Laboratoire Matière et Systèmes Complexes

Video Seminar. Wednesday 30th March.

Coexistence of solitons and extreme events in deep water surface waves.

Annette Cazaubiel Laboratoire Matière et Systèmes Complexes, UMR 7057, Université de Paris

The nonlinear Schrödinger equation (NLSE) is an integrable equation which describes the evolution of weakly nonlinear waves in many different physical systems such as nonlinear optics, plasmas or hydrodynamics. Due to its integrability, the NLSE provides exact solutions for the dynamics of localized structures. Here, we study experimentally, in a large-scale tank, the propagation of unidirectional deep water gravity waves stochastically modulated in phase. We show that a spontaneous formation of coherent localized structures occurs from the initial incoherent waves. We characterize the emergence, the property and the dynamics of these structures immersed in a sea of smaller stochastic waves. Such a coexistence between erratic waves and coherent structures is expected from NLSE integrable turbulence, and has been reported in optics. To our knowledge, this new statistical state predicted by integrable turbulence had never been observed in deep water context, although wave statistics of unidirectional random waves have been extensively reported and compared to NLSE equation.

After a few nonlinear length scales of propagation, we observe the emergence of solitons and extreme events, as well as of a heavy-tailed (distance independent) distribution of the wave field statistics. These results are compatible with integrable turbulence despite unavoidable dissipation in experiments. However, if coherent structures such as envelope solitons or Peregrine solitons are well described by NLSE, the most extreme events deviate from the predictions of the integrable turbulence theory. The experimental wave spectrum is found to be a frequency power-law. This power-law spectrum is not described by NLSE but comes from the specific features of hydrodynamics waves probably related to the random modulation of the harmonics (bound waves) of the carrier wave. Although most of our observations are compatible with the integrable turbulence theory for NLSE, some deviations proper to hydrodynamics such as the occurrence of highly asymmetrical extreme events and the power-law spectrum are highlighted.