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Mode competition in modulated Taylor–Couette flow

Published online by Cambridge University Press:  25 April 2008

M. AVILA ,
M. J. BELISLE ,
J. M. LOPEZ ,
F. MARQUES  and
W. S. SARIC
M. AVILA
Affiliation:
Departament de Física Aplicada, Univ. Politècnica de Catalunya, Barcelona 08034, Spain
M. J. BELISLE
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 5287, USA
J. M. LOPEZ
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
F. MARQUES
Affiliation:
Departament de Física Aplicada, Univ. Politècnica de Catalunya, Barcelona 08034, Spain
W. S. SARIC
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
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Abstract

The effects of harmonically oscillating the inner cylinder about a zero mean rotation in a Taylor–Couette flow are investigated experimentally and numerically. The resulting time-modulated circular Couette flow possesses a Z2 spatio-temporal symmetry which gives rise to two distinct modulated Taylor vortex flows. These flows are initiated at synchronous bifurcations, have the same spatial symmetries, but are characterized by different spatio-temporal symmetries and axial wavenumber. Mode competition between these two states has been investigated in the region where they bifurcate simultaneously. In the idealized numerical model, the two flows have been found to coexist and be stable in a narrow region of parameter space. However, in the physical experiment, neither state has been observed in the coexistence region. Instead, we observe noise-sustained flows with irregular time-dependent axial wavenumber. Movies are available with the online version of the paper.

JFM classification

Geophysical and Geological Flows: Rotating flows Instability: Parametric instability Nonlinear Dynamical Systems: Bifurcation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 601 , 25 April 2008 , pp. 381 - 406
Copyright
Copyright © Cambridge University Press 2008

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References

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Avila et al. supplementary movies

Movie 1 Numerical simulation of type B (non-reversing) Taylor vortex flow between two concentric cylinders. The outer cylinder (right boundary) is held stationary whereas the inner cylinder (left boundary) rotates harmonically about a zero-mean with Re(t)=Rea sin(ωt). Centrifugal instability is triggered every half-period and results in synchronous secondary Taylor vortex flows. In the high-frequency regime shown in this movie, this instability is manifested by angular momentum jets erupting from the inner cylinder at a fixed axial location. Angular momentum (ωθ) and azimuthal vorticity (rvθ) are shown in a meridional cross-section at ω=6.1 and Rea=240. Red (blue) corresponds to positive (negative) values. The wavenumber of the axially periodic pattern is kB=3.4. The movie corresponds to figure 8 in the paper.

Download Avila et al. supplementary movies(Video)
Video 9.2 MB

Avila et al. supplementary movies

Movie 2 Numerical simulation of type A (reversing) Taylor vortex flow at ω=1 and Rea=240 with wavenumber kA=3.0. In the low-frequency regime shown in this movie, the angular momentum jets shift their locations by half the wavelength of the pattern when the inner cylinder reverses its direction of rotation. Angular momentum and azimuthal vorticity are shown in a meridional cross-section. Red (blue) corresponds to positive (negative) values. The movie corresponds to figure 10 in the paper.

Download Avila et al. supplementary movies(Video)
Video 3.3 MB