Flow Structure Identification of a Turbulent Shear Flow with Use of Wavelet Statistics

In identifying the spatial turbulent structure and its evolution in time, the wavelet autocorrelation analysis, which was proposed by author, was employed to analyze the velocity fluctuations in a plane turbulent jet at various positions with help of the complex wavelet function. The wavelet auto-correlation function can extract the most essential scales governing the self-similarity features of eddy motions in terms of period and time delay, which is lost if using traditional statistics methods. It is found that the wavelet autocorrelation function using the Morlet wavelet illustrates better localization in frequency space than that of the Mexican hat wavelet. From the distribution of wavelet autocorrelation strength and phase, the periodic structure of large period consists of that of small period, in other words, in a periodic motion of large eddy contains the periodic motion of small eddies exist.