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Modulation Instability of a Gravity Wave and Generation of a Direct Cascade of Vortex Energy on the Surface of Water

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Abstract

The development of instability of gravity-capillary waves on the surface of water excited by two perpendicular plungers has been experimentally observed. As a result of a four-wave process, waves with a frequency of 8 Hz scatter in pairs into waves with frequencies of 3.92 and 4.08 Hz, as well as 11.98 and 12.02 Hz. The amplitude of low-frequency waves increases exponentially with a characteristic time of about 90 s which exceeds the time of viscous wave dam** almost by an order of magnitude. Along with the main pum** mode, the appeared low-frequency harmonics, propagating on the surface of water at an angle of 15° to each other, form large-scale vortex flows on the surface of water. The wave energy is transferred from the pum** region directly to vortices with a size comparable to the length of a bath wall. In a vortex system, a direct energy cascade with the energy distribution close to E(k) ~ k–5/3 is formed from the region of low wave vectors.

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ACKNOWLEDGMENTS

We are grateful to V.V. Lebedev, I.V. Kolokolov, and E.I. Kats for the useful discussions. The experimental method of velocity measurement was supported by the Russian Science Foundation, grant no. 14-22-00259, and the researches were supported by the Russian Science Foundation, grany no. 17-12-01525.

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Authors and Affiliations

  1. Institute of Solid State Physics, Russian Academy of Sciences, 142432, Chernogolovka, Russia

    S. V. Filatov, M. Yu. Brazhnikov, A. A. Levchenko & L. P. Mezhov-Deglin

  2. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 142432, Chernogolovka, Russia

    S. V. Filatov, M. Yu. Brazhnikov, A. A. Levchenko & L. P. Mezhov-Deglin

  3. Astrakhan State University, 414056, Astrakhan, Russia

    A. A. Levchenko

Authors
  1. S. V. Filatov
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  2. M. Yu. Brazhnikov
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  3. A. A. Levchenko
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  4. L. P. Mezhov-Deglin
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Correspondence to A. A. Levchenko.

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Filatov, S.V., Brazhnikov, M.Y., Levchenko, A.A. et al. Modulation Instability of a Gravity Wave and Generation of a Direct Cascade of Vortex Energy on the Surface of Water. J. Surf. Investig. 12, 1298–1303 (2018). https://doi.org/10.1134/S1027451018050713

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  • DOI: https://doi.org/10.1134/S1027451018050713

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