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

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.