Scattering and Trapping of Wave Energy by a Submerged Truncated Paraboloidal Shoal
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 133, Issue 2
Abstract
In this paper, we study the scattering and trapping of wave energy by a submerged truncated paraboloidal shoal. The analytical approach of Liu et al. in 2004 for solving wave amplification around a circular island mounted on a shoal is extended in this study to investigate waves above a submerged shoal. In this approach, the mild-slope equation is first transformed into an explicit equation by using Hunt’s 1979 Padé approximation to the wave dispersion equation. It is then solved analytically in terms of combined Fourier series and Taylor series. For incident waves varying from short to long waves, wave amplifications in the vicinity of the shoal are calculated using the newly derived analytical model and they agree excellently with the finite difference solutions of Lin in 2004. It is found that, for the particular shoal studied in this paper, there exists an energy focal point where the wave amplitude is the maximum. This point is the result of combined wave refraction, diffraction, and reflection. The point is always located along the -axis and it is behind the shoal center for very short waves. As the increase of wave period, it moves upstream and it can come in front of the shoal center for very long waves when wave reflection is significant. For a particular incident wave, wave amplification increases and the focal point moves toward the shoal center with the reduction of the water depth above the shoal center. The maximum wave amplitude increases exponentially as the decrease of local water depth. It is also found that there exists the so-called “calm” areas for shallowly submerged shoal, which are located behind the focal point and the local amplitude can be as small as nearly zero.
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Acknowledgments
This project is supported, in part, by the research grant from the National University of Singapore (R-264-000-121-112) and research grant from the Meteorological Services of Singapore (R-264-000-121-291). The second writer would like to acknowledge the support by the Natural Science Foundation of P.R. China (UNSPECIFIED10162001, UNSPECIFIED10462001), the Returning Overseas Scholars Program of Ministry of Education P.R. China (2005–35), Guangxi Natural Science Foundation (0575029,0639008) Guangxi Shi-Bai-Qian Scholars Program (2001224) and Guangxi Education Department.
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Information & Authors
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 133 • Issue 2 • March 2007
Pages: 94 - 103
Copyright
© 2007 ASCE.
History
Received: Sep 10, 2004
Accepted: Mar 13, 2006
Published online: Mar 1, 2007
Published in print: Mar 2007
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