Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On the Role of Resonant Interactions in the Short-Term Evolution of Deep-Water Ocean Spectra

On the Role of Resonant Interactions in the Short-Term Evolution of Deep-Water Ocean Spectra The temporal evolution of the energy spectrum of a field of random surface gravity waves in deep water is investigated by means of direct numerical simulations of the deterministic primitive equations. The detected rate of change of the spectrum is shown to be proportional to the cubic power of the energy density and to agree very well with the nonlinear energy transfer S nl as predicted by Hasselmann. Despite the fact that use of various asymptotic relations that are valid only for t → ∞ or integration with respect to time over a time scale much longer than O period × ( ak ) −2 is necessary in the derivation of Hasselmann’s S nl , it is clearly demonstrated that the rate of change of the spectrum given by the numerical simulation agrees very well with Hasselmann’s S nl at every instance of ordinary time scale comparable to the period. The result implies that the four-wave resonant interactions control the evolution of the spectrum at every instant of time, whereas nonresonant interactions do not make any significant contribution even in a short-term evolution. It is also pointed out that the result may call for a reexamination of the process of derivation of the kinetic equation for the spectrum. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Physical Oceanography American Meteorological Society

On the Role of Resonant Interactions in the Short-Term Evolution of Deep-Water Ocean Spectra

Journal of Physical Oceanography , Volume 37 (4) – Apr 15, 2006

Loading next page...
 
/lp/american-meteorological-society/on-the-role-of-resonant-interactions-in-the-short-term-evolution-of-ZWCKbsyD6f
Publisher
American Meteorological Society
Copyright
Copyright © 2006 American Meteorological Society
ISSN
1520-0485
DOI
10.1175/JPO3029.1
Publisher site
See Article on Publisher Site

Abstract

The temporal evolution of the energy spectrum of a field of random surface gravity waves in deep water is investigated by means of direct numerical simulations of the deterministic primitive equations. The detected rate of change of the spectrum is shown to be proportional to the cubic power of the energy density and to agree very well with the nonlinear energy transfer S nl as predicted by Hasselmann. Despite the fact that use of various asymptotic relations that are valid only for t → ∞ or integration with respect to time over a time scale much longer than O period × ( ak ) −2 is necessary in the derivation of Hasselmann’s S nl , it is clearly demonstrated that the rate of change of the spectrum given by the numerical simulation agrees very well with Hasselmann’s S nl at every instance of ordinary time scale comparable to the period. The result implies that the four-wave resonant interactions control the evolution of the spectrum at every instant of time, whereas nonresonant interactions do not make any significant contribution even in a short-term evolution. It is also pointed out that the result may call for a reexamination of the process of derivation of the kinetic equation for the spectrum.

Journal

Journal of Physical OceanographyAmerican Meteorological Society

Published: Apr 15, 2006

References