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The generalized kinetic equation as a model for the nonlinear transfer in third-generation wave models

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Abstract

An alternative model for the nonlinear interaction term S n l in spectral wave models, the so called generalized kinetic equation (Janssen J Phys Oceanogr 33(4):863–884, 2003; Annenkov and Shrira J Fluid Mech 561:181–207, 2006b; Gramstad and Stiassnie J Fluid Mech 718:280–303, 2013), is discussed and implemented in the third generation wave model WAVEWATCH-III. The generalized kinetic equation includes the effects of near-resonant nonlinear interactions, and is therefore able, in theory, to describe faster nonlinear evolution than the existing forms of S n l which are based on the standard Hasselmann kinetic equation (Hasselmann J Fluid Mech 12:481–500, 1962). Numerical simulations with WAVEWATCH have been carried out to thoroughly test the performance of the new form of S n l , and to compare it to the existing models for S n l in WAVEWATCH; the DIA and WRT. Some differences between the different models for S n l are observed. As expected, the DIA is shown to perform less well compared to the exact terms in certain situations, in particular for narrow wave spectra. Also for the case of turning wind significant differences between the different models are observed. Nevertheless, different from the case of unidirectional waves where the generalized kinetic equation represents a obvious improvement to the standard forms of S n l (Gramstad and Stiassnie 2013), the differences seems to be less pronounced for the more realistic cases considered in this paper.

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Acknowledgments

O.G. would like to thank Dr. Stefan Zieger for helpful assistance with WAVEWATCH running and implementation. We would like to thank Gertbrant van Vledder for providing useful details about the WRT code.

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Authors and Affiliations

  1. Swinburne University of Technology, Hawthorn, Victoria, Australia

    Odin Gramstad & Alexander Babanin

  2. DNV GL Strategic Research & Innovation, Høvik, Norway

    Odin Gramstad

  3. Department of Mathematics, University of Oslo, Oslo, Norway

    Odin Gramstad

Authors
  1. Odin Gramstad
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  2. Alexander Babanin
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Correspondence to Odin Gramstad.

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Responsible Editor: Bruno Castelle

This work has been supported by the Australian Research Council (ARC) Grant No. DP1093349 and the Research Council of Norway Grant No. 226239.

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Gramstad, O., Babanin, A. The generalized kinetic equation as a model for the nonlinear transfer in third-generation wave models. Ocean Dynamics 66, 509–526 (2016). https://doi.org/10.1007/s10236-016-0940-4

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