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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
17 Oct 2016
Review status
A revision of this discussion paper is under review for the journal Nonlinear Processes in Geophysics (NPG).
Ocean swell within the kinetic equation for water waves
Sergei Badulin1,2 and Vladimir Zakharov1,2,3,4,5 1P. P. Shirshov Institute of Oceanology of the Russian Academy of Science, Russia
2Novosibirsk State University, Russia
3University of Arizona, Tuscon, USA
4P. N. Lebedev Physical Institute of Russian Academy of Sciences
5Waves and Solitons LLC, Phoenix, Arizona, USA
Abstract. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to 106 seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov–Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions. Weak power-law attenuation of swell within the Hasselmann equation is not consistent with results of ocean swell tracking from satellite altimetry and SAR (Synthetic Aperture Radar) data. At the same time, the relatively fast weakening of wave-wave interactions makes the swell evolution sensitive to other effects. In particular, as shown, coupling with locally generated wind waves can force the swell to grow at rather light winds.

Citation: Badulin, S. and Zakharov, V.: Ocean swell within the kinetic equation for water waves, Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-61, in review, 2016.
Sergei Badulin and Vladimir Zakharov
Sergei Badulin and Vladimir Zakharov
Sergei Badulin and Vladimir Zakharov


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