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Influence of Nonlinear Interaction on the Evolution of Waves in a Shallow Basin

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Abstract

The influence of nonlinear interaction of oppositely directed nonlinear waves in a shallow basin is studied theoretically and numerically within the nonlinear theory of shallow water. It is shown that this interaction leads to a change in the phase of propagation of the main wave, which is forced to propagate along the flow induced by the oncoming wave. The estimates of the undisturbed wave height at the time of interaction agree with the theoretical predictions. The phase shift during the interaction of undisturbed waves is sufficiently small, but becomes noticeable in the case of the propagation of breaking waves.

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FUNDING

This research was performed within the Scientific State Task (theme nos. 5.4568.2017/6.7 and 5.5176.2017/8.9) and supported by grant from the President of the Russian Federation for Leading Scientific Schools of Russia SS-2685.2018.5, the “Nonlinear Dynamics” Program, and the Russian Foundation for Basic Research (grant nos. 17-05-00067 and 18-05-80019).

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Authors and Affiliations

  1. Alexeev Technical University, 603950, Nizhny Novgorod, Russia

    A. A. Rodin, N. A. Rodina & A. A. Kurkin

  2. Lobachevskii National Research State University, 603950, Nizhny Novgorod, Russia

    N. A. Rodina

  3. Institute of Applied Physics, Russian Academy of Sciences, 603950, Nizhny Novgorod, Russia

    E. N. Pelinovsky

  4. Special Design Bureau of Marine Research Automation Far East Branch, Russian Academy of Sciences, 693023, Yuzhno-Sakhalinsk, Russia

    E. N. Pelinovsky

  5. National Research University Higher School of Economics, 603950, Nizhny Novgorod, Russia

    E. N. Pelinovsky

  6. University of Southern Queensland, QLD 4350, Darling Heights, West St, Australia

    E. N. Pelinovsky

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  1. A. A. Rodin
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  2. N. A. Rodina
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  3. A. A. Kurkin
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  4. E. N. Pelinovsky
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Corresponding authors

Correspondence to N. A. Rodina, A. A. Kurkin or E. N. Pelinovsky.

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Translated by E. Morozov

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Rodin, A.A., Rodina, N.A., Kurkin, A.A. et al. Influence of Nonlinear Interaction on the Evolution of Waves in a Shallow Basin. Izv. Atmos. Ocean. Phys. 55, 374–379 (2019). https://doi.org/10.1134/S0001433819040108

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