Poincaré Section Analysis of an Experimental Frequency Intermittency in an Open Cavity Flow

Open flows over a cavity present, even at medium Reynolds number, sustained oscillations resulting from a complex feedback process [1]. Previous works have reveals a mode-switching phenomenon which remains to characterize from a dynamical point of view. In the configuration here investigated, the intermittency between the two dominant modes is characterized using a symbolic dynamics based approach. The first step of the procedure is to reconstruct the phase space from the time series measured by the Laser Doppler Velocimetry (LDV) technique, using the principal components. We show that the quite high dimensionality of the reconstructed space (d < 10), can be overcome by using a Poincaré section of the 2D projection of the phase portrait. The key step consists of a partition of the Poincaré section (the set of intersections of the trajectory in the reconstructed phase space with a transverse plane). The two modes are thus label led 0 and 1, respectively. The partition is based on an angular map, itself based on a first-return map to the Poincaré section. This partition allows, without any arbitrary thresholding (as spectral based modes separation method needs), a very precise quantification of all oscillating events.