Application of wavelet cross-correlation analysis to a plane turbulent jet

A new cross-correlation method, which is called wavelet cross-correlation analysis and is used to express the statistical cross-correlation of two arbitrary signals in terms of scale and time delay, is proposed and its main properties are presented, analyzing two test signals, it is shown that wavelet cross-correlation does not have the limitations of classical cross-correlation. As a practical application to fluid mechanics, wavelet cross-correlation is employed to determine the cross-correlation relationships between the x-components of the fluctuation velocities at two points on opposite sides of the centerline and along the centerline of a plane turbulent jet in terms of period and time delay. In the distributions of the wavelet cross-correlation coefficients, similar structures with various scales are observed instantaneously, and the period of eddy and apparent flapping motions can be determined easily in terms of period and time delay. It is found that the apparent flapping behavior appears first in region with an intermediate period. It is also revealed that a similar structure with a high period consists of similar structures with a low period, i.e., a large eddy contains small eddies.