ORCID
- Stuhlmeier, Raphael: 0000-0002-6568-1543
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.
DOI
10.1016/j.euromechflu.2023.06.008
Publication Date
2023-09-01
Publication Title
European Journal of Mechanics - B/Fluids
Volume
101
ISSN
0997-7546
Embargo Period
2023-08-02
Organisational Unit
School of Engineering, Computing and Mathematics
First Page
320
Last Page
336
Recommended Citation
Andrade, D., & Stuhlmeier, R. (2023) 'Instability of waves in deep water — A discrete Hamiltonian approach', European Journal of Mechanics - B/Fluids, 101, pp. 320-336. Available at: https://doi.org/10.1016/j.euromechflu.2023.06.008
