Recently, two wave models based on the stream-function theory have been derived from Hamilton’s principle for gravity waves. One is the irrotational Green–Naghdi (IGN) equation and the other is the complementary mild-slope equation (CMSE). The IGN equation has been derived to describe refraction and diffraction of nonlinear gravity waves in the time domain and in water of finite but arbitrary bathymetry. The CMSE has been derived to consider the same problem in the (linear) frequency domain. In this paper, we first discuss the two models from the viewpoint of Hamilton’s principle. Then the two models are applied to a resonant scattering of Stokes waves over periodic undulations, or the Bragg scattering problem. The numerical results are compared with existing numerical predictions and experimental data. It is found here that Level 3 IGN equation can describe Bragg scattering well for arbitrary bathymetry.
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Ocean Engineering
Linear and Nonlinear Wave Models Based on Hamilton’s Principle and Stream-Function Theory: CMSE and IGN
R. C. Ertekin,
e-mail: ertekin@hawaii.edu
R. C. Ertekin
Professor
Fellow ASME
University of Hawaii at Manoa
, 2540 Dole Street, Holmes Hall 402, Honolulu, HI 96822-2303
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K. J. Bai
K. J. Bai
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J. W. Kim
R. C. Ertekin
Professor
Fellow ASME
University of Hawaii at Manoa
, 2540 Dole Street, Holmes Hall 402, Honolulu, HI 96822-2303e-mail: ertekin@hawaii.edu
K. J. Bai
J. Offshore Mech. Arct. Eng. May 2010, 132(2): 021102 (6 pages)
Published Online: March 1, 2010
Article history
Received:
September 17, 2007
Revised:
April 17, 2009
Online:
March 1, 2010
Published:
March 1, 2010
Citation
Kim, J. W., Ertekin, R. C., and Bai, K. J. (March 1, 2010). "Linear and Nonlinear Wave Models Based on Hamilton’s Principle and Stream-Function Theory: CMSE and IGN." ASME. J. Offshore Mech. Arct. Eng. May 2010; 132(2): 021102. https://doi.org/10.1115/1.4000503
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