Vortex dynamics in evolutive flows: A weakly chaotic phenomenon

We make use of a wavelet method to extract, from experimental velocity signals obtained in an evolutive flow, the dominating velocity components generated by vortex dynamics. We characterize the resulting time series complexity by means of a joint use of data compression and of an entropy diffusion method. We assess that the time series emerging from the wavelet analysis of the vortex dynamics is a weakly chaotic process with a vanishing Kolmogorov-Sinai entropy and a power-law growth of the information content. To reproduce the Fourier spectrum of the experimental signal, we adopt a harmonic dependence on time with a fluctuating frequency, ruled by an inverse power-law distribution of random events. The complexity of these fluctuations is determined by studying the corresponding artificial sequences. We reproduce satisfactorily both spectral and complex properties of the experimental signal by locating the complexity of the fluctuating process at the border between the stationary and the nonstationary states.