Editorial Type:
Article
Article Type:
Research Article

A New Coastal Wave Model. Part V: Five-Wave Interactions

Ray Q. Lin Hydromechanics Directorate, David Taylor Model Basin, West Bethesda, Maryland

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Will Perrie Ocean Sciences Division, Fisheries and Oceans Canada, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada

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Print Publication:
01 Oct 1997
DOI:
https://doi.org/10.1175/1520-0485(1997)027<2169:ANCWMP>2.0.CO;2
Page(s):
2169–2186
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Abstract

The authors study the action flux associated with three-dimensional wave–wave interactions of ocean surface waves. Over deep water, two-dimensional wave–wave interactions are dominant: the three-dimensional five-wave interactions are two orders of magnitude smaller than the two-dimensional four-wave interactions. However, the five-wave interactions become increasingly important as the water depth decreases. Because of the effects of finite depth, three-dimensional five-wave interactions, involving steep finite-amplitude waves, dominate over two-dimensional four-wave interactions. Specifically, when the water depth h is less than 10 m, or nondimensionalizing with the spectral peak wavenumber Kp when Kph ≤ 3.6 and nonlinearity, ϵ = Ka(3 + tanh2Kh)/4 tanh3Kh ≥ 0.3, the five-wave interactions completely dominate. Results are consistent with the instability study by McLean.

Corresponding author address: Dr. Ray Q. Lin, Hydromechanics Directorate, David Taylor Model Basin, NSWC, Code 5030, Carderock Division, 9500 MacArthur Blvd., West Bethesda, MD 20817-5700.

Abstract

The authors study the action flux associated with three-dimensional wave–wave interactions of ocean surface waves. Over deep water, two-dimensional wave–wave interactions are dominant: the three-dimensional five-wave interactions are two orders of magnitude smaller than the two-dimensional four-wave interactions. However, the five-wave interactions become increasingly important as the water depth decreases. Because of the effects of finite depth, three-dimensional five-wave interactions, involving steep finite-amplitude waves, dominate over two-dimensional four-wave interactions. Specifically, when the water depth h is less than 10 m, or nondimensionalizing with the spectral peak wavenumber Kp when Kph ≤ 3.6 and nonlinearity, ϵ = Ka(3 + tanh2Kh)/4 tanh3Kh ≥ 0.3, the five-wave interactions completely dominate. Results are consistent with the instability study by McLean.

Corresponding author address: Dr. Ray Q. Lin, Hydromechanics Directorate, David Taylor Model Basin, NSWC, Code 5030, Carderock Division, 9500 MacArthur Blvd., West Bethesda, MD 20817-5700.

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