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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Nonlin. Processes Geophys., 22, 325-335, 2015
https://doi.org/10.5194/npg-22-325-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
28 May 2015
Evaluation of a spectral line width for the Phillips spectrum by means of numerical simulation
A. O. Korotkevich1,2 and V. E. Zakharov2,3,4,5 1Department of Mathematics & Statistics, The University of New Mexico, MSC01 1115, 1 University of New Mexico, Albuquerque, NM 87131-0001, USA
2L. D. Landau Institute for Theoretical Physics, 2 Kosygin Str., Moscow, 119334, Russian Federation
3University of Arizona, Department of Mathematics, Tucson, AZ 85721, USA
4P. N. Lebedev Physical Institute, 53 Leninskiy prospekt, Moscow, 119334, Russian Federation
5Laboratory of Nonlinear Wave Processes, Novosibirsk State University, Novosibirsk, Russian Federation
Abstract. The work aims to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to the situations described by the Phillips spectrum. We evaluate a spectral line width of the spectrum from the simulations in the framework of primordial dynamical equations at different levels of nonlinearity in the system, corresponding to the weakly turbulent Kolmogorov–Zakharov spectra ω−4, Phillips spectra ω−5, and intermediate cases. The original motivation of the work was to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to the Phillips spectrum. It is shown that, even in the case of relatively high average steepness, when the Phillips spectrum is present in the system, the spectral lines are still very narrow, at least in the region of the direct cascade spectrum. It allows us to state that, even in the case of the Phillips spectrum, one of the assumptions used for the derivation of the Hasselmann kinetic equation is still valid, at least in the case of moderate whitecapping.

Citation: Korotkevich, A. O. and Zakharov, V. E.: Evaluation of a spectral line width for the Phillips spectrum by means of numerical simulation, Nonlin. Processes Geophys., 22, 325-335, https://doi.org/10.5194/npg-22-325-2015, 2015.
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The work aims to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to situations described by the Phillips spectrum, which includes rough sea. We evaluated a spectral line width of the spectrum from the simulations in the framework of primordial dynamical equations at different levels of nonlinearity in the system, and showed that it remains narrow even for the situations described by the Phillips spectrum.
The work aims to check one of the assumptions under which the kinetic equation for water waves...
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