Velocity Pulse Model for Turbulent Diffusion from Flowing Water into a Sediment Bed
Publication: Journal of Environmental Engineering
Volume 134, Issue 7
Abstract
The “velocity pulse model” simulates the transfer of turbulence from flowing water into a sediment bed, and its effect on the diffusional mass transfer of a solute (e.g., oxygen, sulfate, or nitrate) in the sediment bed. In the “pulse model,” turbulence above the sediment surface is described by sinusoidal variations of vertical velocity in time. It is shown that vertical velocity components dampen quickly inside the sediment when the frequency of velocity fluctuations is high and viscous dissipation is strong. Viscous dissipation inside the sediment is related to the apparent viscosity depending on the structure of the sediment pore space, i.e., the porosity and grain diameter, as well as inertial effects when the flow is turbulent. A value between 1 and 20 ( is kinematic viscosity of water) has been considered. Turbulence penetration into the sediment is parametrized by the Reynolds number and the relative penetration velocity , where =amplitude of the velocity pulse; and =penetration velocity; =wave length of the velocity pulse; and is its period. Amplitudes of vertical velocity components inside the sediment and their autocorrelation functions are computed, and the results are used to estimate eddy viscosity inside the sediment pore system as a function of depth. Diffusivity in the sediment pore system is inferred by using turbulent or molecular Schmidt numbers. Turbulence penetration from flowing water can enhance the vertical diffusion coefficient in a sediment bed by an order of magnitude or more. Penetration depth of turbulence is higher for low frequency velocity pulses. Vertical diffusivity inside the pore system is shown to decrease more or less exponentially with depth below the sediment/water interface. Vertical diffusivities in a sediment bed estimated by the “velocity pulse model” can be used in pore water quality models to describe vertical transport from or into flowing surface water. The analysis has been conducted for a conservative material, but source and sink terms can be added to the vertical transport equation.
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Acknowledgments
The writers thank Maria Spitael, Matt Lueker, and Andrew Fyten for technical support in conducting the experiment. They also acknowledge the helpful comments of the reviewers.
References
Barr, D. W. (2001). “Turbulent flow through porous media.” Ground Water, 39(5), 646–650.
Baver, L. D., Gardner, W. H., and Gardner, W. R. (1972). Soil physics, 4th Ed., Wiley, New York.
Bayani Cardenas, M., and Wilson, J. L. (2004). “Impact of heterogeneity, bedforms and stream curvature on subchannel hyporheic exchange.” Water Resour. Res., 40, 1–13.
Bear, J. (1972). Dynamics of fluids in porous media, American Elsevier, New York.
Belanger, T. V. (1981). “Benthic oxygen demand in Lake Apopka, Florida.” Water Res., 15, 267–274.
Blackwelder, R. F., and Haritonidis, J. H. (1983). “Scaling of the bursting frequency in turbulent boundary layer.” J. Fluid Mech., 132, 87–103.
Boudreau, B. P. (1997). “A mathematical model for sediment-suspended particle exchange.” J. Mar. Syst. 11, 279–303.
Boudreau, B. P., and Joergensen, B. B., eds. (2001). The Benthic boundary layer: Transport processes and biogeochemistry, Oxford University Press, London.
Chien, N., and Wan, Z. (1999). Mechanics of sediment transport, ASCE, Reston, Va.
Dade, W. B. (1993). “Near-bed turbulence and hydrodynamic control of diffusional mass transfer at the sea floor.” Limnol. Oceanogr., 38(1), 52–69.
DePinto, J. V., Lick, W., and Paul, J. (1994). Transport and transformation of contaminants near the sediment-water interface, CRC, Boca Raton, Fla.
Elliott, A. H., and Brooks, N. H. (1997). “Transfer of nonsorbing solutes to a streambed with bed forms: Theory.” Water Resour. Res., 33(1), 123–136.
Garratt, J. R. (1992). The atmospheric boundary layer, Cambridge University Press, Cambridge, U.K.
Higashino, M., Gantzer, C. J., and Stefan, H. G. (2004). “Unsteady sediment oxygen demand: Theory and significance for measurements.” Water Res., 38, 1–12.
