Special Session 48: 

Drifting modulation instability dynamics

Amin Chabchoub
The University of Sydney
Australia
Co-Author(s):    Norbert Hoffmann, Takuji Waseda and Nail Akhmediev
Abstract:
One possible mechanism to explain the formation of extreme nonlinear waves in uni-directional and narrow-banded seas is the modulation instability (MI). The classical MI process in physical space is characterized by the emergence of extreme periodic water wave groups, that can reach substantial wave heights, when initially slightly perturbing periodically a regular Stokes wave train. The MI can be triggered in the Fourier domain, when side-bands around the main frequency are excited and subsequently, follow an exponential growth. We present an experimental study on MI wave groups that propagate with a velocity that is higher than the group velocity within the context of exact Akhmediev breather solutions of the nonlinear Schroedinger equation (NLSE). It is shown that when this additional velocity to the wave groups is small, a good agreement with NLSE is reached. Otherwise, a significant deviation is observed. The latter could be explained when the water wave modelling accuracy exceeds the NLSE limitations.