Stability of quasi-Keplerian Shear Flow in a Laboratory Experiment
Authors: Ethan Schartman, Hantao Ji, Michael J. Burin and Jeremy Goodman
Abstract:
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 di erent type of flow than
Keplerian or without quantitative measurements of angular momentum transport and mean flow profile, and
all of them appear to su er from Ekman e ects, secondary flows induced by nonoptimal axial boundary
conditions. Such Ekman e ects 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 e ects. Methods.We perform a local measurement of the azimuthal-radial component of the Reynolds stress tensor
in a novel laboratory apparatus where Ekman e ects are minimized by flexible control of axial boundary
conditions. Results.We find significant Ekman e ects on angular momentum transport due to nonoptimal axial boundary
conditions in quasi-Keplerian flows. With the optimal control of Ekman e ects, 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.
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Submitted to: Astronomy and Astrophysics (December 2010)
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