Astron. Astrophys. 347, 734-738 (1999)

Turbulence in differentially rotating flows

What can be learned from the Couette-Taylor experiment

Denis Richard and Jean-Paul Zahn

Département d'Astrophysique Stellaire et Galactique/CNRS-UMR8633, Observatoire de Paris-Meudon, F-92195 Meudon Cedex, France

Received 25 November 1998 / Accepted 23 March 1999

Abstract

The turbulent transport of angular momentum plays an important role in many astrophysical objects, but its modelization is still far from satisfactory. We discuss here what can be learned from laboratory experiments. We analyze the results obtained by Wendt (1933) and Taylor (1936) on the classical Couette-Taylor flow, in the case where angular momentum increases with distance from the rotation axis, which is the most interesting for astrophysical applications. We show that when the gap between the coaxial cylinders is wide enough, the criterion for the onset of the finite amplitude instability can be expressed in terms of a gradient Reynolds number. Based on Wendt's results, we argue that turbulence may be sustained by differential rotation when the angular velocity decreases outward, as in keplerian flows. From the rotation profiles and the torque measurements we deduce a prescription for the turbulent viscosity which is independent of gap width; with some caution it may be applied to stellar interiors and to accretion disks.

Key words: hydrodynamics instabilities turbulence

Send offprint requests to: D. Richard (Denis.Richard@obspm.fr)

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Contents

• 1. Introduction
• 2. The Couette-Taylor experiment
  • 2.1. Critical parameters and transition to turbulence
  • 2.2. Transport of angular momentum
• 3. Are keplerian flows unstable?
• 4. Discussion
• Acknowledgements
• Appendix A: on Zeldovich's analysis of Taylor's results
• References

© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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