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, 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.