From modulational instability to focusing dam breaks in water waves

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 wavepacket towards 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 semi-classical limit of the 1D focusing nonlinear Schrodinger equation (1D-NLSE). Our experimental results are shown to be in a good quantitative agreement with the predictions of the semi-classical 1D-NLSE theory. This is the first observation of the persisting dispersive shock wave dynamics in a modulationally unstable water wave system.

arXiv comment7 figures

References in corpus (23)

• Formation and Propagation of Matter Wave Soliton Trains
• Instabilities, breathers and rogue waves in optics
• Dispersive shock waves and modulation theory
• Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams
• On the nonlinear stage of Modulation Instability
• Direct observation of Rogue Waves in optical turbulence using Time Microscopy
• Optical Rogue Waves in integrable turbulence
• Integrable turbulence and formation of rogue waves
• Universal nature of the nonlinear stage of modulational instability
• Universal Peregrine soliton structure in nonlinear pulse compression in optical fiber
• Modulation Instability Induced Frequency Comb Generation in a Continuously Pumped Optical Parametric Oscillator
• Universal nonlinear stage of the locally induced modulational instability in fiber optics
• Dispersive dam-break flow of a photon fluid
• Statistical properties of nonlinear stage of modulation instability in fiber optics
• Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves
• Hydrodynamic Supercontinuum
• Integrable turbulence generated from modulational instability of cnoidal waves
• Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments
• Topological Control of Extreme Waves
• Riemann problems and dispersive shocks in self-focusing media
• Auto-modulation versus breathers in the nonlinear stage of modulational instability
• Optical Random Riemann Waves in Integrable Turbulence
• Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach

Cited by in corpus (7)

• Theory of neuromorphic computing by waves: machine learning by rogue waves, dispersive shocks, and solitons
• Nonlinear spectral synthesis of soliton gas in deep-water surface gravity waves
• Prediction and manipulation of hydrodynamic rogue waves via nonlinear spectral engineering
• Experimental study of integrable turbulence in shallow water
• From rogue waves to solitons
• Solitons in a box-shaped wavefield with noise: perturbation theory and statistics
• Nonlinear stage of modulational instability in repulsive two-component Bose-Einstein condensates