Dispersion and Modulational Instability in Crossing Waves

Ton van den Bremer

Associate Professor and Royal Academy of Engineering Research Fellow, Department of Engineering Science, University of Oxford

Crossing seas, in which waves travel in multiple directions, have been identified as an important challenge to offshore operations, linked to an increased probability of extreme waves. In addition to specific environmental forcing such as wind or (sudden) changes in bathymetry, two important mechanisms play a role in the formation of so-called rogue waves in the ocean, namely random dispersive focusing enhanced by weak bound-wave nonlinearity and modulational instability. Herein, experimental results obtained in the FloWave Ocean Energy Research Facility at the University of Edinburgh are presented that confirm aspects of the dispersive and unstable behaviour of crossing waves predicted by the 2D+1 nonlinear Schrödinger equation (2D+1NLSE) and the crossing nonlinear Schrödinger equation (CNLSE).