Observation of near-heteroclinic cycles in the von Karman flow

The bifurcations and the nonlinear dynamics of the von K\'arm\'an swirling flow between exactly counter-rotating disks in a stationary cylinder are experimentally investigated by means of visualizations and particle image velocimetry. A regime diagram of the different flow states is determined as a function of the height-to-radius ratio $\Gamma$ and the Reynolds number $Re$ based on disks rotation speed and cylinder radius. Among the steady and time-dependent states found in the experiment, robust near-heteroclinic cycles, that link two unstable states of azimuthal wavenumber $m=2$, are observed and characterized in detail for $\Gamma = 2$. These are compared with the numerical findings of Nore et al [{\it J. Fluid Mech} {\bf 477}, 51 (2003)], with a particular emphasis on the influence of the imperfection and the noise of the experimental setup.