Competition between axisymmetric and three-dimensional patterns between exactly counter-rotating disks
Résumé
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. © 2006 American Institute of Physics.