Subcritical transition and spiral turbulence in circular Couette flow

Abstract

We present new observations of a controlled transition to turbulence in a fundamental but little-studied regime: circular Couette flow with only the outer cylinder rotating. Our apparatus consists of an outer cylinder of fixed radius and three inner cylinders having different radii that are used interchangeably to study the effect of flow curvature. With the smallest inner cylinder the end-cap configuration (vertical boundary conditions) may also be varied. The turbulent transition is found to be sensitive to both gap width and end-cap configuration, with wider gaps transitioning at higher rotation rates. All configurations are observed to transition with hysteresis and intermittency. A laser Doppler velocimetry (LDV)-based study of the azimuthal velocity profile as a function of gap width and rotation rate reveals that turbulence, once initiated, is confined to regions of significant shear. For wider gap widths, the radial location of these shear layers is determined by the chosen end-cap configuration. This, in turn, affects the transition Reynolds number, which we posit to be radially dependent. The narrow-gap case in particular features spiral turbulence, whose properties are found to be similar to observations of the phenomenon in related shear flows. The velocity profile in this case is correlated with overlapping boundary layers, suggesting a coupling mechanism for the origin of laminar-turbulent banding phenomena.

Subcritical excitation of the current-driven Tayler instability by super-rotation

“…rotation laws with dΩ /dR > 0, which are linearly stable in the hydrodynamic regime 5,6 . The nonlinear behavior is less clear as some Taylor-Couette experiments have shown instability in this regime 7,8 . Superrotation cannot be destabilized by the standard magnetorotational instability with axial external fields.…”

Subcritical instability of finite circular Couette flow with stationary inner cylinder

“…It would be interesting to explore at what rotation rate of the inner cylinder the instability type switches between the two and how the competition between the two instabilities plays out. Moreover, what is yet to be computed in the present problem is the nonlinear attractor for Re above critical, which from experimental observations (Burin & Czarnocki 2012) is turbulent and presents considerable challenges for direct numerical simulations of the complete system.…”

“…The onset of turbulence in those early experiments were for Reynolds numbers of order 10 5 . Much more recent experiments utilizing both visualization and velocimetry also report subcritical transition to turbulence for Reynolds numbers of the same order in the wide-gap regime, as well as a considerable hysteresis range in Reynolds number between the laminar and turbulent states (Burin & Czarnocki 2012). Other recent experiments with a stationary inner cylinder focused on the fate of the turbulent states at the low-Reynolds-number end of the hysteresis region, where the Reynolds number is of order 10 3 -10 4 (Borrero-Echeverry, Schatz & Tagg 2010).…”

“…Studies of flows in this Rayleigh-stable (centrifugally stable) regime have been motivated by the question of whether hydrodynamic turbulence is important in the dynamics of accretion disks. The issue remains controversial, and it is clear that the finite length of the experimental apparatus and the endwall boundary conditions play major roles in the transition to turbulence (Avila et al 2008;Avila 2012;Burin & Czarnocki 2012). The case where the inner cylinder is stationary does not strictly fall within the abovementioned quasi-Keplerian regime, and has not been investigated as thoroughly as those that more closely mimic the angular momentum distribution of accretion disks.…”

A novel subcritical transition to turbulence in Taylor–Couette flow with counter-rotating cylinders

“…The subcritical transition to turbulence in TCF has a long history (Couette 1890;Mallock 1896;Wendt 1933;Taylor 1936a,b;Schultz-Grunow 1959;Coles 1965;Van Atta 1966;Andereck et al 1986;Prigent & Dauchot 2005). Recently, there has been renewed interest in this regime as a testbed for ideas explaining the subcritical transition to turbulence from the viewpoint of dynamical systems theory (Meseguer et al 2009a;Borrero-Echeverry et al 2010;Avila & Hof 2013;Maretzke et al 2014;Lopez 2016) and as a model for understanding the source of the enhanced angular momentum transport observed in astrophysical disks, which is purportedly caused by turbulence despite the predicted stability of these flows (Richard & Zahn 1999;Ji et al 2006;Paoletti & Lathrop 2011;Burin & Czarnocki 2012;Edlund & Ji 2014). In these studies, which were mostly conducted with Γ 1, transition is typically observed to take place directly from the laminar base flow.…”