Emergence of Peregrine solitons in integrable turbulence of deep water gravity waves

We study experimentally the early stages of integrable turbulence of unidirectional deep water gravity waves. By generating partially coherent waves in a 148 m long wave flume, we observe the emergence of high-amplitude structures formed by nonlinear focusing, commonly referred to as rogue waves. This work confronts the experiment with two recent results obtained in the framework of the nonlinear Schrodinger equation (NLSE), namely that (i) these structures can be locally fitted by a Peregrine soliton and (ii) their emergence leaves a visible trace on the evolution of statistical parameters such as kurtosis. Although Peregrine solitons have been observed for almost ten years in experiments using a deterministic forcing, we report their first systematic study in hydrodynamics with a random forcing. We show that (i) yields accurate results as long as the wave steepness remains moderate, whereas (ii) is very robust and remains valid beyond the assumption of integrability. Numerical simulations of the NLSE and of the fully nonlinear dynamical equations are also performed to support these results.