A hybrid two-dimensional orthogonal wavelet multiresolution and proper orthogonal decomposition technique for the analysis of turbulent wake flow

Abstract

A hybrid two-dimensional orthogonal wavelet multiresolution and proper orthogonal decomposition technique is developed to analyze the wake flow behind a semi cylinder. The two-dimensional orthogonal wavelet analysis is first applied to decompose the measured velocity fields into four wavelet components based on their spatial scales. Then the extracted multi-scale structures are further investigated based on proper orthogonal decomposition. The modal energy distributions of multi-scale flow structures suggest that the dominance of first two POD modes is reduced and the relative energy becomes more distributed as the flow structure changes from large-scale to small-scale. The first two POD modes of intermediate-scale structure also appear in a mode pair and they are related to secondary resonance accompanied with large-scale flow oscillation. The POD mode 3 of intermediate-scale structure suggest the existence of symmetric vortex shedding pattern. The first two POD modes of small-scale structure also display a symmetrically distributed vortex pair and the distance between adjacent vortices is about half of the case of mode 3 of intermediate-scale structure. The PSD distributions of POD modes of multi-scale structures suggest that the bandwidth of PSD becomes less concentrated as the flow structure varies from large-scale to small-scale. Distinctive flow patterns associated with first and second order harmonics of fundamental flow oscillation can be successfully extracted from the dominating POD modes of intermediate-scale and small-scale structures. The proposed hybrid technique provides a tool for relate the most energetic flow events over a period of time with multi-scale structures cascaded in the turbulence flow.