Finite Element Modeling of Nonlinear Coastal Currents
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 111, Issue 2
Abstract
A numerical model describing wave‐induced mean sea level variations and coastal currents in the nearshore region is developed by the finite element method. The model includes nonlinear convective accelerations, lateral mixing and bottom friction. To specify the wave refraction field, a wave model is also developed with a semi‐discrete Galerkin method. The numerical accuracy of the model is verified with the analytic solutions for one‐dimenional longshore currents and two‐dimensional rip currents. The numerical model is also applied to predict realistic meandering currents occurring on a periodic rip channel. Due to the nonlinear inertial effect, the unaccelerated longshore current profile is stretched and causes a decrease in the magnitude of maximum velocity. A comparison with the analytic solution of a one‐dimensional longshore current velocity distribution indicates that the linear analytic solution significantly overestimates the maximum velocity. The numerical results quantitatively demonstrate the relative importance of the nonlinear convective terms in the nearshore current problem.
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References
1.
Arthur, R. S., “A Note on the Dynamics of Rip Currents,” Journal of Geophysical Research, Vol. 67, 1962, pp. 2777–2779.
2.
Bettess, P., et al., “Longshore Currents Due to Surf Zone Barrier,” Proceedings, ASCE, Sixteenth Coastal Engineering Conference, Hamburg, 1978, pp. 776–790.
3.
Birkemeier, W. A., and Dalrymple, R. A., “Nearshore Water Circulation Induced by Wind and Waves,” Proceedings of the Symposium on Modelling Technique, ASCE, 1975, pp. 1062–1081.
4.
Bowen, A. J., “Rip Currents,” thesis presented to the University of California, at San Diego, Calif., in 1967, in partial fulfillment of the requirements for the degree of Doctor of Engineering.
5.
Bowen, A. J., “The Generation of Longshore Currents on a Plane Beach,” Journal of Marine Research, Vol. 27, No. 2, 1969, pp. 206–215.
6.
Dalrymple, R. A., and Lozano, C. J., “Wave‐Current Interaction Models for Rip Currents,” Journal of Geophysical Research, Vol. 83, 1978, pp. 6063–6071.
7.
Ebersole, B., and Dalrymple, R. A., “A Numerical Model of Nearshore Circulation Including Convective Accelerations and Lateral Mixing,” Ocean Engineering Report No. 21, Department of Civil Engineering, University of Delaware, 1979.
8.
Gartling, D. K., Nicell, R. E., and Tanner, R. I., “A Finite Element Convergence Study for Accelerating Flow Problems,” International Journal of Methods Engineering, Vol. 11, 1978, pp. 1155–1174.
9.
Hood, P., and Taylor, C., “Navier‐Stokes Equations Using Mixed Interpolation,” Finite Element Methods in Flow Problems, UAH Press, Huntsville, 1974, pp. 121–132.
10.
Huebner, K. H., The Finite Element Method for Engineers, John Wiley and Sons, New York, N.Y., 1975.
11.
Liu, P. L.‐F., and Mei, C. C., “Effects of a Breakerwater on Nearshore Currents Due to Breaking Waves,” TM‐57, Coastal Engineering Research Center, 1975.
12.
Liu, P. L.‐F., and Lennon, G. P., “Finite Element Modelling of Nearshore Currents,” Journal of the Waterways, Port, Coastal, and Ocean Division, ASCE, Vol. 104, No. WW2, 1978, pp. 175–189.
13.
Long, P. E., and Pepper, D. H., “A Comparison of Six Numerical Schemes for Calculating the Advection of Atmospheric Pollution,” 3rd Symposium on Atmospheric Turbulence, Diffusion and Air Quality, Raleigh, N.C., 1976.
14.
Longuet‐Higgins, M. S., “Longshore Currents Generated by Obliquely Incident Sea Waves,” Journal of Geophysical Research, Vol. 75, 1970, pp. 6778–6801.
15.
Longuet‐Higgins, M. S., “Recent Progress in Study of Longshore Currents,” Waves on Beaches and Resulting Sediment Transport, R. E. Meyer, ed., Academic Press, New York, N.Y., 1972, pp. 202–248.
16.
Mei, C. C., and Liu, P. L.‐F., “Effects of Topography on the Circulation in and Near the Surf Zone—Linear Theory,” Estuarine and Coastal Marine Science, Vol. 5, 1977, pp. 25–37.
17.
Noda, E. K., “Wave‐Induced Nearshore Circulation,” Journal of Geophysical Research, Vol. 79, 1974, pp. 4097–4106.
18.
Phillips, O. M., The Dynamics of the Upper Ocean, Cambridge University Press, 1966.
19.
Sonu, C. J., “Field Observations of Nearshore Circulation and Meandering Currents,” Journal of Geophysical Research, Vol. 77, 1972, pp. 3232–3247.
20.
Thompson, R. Y., “A Potential‐Flow Model of Turbulence Caused by Breaking Surface Waves,” Journal of Geophysical Research, Vol. 87, 1982, pp. 1935–1937.
21.
Thornton, E. B., “Variation of Longshore Current Across its Surf Zone,” Proceedings of the 12th Coastal Engineering Conference, ASCE, 1970, pp. 219–308.
22.
Wind, H. G., and Perrel, P., “Wave‐Driven Coastal Currents,” W439‐1 TOW, Delft Hydraulics Laboratory, 1982.
23.
Wu, C.‐S., “Finite Element Modeling of Nonlinear Nearshore Currents,” thesis presented to Cornell University, at Ithaca, N.Y., in 1983, in partial fulfillment of the requirements for the degree of Doctor of Engineering.
24.
Wu, C.‐S., and Liu, P. L.‐F., “Effects of Nonlinear Forces on Nearshore Currents,” Coastal Engineering, to appear in 1983.
Information & Authors
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 111 • Issue 2 • March 1985
Pages: 417 - 432
Copyright
Copyright © 1985 ASCE.
History
Published online: Mar 1, 1985
Published in print: Mar 1985
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