Higashino, M., and Stefan, H. G. (2005). “Oxygen demand by a sediment bed of finite length.” J. Environ. Eng., 131(3), 350–358.
House, W. A. (2003). “Factors influencing the extent and development of the oxic zone of river-bed sediment.” Biogeochemistry, 63, 317–333.
Huettel, M., and Webster, I. T. (2001). “Porewater flow in permeable sediment.” The Benethic boundary layer: Transport processes and biogeochemistry, B. P. Boudreau and B. B. Joergensen, eds., Oxford University Press, Oxford, U.K., 144–179.
Joergensen, B. B., and DesMarais, D. J. (1990). “Diffusive boundary layer of sediments: Oxygen microgradients over a microbial mat.” Limnol. Oceanogr. 35(6), 1343–1355.
Joergensen, B. B., and Revsbech, N. P. (1985). “Diffusive boundary layers and the oxygen uptake of sediment and detritus.” Limnol. Oceanogr., 30(1), 111–122.
Jones, J. B., and Mulholland, P. J., eds. (2000). Streams and ground waters, Academic Press, Burlington, Mass.
Josiam, R., and Stefan, H. G. (1999). “Effect of flow velocity on sediment oxygen demand: Comparison of theory and experiments.” J. Am. Water Resour. Assoc., 35(2), 433–439.
Mackenthun, A., and Stefan, H. G. (1998). “Effect of flow velocity on sediment oxygen demand: Experiments.” J. Environ. Eng., 124(3), 222–230.
Mendoza, C., and Zhou, D. (1992). “Effects of porous bed on turbulent stream flow above bed.” J. Hydraul. Eng., 118(9), 1222–1240.
Moin, P., and Kim, J. (1982). “Numerical investigation of turbulent channel flow.” J. Fluid Mech., 118, 341–377.
Nagaoka, H., and Ohgaki, S. (1990). “Mass transfer mechanism in porous riverbed.” Water Res., 24(4), 417–425.
Nakamura, Y., and Stefan, H. G. (1994). “Effect of flow velocity on sediment oxygen demand: Theory.” J. Environ. Eng., 120(5), 996–1016.
Nezu, I., and Nakagawa, H. (1993). Turbulence in open-channel flows, IAHR Monograph, Rotterdam, The Netherlands.
Packman, A. I., Salehin, M., and Zaramella, M. (2004). “Hyporheic exchange with gravel beds: Basic hydrodynamic interactions and bedform-induced advective flows.” J. Hydraul. Eng., 130(7), 647–656.
Rahm, L., and Svensson, U. (1989). “On the mass transfer properties of the benthic boundary layer with an application to oxygen fluxes.” Netherlands J. Sea Res., 24(1), 27–35.
Scheidegger, A. E. (1960). The physics of flow through porous media MacMillan, New York.
Schneebeli, G. (1966). Hydraulique souterraine, Eyrolles Editeurs, Paris.
Shimizu, Y., Tsujimoto, T., and Nakagawa, H. (1990). “Experiment and macroscopic modeling of flow in highly permeable porous medium under free-surface flow.” J. Hydrosci. Hydr. Eng., 8(1), 69–78.
Steinberger, N., and Hondzo, M. (1999). “Diffusional mass transfer at the sediment-water interface.” J. Environ. Eng., 125(2), 192–200.
Taylor, G. I. (1921). “Diffusion by continuous movements.” Proc. London Math. Soc., 20, 196–212.
Willmarth, W. W., and Sharma, L. K. (1984). “Study of turbulent structure with hot wires smaller than viscous length.” J. Fluid Mech., 142, 121–149.
Zhou, D., and Mendoza, C. (1993). “Flow through porous bed of turbulent stream.” J. Eng. Mech., 119(2), 365–383.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 134 • Issue 7 • July 2008
Pages: 550 - 560
Copyright
© 2008 ASCE.
History
Received: Sep 8, 2006
Accepted: Nov 19, 2007
Published online: Jul 1, 2008
Published in print: Jul 2008
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