Wavelet multi-scale analysis of the circular cylinder wake under synthetic jets control

The wavelet method is used to study the multi-scale vortical structures of the flow around a circular cylinder without and with synthetic jet control at Re = 950. The velocity field is decomposed into 9 wavelet components, including one approximation component and 8 detail components. The first component shows the flow characteristics at low frequency. The dominant components represent large-scale vortical structures in the flow and they show similar distributions for the same wake pattern. Other detail components reflect the characteristics of relatively small-scale structures. The individual vortex dynamics underlying the complex flow can be extracted and thus reconstructed by the approximation and dominant components. Thus, we show an effective approach to reveal the flow physics from the complex flow.