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From modulational instability to focusing dam breaks in water waves

Félicien Bonnefoy1, Alexey Tikan2, François Copie2, Pierre Suret2, Guillaume Ducrozet1, Gaurav Prabhudesai3, Guillaume Michel4, Annette Cazaubiel5, Eric Falcon5 et al.

Gennady El6 and Stéphane Randoux2,*

  • 1École Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France
  • 2Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
  • 3Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Paris, France
  • 4Sorbonne Université, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75 005 Paris, France
  • 5Université de Paris, Université Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
  • 6Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne, NE1 8ST, United Kingdom

  • *stephane.randoux@univ-lille.fr
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Phys. Rev. Fluids 5, 034802 – Published 27 March, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.034802

Abstract

We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a large-scale rectangular barrier. Our experiments reveal that, for a range of initial parameters, the nonlinear wave packet is not disintegrated by the Benjamin-Feir instability but exhibits a specific, strongly nonlinear modulation, which propagates from the edges of the wave packet toward the center with finite speed. Using numerical tools of nonlinear spectral analysis of experimental data, we identify the observed envelope wave structures with focusing dispersive dam break flows, a peculiar type of dispersive shock waves recently described in the framework of the semiclassical limit of the 1D focusing nonlinear Schrödinger equation (1D-NLSE). Our experimental results are shown to be in a good quantitative agreement with the predictions of the semiclassical 1D-NLSE theory. This is the first observation of the persisting dispersive shock wave dynamics in a modulationally unstable water wave system.

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Phys. Rev. Fluids 5, 034802– Published 27 March, 2020
  • Received 4 November 2019
  • Accepted 19 February 2020
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