Wavelet analysis for the plane turbulent jet (analysis of large eddy structure)

In this study, wavelet analysis is applied to velocity signals of a plane turbulent jet, in order to investigate the eddy structure in the dimensions of time and scale. First, a review of the definitions and the basic properties of wavelet analysis are introduced, and a revised form of the Mexican hat and the wavelet power spectrum are proposed. To illustrate some typical behaviors of the wavelet coefficient phase, a numerically generated signal is analyzed. Then from the velocity signals of a jet on the centerline and in the mixing layer, the structural features of the eddy are analyzed in terms of instantaneous frequency and onset time/position. The results reveal that eddies of very different scale and the breakdown of a large eddy are displayed in the wavelet coefficient phase, as well as the successive branchings of a large eddy structure. Furthermore, it is found that the scale of the eddy and intermittency in the mixing layer can be obtained by wavelet analysis. The wavelet power spectra agree fairly well with the Fourier power spectra and just correspond to the actual kinetic energy per unit time at each wave number.