A 5th-Order Theory for Bichromatic and Bidirectional Ocean Surface Waves

HUANG Hu; LIU Guo-liang

doi:10.3879/j.issn.1000-0887.2016.05.003

Volume 37 Issue 5

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HUANG Hu, LIU Guo-liang. A 5th-Order Theory for Bichromatic and Bidirectional Ocean Surface Waves[J]. Applied Mathematics and Mechanics, 2016, 37(5): 472-482. doi: 10.3879/j.issn.1000-0887.2016.05.003

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A 5th-Order Theory for Bichromatic and Bidirectional Ocean Surface Waves

doi: 10.3879/j.issn.1000-0887.2016.05.003

Shanghai Institute of Applied Mathematics and Mechanics;Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China（11172157）

Received Date: 2016-11-09
Rev Recd Date: 2015-12-23
Publish Date: 2016-05-15

Abstract

Abstract

The classical Stokes wave theory of pure wave motion for the 3rd-order monochromatic and monodirectional waves was expanded to a 5th-order theory for bichromatic and bidirectional ocean surface waves under the ambient uniform current effect in water of finite depth, which, based on the 3rd-order theory for bichromatic and bidirectional waves, comprised the 4th- and the 5th-order explicit expressions for the free surface elevations, the velocity potential and the nonlinear amplitude dispersion relation. The 5th-order nonlinear amplitude dispersion relation playing a key role in the bichromatic and bidirectional wave theory was generalized to one relation of 2 arbitrary interacting waves with different frequencies and ampitudes in pairs out of infinite waves. The typical characteristics of bichromatic and bidirectional short-crested waves were illustrated in detail with diagrams.
- 5th-order theory,
- bichromatic and bidirectional wave,
- ocean surface wave,
- nonlinear amplitude dispersion relation

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References(29)

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