Abstract
A new auto-correlation, which is called a wavelet auto-correlation and expresses the statistical auto-correlation of any signal in terms of scale and time delay, is proposed and its main properties are also presented. As the practical application to fluid mechanics, wavelet auto-correlation is employed to analyze the velocity signals of the plane turbulent jet. From the distributions of wavelet auto-correlation coefficient, the similar structures of motions with various scales are observed instantaneously, and the period of vortex rings and apparent flapping motions can be easily determined in terms of period and time delay.
