Experimental observation of near-heteroclinic cycles in the von Kármán swirling flow

Abstract

The bifurcations and the nonlinear dynamics of the von Kármán swirling flow between exactly counterrotating 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 Γ 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, which link two unstable states of azimuthal wavenumber m=2, are observed and characterized in detail for Γ=2. These are compared with the numerical findings of Nore ["The 1:2 mode interaction in exactly counter-rotating von Kármán swirling flow," J. Fluid Mech 477, 51 (2003)], with a particular emphasis on the influence of the imperfection and the noise of the experimental setup. © 2005 American Institute of Physics.