Stability of quasi-Keplerian shear flow in a laboratory experiment

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 quasiKeplerian 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.

Angular momentum transport and turbulence in laboratory models of Keplerian flows

“…This is somewhat surprising given that quasi-Keplerian flow profiles are linearly stable while the maximum accretion rate occurs when the cylinders counter-rotate, which produces destabilizing shear that dominates the dynamics. This result is in stark contrast to the results presented by Ji et al (2006) and Schartman et al (2012), where β P was measured to be an order of magnitude smaller, specifically β P = 7 × 10 −7 . Thus, they concluded that hydrodynamics alone cannot efficiently transport angular momentum in quasi-Keplerian flows.…”

“…Furthermore, when Ekman circulation is not minimized their measured values of β for quasi-Keplerian flows are approximately half of the typical values presented here. Thus, Schartman et al (2012) argue that our larger values of β are the result of Ekman circulation that is present in other experiments, but is minimized in their apparatus.…”

“…Schartman et al (2012) state that these incompatible results are caused by differing interpretations of finite-size effects, namely Ekman circulation produced by the axial boundaries. In the Princeton experiments (Ji et al 2006;Schartman et al 2009;Burin et al 2010;Schartman et al 2012) the aspect ratio is small (Γ ≈ 2) and therefore finite-size effects would likely dominate. To minimize Ekman circulation, their axial boundaries are split into pairs of rings that can independently rotate with respect to the cylinders.…”

“…The torque is measured over the middle part of the inner cylinder of height L mid = 53.6 cm to minimize the influence of the endplates (similar to Lathrop et al 1992b,a). The torque is measured by a load cell imbedded inside the middle section of the inner cylinder in both the Twente and Maryland experiments, in contrast to measuring the torque on the drive shaft that would be affected by mechanical seals in the end plates or by velocimetry measurements, as in the Princeton experiments (Ji et al 2006;Schartman et al 2009;Burin et al 2010;Schartman et al 2012). …”

Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

“…From the experimental measurement of the torques acting on the cylinders Paoletti & Lathrop (2011) found that efficient angular momentum transport would be possible in accretion disks for purely hydrodynamical reasons; this is in contradiction with experiments conducted by Ji et al (2006) who demonstrated that the required turbulence level could not be achieved in their apparatus. There is still no consensus on this issue despite subsequent complementary experimental runs (Paoletti et al 2012;Schartman et al 2012). As yet, no studies of Taylor-Couette flows motivated by astrophysical problems have considered the effects of compressibility, despite the fact that accretion disk flows have high Mach numbers.…”