Orthogonal wavelet multi-resolution analysis of a turbulent cylinder wake

Abstract

Previous studies of the organized motion mostly focused on large-scale structures; investigations of other scales have been relatively scarce because of the difficulty of extracting the structures of these scales using conventional vortex-detection techniques. A wavelet multi-resolution technique based on an orthogonal wavelet transform has been applied to analysing the velocity data simultaneously obtained in two orthogonal planes in the turbulent near-wake of a circular cylinder. Using this technique, the flow is decomposed into a number of wavelet components based on their characteristic or central frequencies. The flow structure of each wavelet component is examined in terms of sectional streamlines and vorticity contours. The wavelet component at a central frequency of $f_{0}$, the same as the vortex-shedding frequency, exhibits the characteristics of the Kármán vortices, thus providing a validation of the analysis technique. The spanwise vorticity contours of the wavelet component at $f_{0}$ display a secondary spanwise structure near the saddle point, whose vorticity is opposite-signed to that of the Kármán vortices. This structure is observed for the first time and its occurrence is consistent with the streamwise decay in the vorticity strength of the spanwise structures. Two-point velocity correlations of wavelet components in the lateral and spanwise directions and the wavelet auto-correlation function indicate that the wavelet components of $f_{0}$ and 2$f_{0}$ are relatively large-scale and organized, displaying considerable two-dimensionality. The component of 4$f_{0}$ is significantly less organized and highly three-dimensional, as indicated by much smaller spanwise correlation coefficients. The components at frequencies of 8$f_{0}$ and higher have virtually zero correlation coefficients.