Competition between axisymmetric and three-dimensional patterns between exactly counter-rotating disks

The bifurcations and the nonlinear dynamics of the von Kármán swirling flow between exactly counter-rotating disks in a stationary cylinder are numerically and experimentally investigated. The dynamics are governed by two parameters, the radius-to-height ratio A = R ∕ H and the Reynolds number, Re,...

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Bibliographic Details
Published in:Physics of fluids (1994) 2006-05, Vol.18 (5), p.054102-054102-12
Main Authors: Nore, C., Martin Witkowski, L., Foucault, E., Pécheux, J., Daube, O., Le Quéré, P.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fluid mechanics
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Mechanics
Nonlinearity (including bifurcation theory)
Physics
Rotational flow and vorticity
Vortex dynamics
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Summary:The bifurcations and the nonlinear dynamics of the von Kármán swirling flow between exactly counter-rotating disks in a stationary cylinder are numerically and experimentally investigated. The dynamics are governed by two parameters, the radius-to-height ratio A = R ∕ H and the Reynolds number, Re, based on disk rotation speed and cylinder height. The stability analysis performed for 2 ⩽ A ⩽ 20 shows that nonaxisymmetric and axisymmetric modes can be stationary or time dependent in this range. Three-dimensional modes are dominant for A ⩽ 13.25 while axisymmetric modes are critical for A > 13.25 . The patterns of the dominant perturbations are analyzed. In the particular case of A = 15 , nonlinear computations are performed at Reynolds numbers slightly above threshold and are compared to experimental results, showing the competition between axisymmetric and three-dimensional modes.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.2196090