Instability of waves in deep water — A discrete Hamiltonian approach

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...

Full description

Saved in:
Bibliographic Details
Published in:European journal of mechanics, B, Fluids B, Fluids, 2023-09, Vol.101, p.320-336
Main Authors: Andrade, David, Stuhlmeier, Raphael
Format: Article
Language:English
Subjects:
Hamiltonian systems
Instability
Water waves
Wave–wave interaction
Weakly-nonlinear surface waves
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0997-7546
DOI:10.1016/j.euromechflu.2023.06.008