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Time-reversal of nonlinear waves: Applicability and limitations

G. Ducrozet1,*, M. Fink2, and A. Chabchoub3,4

  • 1LHEEA, École Centrale Nantes, UMR CNRS No. 6598, 1 rue de la Noë, 44321 Nantes, France
  • 2Institut Langevin, ESPCI Paris, PSL University, CNRS, UMR CNRS No. 7587, 10 rue Vauquelin, 75005 Paris, France
  • 3Department of Mechanical Engineering, School of Engineering, Aalto University, 02150 Espoo, Finland
  • 4Department of Ocean Technology Policy and Environment, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8563, Japan

  • *guillaume.ducrozet@ec-nantes.fr
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Phys. Rev. Fluids 1, 054302 – Published 22 September, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.054302

Abstract

Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.

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Phys. Rev. Fluids 1, 054302– Published 22 September, 2016
  • Received 21 March 2016

©2016 American Physical Society

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