Evolution of statistically inhomogeneous degenerate water wave quartets | Zendy

Raphael Stuhlmeier | Zendy; Michael Stiassnie | Zendy

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Evolution of statistically inhomogeneous degenerate water wave quartets

Author(s) -

Raphael Stuhlmeier,

Michael Stiassnie

Publication year - 2017

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2017.0101

Subject(s) - degenerate energy levels , statistical physics , physics , mathematics , theoretical physics , quantum mechanics

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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