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The strato-rotational instability of Taylor–Couette and Keplerian flows

Published online by Cambridge University Press:  23 August 2010

S. LE DIZÈS  and
X. RIEDINGER
S. LE DIZÈS*
Affiliation:
IRPHE, UMR 6594 CNRS, 49 rue F. Joliot Curie, F-13013 Marseille, France
X. RIEDINGER
Affiliation:
IRPHE, UMR 6594 CNRS, 49 rue F. Joliot Curie, F-13013 Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

The linear inviscid stability of two families of centrifugally stable rotating flows in a stably stratified fluid of constant Brunt–Väisälä frequency N is analysed by using numerical and asymptotic methods. Both Taylor–Couette and Keplerian angular velocity profiles ΩTC = (1 − μ)/r2 + μ and ΩK = (1 − λ)/r2 + λ/r3/2 are considered between r = 1 (inner boundary) and r = d > 1 (outer boundary, or without boundary if d = ∞). The stability properties are obtained for flow parameters λ and μ ranging from 0 to +∞, and different values of d and N. The effect of the gap size is analysed first. By considering the potential flow (λ = μ = 0), we show how the instability associated with a mechanism of resonance for finite-gap changes into a radiative instability when d → ∞. Numerical results are compared with large axial wavenumber results and a very good agreement is obtained. For infinite gap (d = ∞), we show that the most unstable modes are obtained for large values of the azimuthal wavenumber for all λ and μ. We demonstrate that their properties can be captured by performing a local analysis near the inner cylinder in the limit of both large azimuthal and axial wavenumbers. The effect of the stratification is also analysed. We show that decreasing N is stabilizing. An asymptotic analysis for small N is also performed and shown to capture the properties of the most unstable mode of the potential flow in this limit.

JFM classification

Geophysical and Geological Flows: Stratified flows Vortex Flows: Vortex instability Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 660 , 10 October 2010 , pp. 147 - 161
Copyright
Copyright © Cambridge University Press 2010

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