A generalized action-angle representation of wave interaction in stratified shear flows
Fluid Dynamics
2018-02-14 v2
Abstract
In this paper we express the linearized dynamics of interacting interfacial waves in stratified shear flows in the compact form of action-angle Hamilton equations. The pseudo-energy serves as the Hamiltonian of the system, the action coordinates are the contribution of the interfacial waves to the wave-action, and the angles are their phases. The term "generalized action-angle" aims to emphasize that the action of each wave is generally time dependent and this allows instability. An attempt is made to relate this formalism to the action at a distance resonance instability mechanism between counter-propagating vorticity waves via the global conservations of pseudo-energy and pseudo-momentum.
Cite
@article{arxiv.1703.03032,
title = {A generalized action-angle representation of wave interaction in stratified shear flows},
author = {Eyal Heifetz and Anirban Guha},
journal= {arXiv preprint arXiv:1703.03032},
year = {2018}
}