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Wind-wave generation by energy and momentum flux to the forced components of a wave field

Published online by Cambridge University Press:  12 April 2006

Dieter E. Hasselmann
Dieter E. Hasselmann
Affiliation:
Meteorologisches Institut, Universität Hamburg, Germany
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Abstract

The response of surface gravity waves with profile ζ to forcing by the atmospheric pressure p(a) is studied. It is shown that not only the usually considered cross-spectrum 〈p(a)ζ〉 is responsible for wave growth. All higher-order spectra 〈p(a)ζ1,…,ζn〉 also lead to wave growth linear in ε = ρ(a)/ρ,ρ(a) and ρ being the density of air and water respectively. The bispectral contribution is investigated in detail and is calculated for three models of the bispectrum. The results indicate that bispectral contributions are not negligible and may account for typically 30-50%, and possibly more, of the usually considered cross-spectral contribution. The bispectral growth mechanism contains the fluctuating-stress mechanism discussed by Longuet-Higgins (1969) as a special case. As a byproduct new information on the symmetry properties of the hydrodynamic coupling off the dispersion shell is obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 85 , Issue 3 , 13 April 1978 , pp. 543 - 572
Copyright
© 1978 Cambridge University Press

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