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

1. Introduction

Differential rotation is observed in various astrophysical objects, from planets to galaxies, and one suspects that it gives rise to turbulence, since shear flows are liable to hydrodynamical and MHD instabilities. When these instabilities are of the linear type, they are relatively easy to study by perturbing slightly the equilibrium state. But some of them occur only at finite amplitude, in which case the answer must be sought in computer simulations or laboratory experiments, with their inherent limitations.

There has been some debate recently on whether a keplerian disk, which is linearily stable (Rayleigh 1916), may be unstable to finite amplitude perturbations. It may look as if this question presents little interest, since it has been proved that a very weak magnetic field suffices to render such a disk linearly unstable (Chandrasekhar 1960; Balbus and Hawley 1991). However the properties of angular momentum transport depend sensitively on which instability dominates in the considered regime, and a finite amplitude instability can overpower the linear instability which is the first to occur, as the relevant control parameter increases. One example is the Couette-Taylor flow, with the outer cylinder at rest and the inner cylinder rotating with angular velocity . When is increased, the transport of angular momentum first scales as , but thereafter it varies as , once the flow has become fully turbulent (Taylor 1936), as if the initial linear instability were superseded by a stronger shear instability (see also Lathrop et al. 1992). By extrapolating the law to high one would clearly underestimate the transport.

In the present article, we take as working assumption that any differentially rotating flow experiences, at high Reynolds number, the turbulent regime observed in the Couette-Taylor (CT) experiment, and that this turbulence will then transport angular momentum in the same way as in that experiment. The CT flow has been chosen as reference because it is the simplest flow to realize in the laboratory, with both shear and rotation that can be varied independently. We examine whether the experimental data suggest a prescription for the angular momentum transport, which may be used to model astrophysical objects. A similar approach has been taken by Zeldovich (1981), but our conclusions will differ from his (see Appendix).

© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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