Turbulence in differentially rotating flows - What can be learned from theCouette-Taylor experiment

The turbulent transport of angular momentum plays an important role in many astrophysical. objects, but its modelization is still far from satisfactor y. We discuss here what can be learned from laboratory experiments. We anal yze the results obtained by Wendt (1933) and Taylor (1936) on the classical Couette-Taylor flow, in the case where angular momentum increases with dis tance from the rotation axis, which is the most interesting for astrophysic al applications. We show that when the gap between the coaxial cylinders is wide enough, the criterion for the onset of the finite amplitude instabili ty can be expressed in terms of a gradient Reynolds number. Based on Wendt' s results, we argue that turbulence may be sustained by differential rotati on 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 c aution it may be applied to stellar interiors and to accretion disks.