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.
Skip Nav Destination
e-mail: ertekin@hawaii.edu
Article navigation
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
Search for other works by this author on:
K. J. Bai
K. J. Bai
Search for other works by this author on:
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
Download citation file:
Get Email Alerts
Numerical Research on Impacting Load and Structural Response for a Model Experiment of High-speed Craft
J. Offshore Mech. Arct. Eng
On the Natural Keulegan–Carpenter Number for Subsea Industrial Modulus Installation
J. Offshore Mech. Arct. Eng (February 2025)
Semi-Active Groundhook Control of Offshore Tension Leg Platforms Using Tuned Mass Damper With Optimized Parameters and Magneto-Rheological Damper Under Multiple Hazards
J. Offshore Mech. Arct. Eng (February 2025)
Mechanism analysis of the effect of wake vortex on cylinder vibration in flow induced motion
J. Offshore Mech. Arct. Eng
Related Articles
Application of the Singularity Expansion Method to Elastic Wave Scattering
Appl. Mech. Rev (October,1990)
Acoustic Scattering Resonances: Relation to External and Internal Surface Waves
Appl. Mech. Rev (October,1996)
Mid-Frequency Range Acoustic Radiation From Slender Elastic Bodies Using the Surface Variational Principle
J. Vib. Acoust (April,1998)
Wave Trapping by Axisymmetric Concentric Cylinders
J. Offshore Mech. Arct. Eng (February,2003)
Related Proceedings Papers
Related Chapters
Short-Pulse Collimated Radiation in a Participating Medium Bounded by Diffusely Reflecting Boundaries
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
The MCRT Method for Participating Media
The Monte Carlo Ray-Trace Method in Radiation Heat Transfer and Applied Optics
Modeling Grain Boundary Scattering in Nanocomposites
Inaugural US-EU-China Thermophysics Conference-Renewable Energy 2009 (UECTC 2009 Proceedings)