxygen transfer from flowing water to microbes in an organic sediment bed. Hydrobiologia, 614, 219–231 (2008)

    Article  Google Scholar 

  10. DADE, W. Near-bed turbulence and hydrodynamic control of diffusional mass transfer at the sea floor. Limnology and Oceanography, 38, 52–69 (1993)

    Article  Google Scholar 

  11. HIGASHINO, M., CLARK J. J., and STEFAN, H. G. Pore water flow due to near-bed turbulence and associated solute transfer in a stream or lake sediment bed. Water Resources Research, 45, 981–989 (2009)

    Article  Google Scholar 

  12. SCALO, C., PIOMELLI, U., and BOEGMAN, L. Large-eddy simulation of oxygen transfer to organic sediment beds. Journal of Geophysical Research: Oceans, 117, 6005 (2012)

    Article  Google Scholar 

  13. TIAN, H. J., LI, Q. X., PAN, M., ZHOU, Q., and DONG, Y. H. High-schmidt-number dissolved oxygen transfer from turbulent flows to permeable microbial sediment bed. Advances in Water Resources, 125, 1–12 (2019)

    Article  Google Scholar 

  14. LORKE, A., MÜLLER, B., MAERKI, M., and WÜEST, A. Breathing sediments: the control of diffusive transport across the sediment-water interface by periodic boundary-layer turbulence. Limnology and Oceanography, 48, 2077–2085 (2003)

    Article  Google Scholar 

  15. BRYANT, L. D., LORRAL, C., MCGINNIS, D. F., BRAND, A., WUEST, A., and LITTLE, J. C. Variable sediment oxygen uptake in response to dynamic forcing. Limnology and Oceanography, 55, 950–964 (2010)

    Article  Google Scholar 

  16. BRYANT, L. D., MCGINNIS, D. F., LORRAI, C., BRAND, A., and LITTLE, J. C. Evaluating oxygen fluxes using microprofiles from both sides of the sediment-water interface. Limnology and Oceanography Methods, 8, 610–627 (2010)

    Article  Google Scholar 

  17. TIAN, H. J., LI, Q. X., and DONG, Y. H. Dissolved oxygen transfer from oscillatory flows to microbes in a permeable organic sediment bed. International Journal of Heat and Mass Transfer, 157, 119721 (2020)

    Article  Google Scholar 

  18. WHITAKER, S. Advances in theory of fluid motion in porous media. Industrial and Engineering Chemistry, 61, 14–28 (1969)

    Article  Google Scholar 

  19. BOUDREAU, B. P. The diffusive tortuosity of fine-grained unlithified sediments. Geochimica et Cosmochimica Acta, 60, 3139–3142 (1996)

    Article  Google Scholar 

  20. ROSTI, M. E., CORTELEZZI, L., and QUADRIO, M. Direct numerical simulation of turbulent channel flow over porous walls. Journal of Fluid Mechanics, 784, 396–442 (2015)

    Article  MathSciNet  Google Scholar 

  21. KIM, J. and MOIN, P. Application of a frational-step method to incompressible Navier-Stokes equations. Journal of Computational Physics, 59, 308–323 (1985)

    Article  MathSciNet  Google Scholar 

  22. VERZICCO, R. and ORLANDI, P. A. Finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. Journal of Computational Physics, 123, 402–414 (1996)

    Article  MathSciNet  Google Scholar 

  23. HARLOW, F. H. and WELCH, J. E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids, 8, 2182–2189 (1965)

    Article  MathSciNet  Google Scholar 

  24. DONG, Y. H., LU, X. Y., and ZHUANG, L. X. Large eddy simulation of turbulent channel flow with mass transfer at high-Schmidt numbers. International Journal of Heat and Mass Transfer, 46, 1529–1539 (2003)

    Article  Google Scholar 

  25. WANG, L., DONG, Y. H., and LU, X. Y. An investigation of turbulent open channel flow with heat transfer by large eddy simulation. Computers and Fluids, 34, 23–47 (2005)

    Article  Google Scholar 

  26. HANDLER, R. A., SAYLOR, J. R., LEIGHTON, R. I., and ROVELSTAD, A. L. Transport of a passive scalar at a shear-free boundary in fully developed turbulent open channel flow. Physics of Fluids, 11, 2607–2625 (1999)

    Article  Google Scholar 

  27. KOMORI, S., NAGAOSA, R., MURAKAMI, Y., CHIBA, S., ISHII, K., and KUWAHARA, K. Direct numerical simulation of three-dimensional open-channel flow with zero-shear gas-liquid interface. Physics of Fluids A: Fluid Dynamics, 5, 115–125 (1993)

    Article  Google Scholar 

  28. HUNT, J. C. R., WRAY, A. A., and MOIN, P. Eddies, streams, and convergence zones in turbulent flows. Proceedings of the Summer Program in Center for Turbulence Research, Stanford University, California, 193–208 (1988)

    Google Scholar 

  29. BARON, A. and QUADRIO, M. Turbulent drag reduction by spanwise wall oscillations. Applied Scientific Research, 55, 311–326 (2007)

    Article  Google Scholar 

  30. PINCZEWSKI, W. V. and SIDEMAN, S. A model for mass (heat) transfer in turbulent tube flow: moderate and high Schmidt (Prandtl) numbers. Chemical Engineering Science, 29, 1969–1976 (1974)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, China

    Kunpeng Wang, Qingxiang Li & Yuhong Dong

Authors
  1. Kunpeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qingxiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuhong Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuhong Dong.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 91852111 and 92052201) and the Program of the Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, K., Li, Q. & Dong, Y. Transport of dissolved oxygen at the sediment-water interface in the spanwise oscillating flow. Appl. Math. Mech.-Engl. Ed. 42, 527–540 (2021). https://doi.org/10.1007/s10483-021-2719-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-021-2719-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation