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Instability of a rotating shear layer in the transonic regime

Published online by Cambridge University Press:  26 April 2006

M. Tomasini ,
N. Dolez  and
J. Léorat
M. Tomasini
Affiliation:
Observatoire Midi-Pyrénées, 14 Avenue E. Belin, 31400 Toulouse, France
N. Dolez
Affiliation:
Observatoire Midi-Pyrénées, 14 Avenue E. Belin, 31400 Toulouse, France
J. Léorat
Affiliation:
Observatoire de Paris-Meudon, DAEC, Place J. Janssen, 92195 Meudon, France
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Abstract

We have studied numerically the stability of a two-dimensional Couette flow in a polytropic fluid subjected to a localized shear, using a pseudo-spectral method (Fourier-Chebyshev). The polytropic index has been chosen equal to 2 and a radial force (pseudo-gravity) is introduced in order to perform comparisons with the shallow water experimental results. When the Reynolds number is not too low, the initial flow which is purely azimuthal becomes unstable and a stable rotating pattern is formed, with a number of azimuthal modes which decreases when the Mach number increases. A qualitative agreement is found with the experimental results, although the spatial resolution constraint strongly limits the numerical Reynolds and Mach numbers. From the variation of the linear growth rate of the unstable modes with the Mach number, we are able to show the transition between a flow subjected to Kelvin-Helmholtz instability towards one essentially driven by a centrifugal instability, which is efficient for rotating supersonic flows if the angular momentum decreases outwards. The latter situation may occur for some flows in astrophysical disks.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 306 , 10 January 1996 , pp. 59 - 82
Copyright
© 1996 Cambridge University Press

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