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Implementing New Nonlinear Term in Third Generation Wave Models

[+] Author Affiliations
Odin Gramstad

Swinburne University of Technology, Melbourne, AustraliaUniversity of Oslo, Norway

Alexander Babanin

Swinburne University of Technology, Melbourne, Australia

Paper No. OMAE2014-24677, pp. V04BT02A057; 7 pages
doi:10.1115/OMAE2014-24677
From:
  • ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering
  • Volume 4B: Structures, Safety and Reliability
  • San Francisco, California, USA, June 8–13, 2014
  • Conference Sponsors: Ocean, Offshore and Arctic Engineering Division
  • ISBN: 978-0-7918-4543-1
  • Copyright © 2014 by ASME

abstract

The non-linear interaction term is one of the three key source functions in every third-generation spectral wave model. An update of physics of this term is discussed.

The standard statistical/phase-averaged description of the nonlinear transfer of energy in the wave spectrum (wave-turbulence) is based on Hasselmann’s kinetic equation [1]. In the derivation of the kinetic equation (KE) it is assumed that the evolution takes place on the slow O(ε−4) time scale, where ε is the wave steepness. This excludes the effects of near-resonant quartet interactions that may lead to spectral evolution on the ‘fast’ O(ε−2) time scale.

Generalizations of the KE (GKE) that enable description of spectral evolution on the O(ε−2) time scale [2–4] are discussed. The GKE, first solved numerically in [4], is implemented as a source term in the third generation wave model WAVEWATCH-III. The new source term (GKE) is tested and compared to the other nonlinear-interaction source terms in WAVEWATCH-III; the full KE (WRT method) and the approximate DIA method. It is shown that the GKE gives similar results to the KE in the case of a relatively broad banded and directional spread spectrum, while it shows somewhat larger difference in the case of a more narrow banded spectrum with narrower directional distribution.

We suggest that the GKE may be a suitable replacement to the KE in situations where ‘fast’ spectral evolution takes place.

Copyright © 2014 by ASME
Topics: Waves

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