Freak waves in crossing sea with counterpropagating wave systems

Abstract

This work presents a theoretical and experimental investigation on the statistical properties of the surface elevation in a special case of crossing sea conditions. The special case considered is the case of two irregular wave trains propagating in opposite directions, with the same characteristic frequency and wave number. The modulational instability of two crossing Stokes waves according to two coupled nonlinear Schrödinger equations describing the problem is investigated. Experiments are performed in the Hydrodynamic Laboratory at the University of Oslo, Blindern. The stability analysis shows that the unstable domain of the perturbation is reduced in the case of a crossing sea compared to a non-crossing sea, at the same time as the growth rates are reduced. Such behaviour is usually interpreted as an indication that the occurrence of extreme events is reduced. Experimental results show that the kurtosis, a measure of the probability of the occurrence of extreme events, is generally lower for crossing sea than non-crossing sea. Results of both the stability analysis and the experiments were in contradiction to the wide-spread mindset that crossing sea is more dangerous than non-crossing sea. The work presented in this thesis has demonstrated the need of further investigation, in order to fully understand the occurrence of freak waves in crossing sea with counterpropagating wave systems.