Solute Mixing in the Surf Zone
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 135, Issue 4
Abstract
An experimental study has been undertaken within the U.K. Coastal Research Facility (CRF), located at HR Wallingford Ltd. Detailed measurements were made to examine the on–off shore spreading of a solute, mostly inside the surf zone, for shore normal waves combined with a longshore current. The results show that the on–off shore mixing is significantly increased by almost 70 times, when compared to current-only conditions. A theoretical advection–dispersion mixing mechanism has been postulated. Using suitable estimates for the turbulent diffusion and on–off shore wave-induced velocity, a theoretical approximation to the overall mixing within the surf zone can be obtained. This theoretical analysis suggests that the on–off shore mixing in the surf zone is proportional to , where is the breaker wave height. It is demonstrated that within the surf zone, the on–off shore mixing is dominated by the effects of the on–off shore velocity. Some previous experimental studies to determine the magnitude of the mixing within the surf zone have been performed. However, the mechanisms responsible for generating the mixing were neither fully investigated nor reported. The previous studies, together with the results obtained from the CRF, are compared to estimates for the theoretical description of mixing developed within this present study. A good agreement exists.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers gratefully acknowledge the UK Engineering and Physical Sciences Research Council (Grant Nos. GR/J/12499 and GR/T24081) for their financial support and the technical assistance of HR Wallingford for the research undertaken on the CRF.
References
Bowen, A. J. (1969). “The generation of longshore currents on a plane beach.” J. Mar. Res., 27(2), 206–215.
Bowen, A. J., and Inman, D. L. (1974). “Nearshore mixing due to waves and wave-induced currents.” Rapp. P.-V. Reun.-Cons. Int. Explor. Mer, 167, 6–12.
Bowen, A. J., Inman, D. L., and Simmons, V. P. (1968). “Wave ‘set-down’ and ‘set-up’.” J. Geophys. Res., 73(8), 2569–2577.
Chadwick, A. J., and Morfett, J. C. (1986). Hydraulics in civil engineering, Allen & Unwin, London.
Chikwendu, S. C. (1986). “Calculation of longshore shear dispersivity using an N-zone model as .” J. Fluid Mech., 167, 19–30.
DeVriend, H. J., and Stive, M. J. F. (1987). “Quasi-3D modelling of near-shore current.” Coastal Eng., 11, 565–601.
Fischer, H. B. (1967). “The mechanics of dispersion in natural streams.” J. Hydr. Div., 93(6), 187–216.
Fischer, H. B. (1978). “On the tensor form of bulk dispersion coefficient in a bounded skewed shear flow.” J. Geophys. Res., 83(C5), 2373–2375.
Fischer, H. B., List, J. E., Koh, R. C. Y., Imberger, J., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic, New York.
Galvin, C. J. (1972). “Wave breaking in shallow water.” Waves on beaches, R. E. Meyer, ed., Academic, New York, 413–455.
Hansen, J. B., and Svendsen, I. A. (1984). “A theoretical and experimental study of undertow.” Proc., 19th Int. Conf. on Coastal Engineering, Houston, ASCE, New York, 2246–2262.
Harris, T. F. W., Jordan, J. M., McMurry, W. R., Verwey, C. J., and Anderson, F. P. (1963). “Mixing in the surf zone.” Air Water Pollut., 7, 649–667.
Hattori, M., and Aono, T. (1985). “Experimental study on turbulence structures under spilling breakers.” Ocean surface, F. Toba and H. Mitsuyasu, eds., Reidel, Dordrecht, 419–424.
Inman, D. L., Tait, F. J., and Nordstrom, C. E. (1971). “Mixing in the surf zone.” J. Geophys. Res., 76(15), 3493–3514.
Karambas, T. V. (1986). “On the pollutant dispersion subjected to nearshore circulation.” Proc., 3rd Int. Conf. on Environmental Pollution, Univ. Thessaloniki, Greece.
Longuet-Higgins, M. S. (1970). “Long-shore currents generated by obliquely incident sea waves: Parts 1 and 2.” J. Geophys. Res., 75(33), 6778–6801.
Longuet-Higgins, M. S., and Stewart, R. W. (1960). “Changes in the form of short gravity waves on long waves and tidal currents.” J. Fluid Mech., 13, 481–504.
Longuet-Higgins, M. S., and Stewart, R. W. (1963). “A note on wave setup.” J. Mar. Res., 21(1), 4–10.
Longuet-Higgins, M. S., and Stewart, R. W. (1964). “Radiation stress in water waves, a physical discussion with application.” Deep-Sea Res., 11, 529–563.
Nadaoka, K., and Kondoh, T. (1982). “Laboratory measurements of velocity field structure in the surf zone by LDV.” Coast. Eng. Japan, 25, 125–145.
Pearson, J. M., Guymer, I., West, J. R., and Coates, L. E. (2002). “Effect of wave height on cross-shore solute mixing.” J. Waterway, Port, Coastal, Ocean Eng., 128(1) 10–20.
Prandtl, L. (1952). Essentials of fluid dynamics, Hafner, New York.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, U.K.
Stive, M. J. F., and Wind, H. G. (1982). “A study of radiation stress and setup in the nearshore region.” Coastal Eng., 6, 1–25.
Svendsen, I. A. (1987). “Analysis of surf zone turbulence.” J. Geophys. Res., 92(C5), 5115–5124.
Svendsen, I. A., and Putrevu, U. (1994). “Near-shore mixing and dispersion.” Proc. R. Soc. London, Ser. A, 445, 561–576.
Tanaka, H., Wada, A., Komori, S., and Tekeuchi, I. (1980). “Effects of nearshore currents on diffusion in the surf zone.” Coast. Eng. Japan, 23, 231–50.
Taylor, G. I. (1954). “The dispersion of matter in a turbulent flow through a pipe.” Proc. R. Soc. London, Ser. A, 223, 446–468.
Thornton, E. B. (1970). “Variation of longshore currents across the surf zone.” Proc., 12th Int. Conf. on Coastal Engineering, Washington, D.C., ASCE, New York, 291–308.
Information & Authors
Information
Published In
Copyright
© 2009 ASCE.
History
Received: May 23, 2006
Accepted: Dec 10, 2008
Published online: Jun 15, 2009
Published in print: Jul 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.