Stability of quasi-Keplerian shear flow in a laboratory experiment

¹ Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA
e-mail: hji@pppl.gov
² Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA

Received: 2 December 2010
Accepted: 20 May 2012

Abstract

Context. Subcritical transition to turbulence has been proposed as a source of turbulent viscosity required for the associated angular momentum transport for fast accretion in Keplerian disks. Previously cited laboratory experiments in supporting this hypothesis were performed either in a different type of flow than Keplerian or without quantitative measurements of angular momentum transport and mean flow profile, and all of them appear to suffer from Ekman effects, secondary flows induced by nonoptimal axial boundary conditions. Such Ekman effects are expected to be absent from astronomical disks, which probably have stress-free vertical boundaries unless strongly magnetized.

Aims. To quantify angular momentum transport due to subcritical hydrodynamic turbulence, if exists, in a quasi-Keplerian flow with minimized Ekman effects.

Methods. We perform a local measurement of the azimuthal-radial component of the Reynolds stress tensor in a novel laboratory apparatus where Ekman effects are minimized by flexible control of axial boundary conditions.

Results. We find significant Ekman effects on angular momentum transport due to nonoptimal axial boundary conditions in quasi-Keplerian flows. With the optimal control of Ekman effects, no statistically meaningful angular momentum transport is detected in such flows at Reynolds number up to two millions.

Conclusions. Either a subcritical transition does not occur, or, if a subcritical transition does occur, the associated radial transport of angular momentum in optimized quasi-Keplerian laboratory flows is too small to directly support the hypothesis that subcritical hydrodynamic turbulence is responsible for accretion in astrophysical disks. Possible limitations in applying laboratory results to astrophysical disks due to experimental geometry are discussed.