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Evolution of statistically inhomogeneous degenerate water wave quartets
1Faculty of Civil and Environmental Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel raphaels@technion.ac.il.
Abstract:
A discretized equation for the evolution of random surface wave fields on deep water is derived from Zakharov's equation, allowing for a general treatment of the stability and long-time behaviour of broad-banded sea states. It is investigated for the simple case of degenerate four-wave interaction, and the instability of statistically homogeneous states to small inhomogeneous disturbances is demonstrated. Furthermore, the long-time evolution is studied for several cases and shown to lead to a complex spatio-temporal energy distribution. The possible impact of this evolution on the statistics of freak wave occurrence is explored.This article is part of the theme issue 'Nonlinear water waves'.
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