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

TL;DR

This paper reviews laboratory Couette-Taylor experiments to understand turbulence driven by differential rotation, with implications for astrophysical phenomena like accretion disks and stellar interiors.

Contribution

It demonstrates how laboratory experiments can inform models of astrophysical turbulence, especially in Keplerian-like flows, and proposes a turbulence prescription applicable to stellar and disk environments.

Findings

Turbulence can be sustained by differential rotation with decreasing angular velocity outward.

A gradient Reynolds number criterion predicts the onset of finite amplitude instability.

A turbulence prescription is proposed for astrophysical applications.

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.