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Ocean Engineering

Linear and Nonlinear Wave Models Based on Hamilton’s Principle and Stream-Function Theory: CMSE and IGN

[+] Author and Article Information
J. W. Kim

 Technip USA, Inc., 11700 Old Katy Road, Suite 150, Houston, TX 77079jwkim@technip.com

R. C. Ertekin

 University of Hawaii at Manoa, 2540 Dole Street, Holmes Hall 402, Honolulu, HI 96822-2303ertekin@hawaii.edu

K. J. Bai

 Seoul National University, Shinlim Dong San 56-1, Seoul 151-742, Koreakjbai@snu.ac.kr

In this paper, periodic progressive gravity wave is referred to as ”Stokes wave,” regardless whether it is linear, weakly nonlinear, or fully nonlinear.

J. Offshore Mech. Arct. Eng 132(2), 021102 (Mar 01, 2010) (6 pages) doi:10.1115/1.4000503 History: Received September 17, 2007; Revised April 17, 2009; Published March 01, 2010; Online March 01, 2010

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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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sinusoidal ripple beds: (a) sinusoidal and (b) doubly-sinusoidal bed

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Figure 2

Reflection coefficient near class I Bragg scattering: kA=0.05, d/h=0.16, kbd=0.31, and N=10

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Figure 4

Comparisons of reflection coefficient near class II resonant condition; same condition as in Fig. 3

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Figure 5

Reflection coefficient of second-harmonic wave due to class III Bragg scattering

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Figure 3

Reflection coefficient for doubly-sinusoidal bed by (a) linear and (b) IGN models: kA=0.05, d1/h0=d2/h0=0.25, and L/h0=12

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