Comparing wavelet transform with proper orthogonal decomposition

The wake flow of triangle cylinder was measured by PIV experiment at Reynolds number of 14,440. One dimensional orthogonal wavelet and POD analyses are employed to decompose the fluctuating velocity field into different wavelet components and modes. The reconstructed flow fields are analyzed in terms of fluctuating energy, time frequency distribution, and Reynolds shear stress. It is found that the first two wavelet components and POD modes can give representations to the most energetic large scale structures, contributing about 77% and 73% to the total fluctuating energy respectively. Comparing with the first two wavelet components, the first two POD modes are more appropriate to represent the Karman like vortical structure. The time-frequency characteristics of wavelet components and POD modes suggest that wavelet analysis can be used to extract turbulent structures of different scales and the POD modes are not capable of extracting small scale turbulent structures. Similar with the energy distribution, the most significant contribution to the Reynolds shear stresses comes from the large scale structures that composed of first two wavelet components and POD modes, accounts for 88% and 80% of the measured maximum Reynolds shear stress, respectively.