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Aspect-ratio dependence of transient Taylor vortices close to threshold

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Abstract

We perform a detailed numerical study of transient Taylor vortices arising from the instability of cylindrical Couette flow with the exterior cylinder at rest for radius ratio η = 0.5 and variable aspect ratio Γ. The result of Abshagen et al. (J Fluid Mech 476:335–343, 2003) that onset transients apparently evolve on a much smaller time–scale than decay transients is recovered. It is shown to be an artefact of time scale estimations based on the Stuart–Landau amplitude equation which assumes frozen space dependence while full space–time dependence embedded in the Ginzburg–Landau formalism needs to be taken into account to understand transients already at moderate aspect ratio. Sub-critical pattern induction is shown to explain the apparently anomalous behaviour of the system at onset while decay follows the Stuart–Landau prediction more closely. The dependence of time scales on boundary effects is studied for a wide range of aspect ratios, including non-integer ones, showing general agreement with the Ginzburg–Landau picture able to account for solutions modulated by Ekman pumping at the disks bounding the cylinders.

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Authors and Affiliations

  1. Laboratoire d’Hydrodynamique, École Polytechnique, Palaiseau, France

    Paul Manneville

  2. M2P2, UMR 6181 CNRS, Universités d’Aix-Marseille, I.M.T. La Jetée, Technopôle de Château-Gombert, 13451, Marseilles Cedex 20, France

    Olivier Czarny

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  1. Paul Manneville
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  2. Olivier Czarny
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Correspondence to Paul Manneville.

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Communicated by P. Hall

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Manneville, P., Czarny, O. Aspect-ratio dependence of transient Taylor vortices close to threshold. Theor. Comput. Fluid Dyn. 23, 15–36 (2009). https://doi.org/10.1007/s00162-009-0093-x

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  • DOI: https://doi.org/10.1007/s00162-009-0093-x

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