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December 2007 Instability of marginally stable streamwise varying shear flow to long rossby waves
Daniel Hodyss, Terrence R. Nathan
Commun. Math. Sci. 5(4): 833-849 (December 2007).


The instability of streamwise varying shear flow that is marginally stable to long Rossby waves is examined. Both Hamiltonian and non-Hamiltonian flows are considered within the framework of coupled wave instability (CWI). The CWI is shown to be mediated by a ‘physical’ wave and a ‘virtual’ wave. The physical/virtual wave model concisely describes the differences between the instabilities that develop on locally supercritical flow and those that develop on globally subcritical flow. Globally subcritical Hamiltonian flows are proven to be stable. In contrast, non- Hamiltonian flows may be unstable in both locally supercritical and globally subcritical regimes. In locally supercritical flow, the CWI grows via wave-resonance between the physical/virtual wave pair and is highly localized to the supercritical region. In contrast, in globally subcritical flow, the CWI grows via pseudomomentum extraction from the background flow and either radiates away or remains attached to the streamwise variation in the flow.


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Daniel Hodyss. Terrence R. Nathan. "Instability of marginally stable streamwise varying shear flow to long rossby waves." Commun. Math. Sci. 5 (4) 833 - 849, December 2007.


Published: December 2007
First available in Project Euclid: 3 January 2008

zbMATH: 1218.76013
MathSciNet: MR2375049

Primary: 76B65 , 76E09 , 76E15 , 76E20

Keywords: coupled wave , Linear instability , long Rossby waves , streamwise varying

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 4 • December 2007
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