Wavelet-based phase average on the multi-scale wake structures of square cylinder

Abstract

Phase-average technique based on wavelet multi-resolution analysis and continuous wavelet transform are used to reveal the phase-averaged features of square cylinder wake measured by high-speed PIV. The one-dimensional orthogonal wavelet analysis is first applied to decompose the measured velocity fields into large-, intermediate- and small-scale structures. Then the phase information referenced with large- and intermediate-scale flow structures are clearly identified based on Morlet wavelet transform. Finally, the data ensembles are phase-sorted to give phase-averaged representations of measured flow field. The instantaneous multi-scale structures suggest that large-scale vortices are weakened and begin to transfer into intermediate-vortices at the downstream of separation region. The intermediate-scale vortex observed at the upper boundary of shear layer is considered to be associated with the secondary vortex movement. The phase-averaged intermediate-scale structures tend to convey downstream along streamwise direction, with the rotation sense varying from the first half period to the last half period. The peaks of phase-averaged large-scale Reynolds stress tend to move back and forth in the near-wake region. These findings suggest that the proposed phase-average technique is effective in revealing multi-scale fluid dynamics of wake flow structures.