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Prediction and manipulation of hydrodynamic rogue waves via nonlinear spectral engineering

Alexey Tikan1,*, Felicien Bonnefoy2, Giacomo Roberti3, Gennady El3, Alexander Tovbis4, Guillaume Ducrozet2, Annette Cazaubiel5, Gaurav Prabhudesai6, Guillaume Michel7 et al.

Francois Copie1, Eric Falcon5, Stephane Randoux1, and Pierre Suret1

  • 1Université Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
  • 2École Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France
  • 3Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
  • 4Department of Mathematics, University of Central Florida, Orlando, Florida 32816, USA
  • 5Université de Paris, MSC, UMR 7057 CNRS, F-75 013 Paris, France
  • 6Laboratoire de Physique de lÉcole Normale Superieure, ENS, Universite PSL, CNRS, Sorbonne Université, Université Paris-Diderot, 75005 Paris, France
  • 7Institut Jean Le Rond dAlembert, Sorbonne Université, CNRS, UMR 7190, F-75 005 Paris, France

  • *alexey.tikan@epfl.ch; Present address: Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
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Phys. Rev. Fluids 7, 054401 – Published 3 May, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.054401

Abstract

The Peregrine soliton (PS) is widely regarded as a prototype nonlinear structure capturing properties of rogue waves that emerge in the nonlinear propagation of unidirectional wave trains. It has been recently demonstrated that the PS can emerge locally, as an asymptotic structure arising from the propagation of an arbitrary large decaying pulse, independently of its solitonic content. This mathematical discovery has changed the widely accepted paradigm of the solitonic nature of rogue waves by enabling the PS to emerge from partially radiative or even completely solitonless initial data. In this work, we realize this scenario in a water tank experiment with a particular aim to control the point of the PS occurrence in space-time by imposing an appropriately chosen initial chirp. By employing the inverse scattering transform for the synthesis of the initial data, we are able to engineer a localized wave packet with a prescribed solitonic and radiative content. This enables us to control the position of the emergence of the rogue wave by adjusting the inverse scattering spectrum. The proposed method of nonlinear spectral engineering is found to be robust to higher-order nonlinear effects, preceding the wave breaking dynamics, that are inevitable in realistic wave propagation conditions.

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Phys. Rev. Fluids 7, 054401– Published 3 May, 2022
  • Received 15 December 2021
  • Accepted 29 March 2022
Article part of CHORUS
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