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Laboratory Modeling of Resonance Phenomena in the Long Wave Dynamics

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Nonlinear Waves and Pattern Dynamics

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Abstract

Two sets of experiments in a wave flume to demonstrate resonance phenomena in laboratory conditions have been performed. The first set was performed to investigate nonlinear wave run-up on the beach. It is revealed that under certain wave excitation frequencies, a significant increase in run-up amplification is observed Ezersky et al. (Nonlin Processes Geophys 20:35, 2013, [1]). It is found that this amplification is due to the excitation of resonant mode in the region between the shoreline and wave maker. The second set of experiments was performed to model an excitation of localized mode (edge waves) by breaking waves propagating towards shoreline. It is shown that the excitation of edge waves is due to parametric instability similar to pendulum with vibrating point of suspension. The domain of instability in the plane of parameters (amplitude—frequency) of surface wave is found. It was found that for amplitude of surface wave slightly exceeding the threshold, the amplitude of edge wave grows exponentially with time, whereas for the large amplitude, the wave breaking appears and excitation of edge wave does not occur. It was shown that parametric excitation of edge wave can increase significantly (up to two times) the maximal run-up height.

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Acknowledgements

This work is dedicated to the memory of a dear friend and colleague Professor Alexander Ezersky, who sadly passed away after a long-lasting fight with the cancer. Until his last days, he tried to dedicate his time to work, the results of which are also presented in this Chapter.

The present study was supported by the Russian state contract 5.5176.2017/8.9, Russian President Grant NSh-2685.2018.5, RFBR grant 17-05-00067 and ETAG project PUT1378. ID and EP also thank the University of Caen for its visitor program, who allowed this fruitful collaboration.

Author information

Authors and Affiliations

  1. Normandie Université, UNICAEN, UNIROUEN, CNRS, UMR 6143, M2C, 14000, Caen, France

    Nizar Abcha

  2. Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 603950, Nizhny Novgorod, Russia

    Efim Pelinovsky & Ira Didenkulova

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

    Efim Pelinovsky

  4. Institute of Applied Physics, 603950, Nizhny Novgorod, Russia

    Efim Pelinovsky

  5. Department of Marine Systems, Tallinn University of Technology, 12618, Tallinn, Estonia

    Ira Didenkulova

Authors
  1. Nizar Abcha
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  2. Efim Pelinovsky
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  3. Ira Didenkulova
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Corresponding author

Correspondence to Nizar Abcha .

Editor information

Editors and Affiliations

  1. Normandie Université, UNICAEN, UNIROUEN, CNRS, UMR 6143, M2C, Caen, France

    Nizar Abcha

  2. Department of Nonlinear Geophysical Processes, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    Efim Pelinovsky

  3. Normandie Université, Unihavre, CNRS, UMR 6294, LOMC, Le Havre CX, France

    Innocent Mutabazi

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Abcha, N., Pelinovsky, E., Didenkulova, I. (2018). Laboratory Modeling of Resonance Phenomena in the Long Wave Dynamics. In: Abcha, N., Pelinovsky, E., Mutabazi, I. (eds) Nonlinear Waves and Pattern Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-78193-8_2

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