Communications in Mathematical Sciences

Volume 5 (2007)

Number 4

Instability of marginally stable streamwise varying shear flow to long rossby waves

Pages: 833 – 849



Daniel Hodyss

Terrence R. Nathan


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.


linear instability; coupled wave; long Rossby waves; streamwise varying

2010 Mathematics Subject Classification

76B65, 76E09, 76E15, 76E20

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