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  A similarity relation for the non-linear energy-transfer in a finite-depth gravity-wave spectrum

Herterich, K., & Hasselmann, K. F. (1980). A similarity relation for the non-linear energy-transfer in a finite-depth gravity-wave spectrum. Journal of Fluid Mechanics, 97, 215-224. doi:10.1017/S0022112080002522.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0006-03F9-E Version Permalink: http://hdl.handle.net/21.11116/0000-0006-3D5E-E
Genre: Journal Article

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similarity_relation_for_the_nonlinear_energy_transfer_in_a_finitedepth_gravitywave_spectrum.pdf (Publisher version), 2MB
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Herterich, Klaus1, Author
Hasselmann, Klaus F.1, Author              
Affiliations:
1MPI for Meteorology, Max Planck Society, Bundesstraße 53, 20146 Hamburg, DE, ou_913545              

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 Abstract: The energy transfer in a finite-depth gravity-wave spectrum is investigated in the approximation of a narrow spectrum. It is shown that for ocean depths larger than approximately one tenth of the wavelength (kh [ges ] 0·7) the finite-depth case can be reduced to Longuet-Higgins’ (1976) result for an infinitely deep ocean by a similarity transformation involving changes in scale of the angular spreading function and the transfer rate. For shallower water (kh < 0·7) Longuet-Higgins’ expansion technique is no longer applicable without modification, as the nonlinear coupling coefficient develops a discontinuity at the origin of the expansion. In the range kh [ges ] 0·7 both the magnitude and the two-dimensional frequency-directional distribution of the energy transfer are found not to differ significantly (to within variations by a factor of 2) from the case of an infinitely deep ocean. The transformation rules relating the infinite-depth and finite-depth cases may provide a useful guide for constructing parametrizations of the nonlinear transfer for finite-depth wave prediction models.

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Language(s): eng - English
 Dates: 20061980
 Publication Status: Published in print
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 Rev. Type: Peer
 Identifiers: ISI: A1980JJ41900013
DOI: 10.1017/S0022112080002522
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Title: Journal of Fluid Mechanics
Source Genre: Journal
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Publ. Info: Cambridge [etc.] : Cambridge University Press [etc.]
Pages: - Volume / Issue: 97 Sequence Number: - Start / End Page: 215 - 224 Identifier: ISSN: 0022-1120
n.a.: /journals/resource/954925340716