Short‐Wave Instability in a Three‐Layer Stratified Shear Flow

In inviscid fluid flows instability arises generically due to a resonance between two wave modes. Here, it is shown that the structure of the weakly nonlinear regime depends crucially on whether the modal structures coincide, or remain distinct, at the resonance point, where the wave phase speeds co...

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Bibliographic Details
Published in:Quarterly journal of mechanics and applied mathematics 2001-09, Vol.54 (3), p.375-388
Main Authors: Grimshaw, Roger, Christodoulides, Paul
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Nonhomogeneous flows
Physics
Stratified flows
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Summary:In inviscid fluid flows instability arises generically due to a resonance between two wave modes. Here, it is shown that the structure of the weakly nonlinear regime depends crucially on whether the modal structures coincide, or remain distinct, at the resonance point, where the wave phase speeds coincide. For short waves, the generic model is correspondingly either a nonlinear Klein–Gordon equation for the wave envelope, or a pair of coupled first‐order envelope equations. A specific case, namely a three‐layered stratified shear flow is examined to illustrate this, with a typical derivation.
ISSN:0033-5614
1464-3855
DOI:10.1093/qjmam/54.3.375