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 2f 0 are relatively large-scale and organized, displaying considerable two-dimensionality. The component of 4f 0 is significantly less organized and highly three-dimensional, as indicated by much smaller spanwise correlation coefficients. The components at frequencies of 8f 0 and higher have virtually zero correlation coefficients.

Identification of large coherent structures in supersonic axisymmetric wakes

“…Most methods are based on Fourier transforms, e.g. band-pass/band-reject filters (for examples see the review of Bonnet & Delville [28]) and decomposition of the flow field based upon a wavelet analysis ( [29,30]). …”

Strouhal numbers, forces and flow structures around two tandem cylinders of different diameters

“…While W 2 ðs; bÞ ¼ W R 2 ðs; bÞ þ W I 2 ðs; bÞ provides the information on the frequency domain of a signal, W R (s, b) is important to identify the minima and maxima of a signal with regard to frequency (Farge, 1992). The choice of appropriate mother wavelet depends on the information we need to extract from the signal (Rinoshika and Zhou, 2005b). For example, information extracted using the Mexican hat wavelet is highly localized in the time domain and poorly localized in the frequency domain.…”

Wavelet analysis of unsteady flows: Application on the determination of the Strouhal number of the transient wake behind a single cylinder

“…For the interpretation of switching flows, wavelet analysis in addition to Fourier analysis was used [19,20]. Wavelet transforms were also used to study the vorticity structure in the far wake downstream of a cylinder [21,22], transient phenomena in tube banks [23] and the bistable flows in tube banks [24].…”