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Stability of Kolmogorov spectra for surface gravity waves

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Abstract

The Kolmogorov spectrum of waves on water is a result of cascading energy via four-wave interactions. For this spectrum in the isotropic case, we introduce basic small perturbations and calculate the decrement of their damping depending on the frequency. We confirm the stability of the Kolmogorov spectrum. The calculation results are applicable for analyzing the stability of numerical methods for solving the kinetic equation. We show that using the discrete-interaction approximation strongly reduces the damping in certain cases.

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Authors and Affiliations

  1. Shirshov Institute of Oceanology, RAS, Moscow, Russia

    V. V. Geogjaev

  2. Skolkovo Institute of Science and Technology, Moscow, Russia

    V. V. Geogjaev

Authors
  1. V. V. Geogjaev
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Correspondence to V. V. Geogjaev.

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The author declares no conflicts of interest.

Additional information

This research is supported by a grant from the Russian Science Foundation (Project No. 19-72-30028).

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 203, No. 1, pp. 3–9, April, 2020.

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Geogjaev, V.V. Stability of Kolmogorov spectra for surface gravity waves. Theor Math Phys 203, 437–442 (2020). https://doi.org/10.1134/S0040577920040017

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  • DOI: https://doi.org/10.1134/S0040577920040017

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