Nonlinear Diffraction of Waves by a Submerged Shelf in Shallow Water

[+] Author and Article Information
R. C. Ertekin, J. M. Becker

Department of Ocean Engineering, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 2540 Dole Street, Holmes Hall 402, Honolulu, HI 96822

J. Offshore Mech. Arct. Eng 120(4), 212-220 (Nov 01, 1998) (9 pages) doi:10.1115/1.2829542 History: Received December 01, 1996; Revised May 12, 1998; Online December 17, 2007


The diffraction of water waves by submerged obstacles in shallow water generally requires the use of a nonlinear theory since both dispersive and nonlinear effects are important. In this work, wave diffraction is studied in a numerical wave tank using the Level I Green-Naghdi (GN) equations. Cnoidal waves are generated numerically by a wave maker situated at one end of a two-dimensional numerical wave tank. At the downwave end of the tank, an open-boundary condition is implemented to simulate a wave-absorbing beach, and thus to reduce reflections. The GN equations are solved in the time-domain by employing a finite-difference method. The numerical method is applied to diffraction of cnoidal waves by a submerged shelf, or a sand bar, of considerable height relative to water depth. The predicted results are compared with the available experimental data which indicate the importance of nonlinearity for the shallow-water conditions.

Copyright © 1998 by The American Society of Mechanical Engineers
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