Disintegration of linear edge waves
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Abstract
It is demonstrated that offshore wavenumbers of edge waves change from imaginary wavenumbers in deep water to real wavenumbers in shallow water. This finding indicates that edge waves in the offshore direction exist as evanescent waves in deep water and as propagating waves in shallow water. Since evanescent waves can stably exist in a limited region while propagating waves cannot, energy should be released from nearshore regions. In the present study, the instability region is predicted based on both the full water wave solution and the shallow-water wave approximation.
Key words
edge waves evanescent waves propagating waves water wavesPreview
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References
- Blondeaux, P. and Vittori, G., 1995. The nonlinear excitation of synchronous edge waves by a monochromatic wave normally approaching a plane beach, J. Fluid Mech., 301, 251–268.MathSciNetMATHCrossRefGoogle Scholar
- Bowen, A. J. and Inman, D. L., 1969. Rip currents 2. Laboratory and field observations, J. Geophys. Res., 74(23): 5479–5490.CrossRefGoogle Scholar
- Bryan, K. R. and Bowen, A. J., 1998. Bar-trapped edge waves and longshore currents, J. Geophys. Res., 103(C12): 27867–27884.CrossRefGoogle Scholar
- Caballeria, M., Coco, G., Falques, A. and Huntley, D., 2002. Self-organization mechanisms for the formation of nearshore crescentic and transverse sand bars, J. Fluid Mech., 465, 379–410.MATHCrossRefGoogle Scholar
- Didenkulova, I., Pelinovsky, E. and Soomere, T., 2009. Long surface wave dynamics along a convex bottom, J. Geophys. Res., 114(C07): C07006.CrossRefGoogle Scholar
- Eckart, C., 1951. Surface Waves on Water of Variable Depth, Wave Report No. 100, Scripps Institution of Oceanography, University of California, 124.Google Scholar
- Galletta, V. and Vittori, G., 2004. Nonlinear effects on edge wave development, Eur. J. Mech. B-Fluid., 23(6): 861–878.MathSciNetMATHCrossRefGoogle Scholar
- Guza, R. T. and Bowen, A. J., 1976. Finite amplitude edge waves, J. Mar. Res., 34(2): 269–293.Google Scholar
- Guza, R. T. and Inman, D. L., 1975. Edge waves and beach cusps, J. Geophys. Res., 80(21): 2997–3012.CrossRefGoogle Scholar
- Kurkin, A. and Pelinovsky, E., 2003. Shallow-water edge waves above an inclined bottom slowly varied in along-shore direction, Eur. J. Mech. B-Fluid., 22(4): 305–316.MathSciNetMATHCrossRefGoogle Scholar
- Mathew, J. and Akylas, T. R., 1990. On the radiation damping of finite-amplitude progressive edge waves, Proceedings: Mathematical and Physical Sciences, 431, 419–431.MATHCrossRefGoogle Scholar
- Porter, D., 2003. The mild-slope equations, J. Fluid Mech., 494, 51–63.MathSciNetMATHCrossRefGoogle Scholar
- Rockliff, N., 1978. Finite amplitude effects in free and forced edge waves, Mathematical Proceedings of the Cambridge Philosophical Society, 83(3): 463–479.MathSciNetMATHCrossRefGoogle Scholar
- Schäffer, H. A. and Jonsson, I. G., 1992. Edge waves revisited, Coast. Eng., 16(4): 349–368.CrossRefGoogle Scholar
- Stokes, G. G., 1846. Report on Recent Researches on Hydrodynamics, British Association for the Advancement of Science Report, 1, 1–20.Google Scholar
- Ursell, F., 1952. Edge waves on a sloping beach, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 214(1116): 79–97.MathSciNetMATHCrossRefGoogle Scholar
- Yeh, H. H., 1986. Experimental study of standing edge waves, J. Fluid Mech., 168, 291–304.CrossRefGoogle Scholar
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© Chinese Ocean Engineering Society and Springer-Verlag Berlin Heidelberg 2013