Extraction of Coherent Structure from PIV Data Using Wavelet Transform

Velocity fields measured by a particle image velocimetry (PIV) are analyzed by using the wavelet transform. Considered here are coherent structures in the mixing layer of turbulent open-channel flow over a concave bed. At first, we examine the capability of the continuous wavelet transform (CWT) for the coherent structure detection. By applying CWT to an instantaneous velocity distribution measured by PIV, the locations and spatial scales of the coherent structures along the mixing layer have been successfully obtained from the locations of the extremal values of wavelet coefficient in the space-wavenumber domain. Then, a conditional sampling is used to extract the locations and the respective spatial scales for the maximal values of the wavelet coefficient in each time step. Consequently, the characteristics of the coherent structures along the mixing layer, such as the evolution of the spatial scale, advection velocity, and occurrence interval, are clearly illustrated as functions of the location and the time. Furthermore, by applying CWT to the time series of the velocities in each location of the channel instead of the velocity distribution, the frequencies of the coherent structures are found out in addition to the above characteristics. The joint probability distribution of the spatial scale and the frequency shows that there is a linear relationship between them. These results strongly suggest that the wavelet transform is a useful tool for extracting the coherent structures embedded on the velocities obtained by PIV measurement.