Advective Diffusion of Contaminants in the Surf Zone
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 139, Issue 6
Abstract
A theory on the horizontal spreading of contaminants in the surf zone is described in this paper. The surf zone is viewed as a narrow strip comparable to the characteristic wavelength, in which turbulence caused by wave breaking is strong. Flows inside the surf zone consist of both oscillatory motions and a steady current induced by breaking waves. The wave field in the shoaling zone is modeled by the linear theory for monochromatic waves, and it is assumed that the breaking wave height is proportional to the local depth in the surf zone. The simplest scenario of longshore current on a straight beach of constant slope is considered, for which the longshore current velocity is predicted by a slightly modified version of Longuet-Higgins' original theory developed in the 1970s. On the basis of the estimation that the time scale of horizontal diffusion is much longer than the wave period, the perturbation method of multiple scales is applied to derive the transport equation for the advective diffusion of a solute. The total advection velocity is found to be the sum of the steady current caused by radiation stresses and a contribution from the covariance of fluctuating velocity and concentration, which is the same as the Stokes drift in periodic waves. Numerical predictions for the movement of a solute cloud released, instantaneously or continuously, in a longshore current along a plane beach are examined. The solute is found to drift shoreward in addition to the expected transport along the shore. Computed examples are presented and comparisons with available laboratory experiments are also discussed.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is supported by National Science Foundation grants to Cornell University. P. Winckler thanks Fulbright and Universidad de Valparaiso for financial assistance in the form of a studentship. C. C. Mei acknowledges the support of the Mary Upson visiting professorship at Cornell University for this collaboration.
References
Clark, D. B., Feddersen, F., and Guza, R. T. (2010). “Cross-shore surfzone tracer dispersion in an alongshore current.” J. Geophys. Res. Oceans, 115(C10035), 1–18.
Clarke, L. B., Ackerman, D., and Largier, J. (2007). “Dye dispersion in the surf zone: Measurements and simple models.” Cont. Shelf Res., 27(5), 650–669.
Erdelyi, A., Magnus, W., and Tricomi, F. G. (1954). Tables of integral transform. Bateman manuscript project, Vol. 1, McGraw Hill, New York.
Feddersen, F. (2007). “Breaking wave induced cross-shore tracer dispersion in the surfzone: Model results and scalings.” J. Geophys. Res. Oceans, 112(C0912), 1–12.
Fischer, H. B., List, J. E., Koh, R. C. Y., Imberber, J., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic Press, New York.
Harris, T. F. W., Jordaan, J. M., McMurray, W. R., Verwey, C. J., and Anderson, F. P. (1963). “Mixing in the surf zone.” Int. J. Air Water Pollut., 7(2), 649–667.
Hunt, J. N., and Johns, B. (1963). “Currents induced by tides and gravity waves.” Tellus, 15(4), 343–351.
Inman, D. L., Tait, R. J., and Nordstrom, C. E. (1971). “Mixing in the surf zone.” J. Geophys. Res., 76(15), 3493–3514.
Longuet-Higgins, M. S. (1964). “Radiation stresses in water waves: A physical discussion, with applications.” Deep-Sea Res., 11, 529–562.
Longuet-Higgins, M. S. (1970a). “Longshore currents generated by obliquely incident sea waves, 1.” J. Geophys. Res., 75(33), 6778–6789.
Longuet-Higgins, M. S. (1970b). “Longshore currents generated by obliquely incident sea waves, 2.” J. Geophys. Res., 75(33), 6790–6801.
Mariani, A. (2004). “A field investigation of dispersion in a surfzone dominated by longshore currents.” M. Ocean Eng. thesis, Facolta di Ingegneria, Politecnico di Milano, Milan, Italy, and Coastal Oceanography Group, Univ. of Western Australia, Perth, Australia.
Mei, C. C., and Chian, C. M. (1994). “Dispersion of small suspended particles in wave boundary layers.” J. Phys. Oceanogr., 24(12), 2479–2495.
Mei, C. C., Chian, C. M., and Ye, F. (1998). “Transport and resuspension of fine particles in a tidal boundary near a small peninsula.” J. Phys. Oceanogr., 28(11), 2313–2331.
Mei, C. C., Fan, S. J., and Jin, K. R. (1997). “Resuspension and transport of fine sediments by waves.” J. Geophys. Res. Oceans, 102(C7), 15,807–15,821.
Mei, C. C., Stiassnie, M., and Yue, D. K.-P. (2005). Theory and applications of ocean surface waves. Part 2: Nonlinear aspects, World Scientific, Singapore.
Munk, W. H. (1949). “The solitary wave theory and its applications to surf problems.” Ann. N.Y. Acad. Sci., 51, 376–424.
Pearson, J. M., Guymer, I., West, J. R., and Coates, L. E. (2009). “Solute mixing in the surf zone.” J. Waterway, Port, Coastal Ocean Eng., 135(4), 127–134.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, U.K.
Spydell, M., Feddersen, F., and Guza, R. T. (2007). “Observing surf-zone dispersion with drifters.” J. Phys. Oceanogr., 37(12), 2920–2939.
Spydell, M. S., Feddersen, F., and Guza, R. T. (2009). “Observations of drifter dispersion in the surfzone: The effect of sheared alongshore currents.” J. Geophys. Res., 114(C7), 1–12.
Sun, T., and Tao, J.-H. (2003). “Numerical modelling and experimental verification of pollutant transport under waves in the nearshore zone.” Acta Oceanol. Sin., 25, 104–112.
Svendsen, I. (2006). Introduction to nearshore hydrodynamic. Advances series in ocean engineering, Vol. 24, World Scientific, Singapore.
Takewaka, S., Misaki, S., and Nakamura, T. (2003). “Dye diffusion experiment in a longshore current field.” Coast. Eng. J., 45(03), 471–487.
Tao, J.-H., and Han, G. (2002). “Effects of wave motion on pollutant transport in shallow coastal water.” Sci. China, Series E-Technol., 45(6), 593–605.
Information & Authors
Information
Published In
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Sep 8, 2012
Accepted: Jan 15, 2013
Published online: Jan 17, 2013
Published in print: Nov 1, 2013
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.