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Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flows

Published online by Cambridge University Press:  17 November 2009

CARI S. DUTCHER  and
SUSAN J. MULLER
CARI S. DUTCHER
Affiliation:
Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 94720, USA
SUSAN J. MULLER*
Affiliation:
Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 94720, USA
*
†Email address for correspondence: [email protected]
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Abstract

Spatial and temporal frequency dynamics were experimentally tracked via flow visualization for Newtonian fluids as a function of the inner cylinder Reynolds number (Rei) in the flow between concentric, independently rotating cylinders with a radius ratio of 0.912 and an aspect ratio of 60.7. Eight transitions from laminar to turbulent flow were characterized in detail for a stationary outer cylinder, producing highly resolved space–time and frequency–time plots for wavy, modulated and weakly turbulent states. A previously unreported early-modulated wavy vortex flow was found in our high aspect ratio geometry both with and without the presence of a dislocation. The envelope of stability for this flow state was shown to cross into the co-rotating regime, and is present up to Reo ~ 60, where Reo is the outer cylinder Reynolds number. This early modulation is independent of acceleration in the range 0.18 < dRei/dτ < 2.9, where τ is the time nondimensionalized with a viscous time scale. While many of the flow states have been previously observed in geometries with somewhat different radius ratios, we provide new characterization of transitional structures for Reo = 0 in the range 0 < Re* < 21.4, where Re* = Rei/Rec and Rec is the value of Rei at the primary instability. Special attention has been given to ramp rate. For quasi-static ramps, axisymmetric states are stable over the ranges of Re* = [(0–1.17), > 15.4], states characterized by a single distinct temporal frequency for Re* = [(1.17–1.41), (3.56–5.20), (7.85–15.4)], states with multiple temporal frequencies for Re* = [(1.41–3.56), (5.20–7.85)], and a transition from laminar to weakly turbulent vortices occurs at Re* = 5.49. All flow states are characterized by symmetry/symmetry-breaking features as well as azimuthal and axial wavenumbers.

JFM classification

Instability: Instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 85 - 113
Copyright
Copyright © Cambridge University Press 2009

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