Wavelet auto-correlation analysis applied to eddy structure identification of free turbulent shear flow

To investigate the eddy structure of turbulent hear flow in both physical-space and Fourier-space, a new combination of conventional techniques of signal processing called wavelet auto-correlation analysis, has been developed based on wavelet transform. The wavelet auto-correlation analysis provides the unique capability for describing the auto-correlation characteristics of arbitrary signals in terms of period and time delay. The wavelet auto-correlation technique was used to analyze the fluctuating velocities at various positions in a plane turbulent jet. It was found that the peaks of WR(a, tau) in the high period region correspond to the large peaks of R(tau), and the peaks of WR(a, tau) in the low period region are equivalent to the small peaks of R(tau). The branching structures in WR(a, tau) reveal that a periodic large eddy motion contains the periodic small eddy motions. In the shear layer at x/d=10, the periodic eddy motions with a=15, 40, 75, 100 and 150 ms are clearly observed.