From modulational instability to focusing dam breaks in water waves

TL;DR

This study experimentally demonstrates the formation of focusing dispersive dam break flows in water waves, aligning with semi-classical 1D-NLSE predictions, and highlights a nonlinear modulation mechanism distinct from Benjamin-Feir instability.

Contribution

First experimental observation of dispersive shock wave dynamics in a modulationally unstable water wave system consistent with 1D-NLSE theory.

Findings

Nonlinear wave packets exhibit strong modulation propagating from edges to center.

Experimental results agree quantitatively with semi-classical 1D-NLSE predictions.

Dispersive shock waves observed without disintegration by Benjamin-Feir instability.

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.