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A generalized action-angle representation of wave interaction in stratified shear flows

Published online by Cambridge University Press:  17 November 2017

Eyal Heifetz  and
Anirban Guha Open the ORCID record for Anirban Guha [Opens in a new window]
Eyal Heifetz
Affiliation:
Department of Geophysics, School of Earth Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Anirban Guha*
Affiliation:
Mechanical Engineering Department, Indian Institute of Technology Kanpur, U.P. 208016, India
*
†Email address for correspondence: [email protected]
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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’s 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 the phases of the interfacial waves. The term ‘generalized action angle’ aims to emphasize that the action of each wave is generally time dependent and this allows for 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.

JFM classification

Mathematical Foundations: Hamiltonian theory Instability: Instability Wakes/Jets: Shear layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 834 , 10 January 2018 , pp. 220 - 236
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Copyright
© 2017 Cambridge University Press 

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