Instability of waves in deep water — A discrete Hamiltonian approach

David Andrade, Raphael Stuhlmeier

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The stability of waves in deep water has classically been approached via linear stability analysis, with various model equations, such as the nonlinear Schrödinger equation, serving as points of departure. Some of the most well-studied instabilities involve the interaction of four waves – so called Type I instabilities – or five waves – Type II instabilities. A unified description of four and five wave interaction can be provided by the reduced Hamiltonian derived by Krasitskii (1994). Exploiting additional conservation laws, the discretised Hamiltonian may be used to shed light on these four and five wave instabilities without restrictions on spectral bandwidth. We derive equivalent autonomous, planar dynamical systems which allow for straightforward insight into the emergence of instability and the long time dynamics. They also yield new steady-state solutions, as well as discrete breathers associated with heteroclinic orbits in the phase space.

Original languageEnglish (US)
Pages (from-to)320-336
Number of pages17
JournalEuropean Journal of Mechanics, B/Fluids
Volume101
DOIs
StatePublished - Sep 1 2023

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • General Physics and Astronomy

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