A numerical model for edge waves on a compound slope
An edge wave is a kind of surface gravity wave basically travelling along a shoaling beach. Based on the periodic assumption in the longshore direction, a second order ordinary differential equation is obtained for numerical simulation of the cross-shore surface elevation. Given parameters at the shoreline, a cross-shore elevation profile is obtained through integration with fourth-order Runge–Kutta technique. For a compound slope, a longshore wavenumber is obtained by following a geometrical approach and solving a transcendental equation with an asymptotic method. Numerical results on uniform and compound sloping beaches with different wave periods, slope angles, modes and turning point positions are presented. Some special scenarios, which cannot be predicted by analytical models are also discussed.
Key wordsedge wave compound slope full water wave equation geometrical approach numerical integration
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- Darbyshire, J., 1977. An investigation of beach cusps in Hell’s Mouth Bay, A Voyage of Discovery, Pergamon, Oxford, 405–427.Google Scholar
- Eckart, C., 1951. Surface Waves on Water of Variable Depth, Lecture Notes, University of California, Scripps.Google Scholar
- Mei, C.C., Stiassmie, M. and Yue, D.K.P., 2005. Theory and Applications of Ocean Surface Waves, World Scientific Publishing Co. Pte. Ltd, New Jersey, Linear Aspects: 1–506. Nonlinear Aspects, 1–1071.Google Scholar
- Stokes, G.G., 1846. Report on recent researches in hydro-dynamics, Rep. 16th Meeting Brit. Assoc. Adv. Sci., 1–20.Google Scholar
- Zhang, Y., Hong, G.W. and Feng, W.B., 2009. Solutions of kinematicdynamic elements for edge waves on sloping bottom, Proceedings of the 19th International Offshore and Polar Engineering Conference, Osaka, Japan.Google Scholar