Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian TaylorCouette flows

Cari S. Dutcher, Susan J. Muller

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30 Scopus citations

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 spacetime and frequencytime 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* = Re i/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* = [(01.17), > 15.4], states characterized by a single distinct temporal frequency for Re* = [(1.171.41), (3.565.20), (7.8515.4)], states with multiple temporal frequencies for Re* = [(1.413.56), (5.207.85)], 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.

Original languageEnglish (US)
Pages (from-to)85-113
Number of pages29
JournalJournal of Fluid Mechanics
Volume641
DOIs
StatePublished - Dec 2009

Bibliographical note

Funding Information:
The National Science Foundation has supported this work through Grant CTS-0335169. C. S. Dutcher gratefully acknowledges support from the National Science Foundation Graduate Research Fellowship and the American Association of University Women Engineering Dissertation Year Fellowship.

Keywords

  • Instability
  • TaylorCouette flow
  • Transition to turbulence

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