SPATIOTEMPORAL MULTI-SCALE ANALYSIS AND CONDITIONAL PHASE-AVERAGED WAVEFORM OF WALL TURBULENCE

The experimental database of turbulent boundary layer TRPIV(time-resolved particle image velocimetry) measurement with a large field of view and high time resolution of a four-camera array is employed in order to carry out the multi-scale analysis of the instantaneous velocity field of the turbulent boundary layer and investigate the spatiotemporal multi-scale conditional-averaged modes of coherent structures in wall-bounded turbulence. Firstly, at different wall-normal heights, the fluctuating longitudinal velocity signals along the streamwise spatial direction is decomposed into multi-scale components using wavelet analysis. Based on the maximum energy criterion, the fluctuating velocity signals corresponding to maximum-energy space-scale (the 9th scale) is obtained, where the turbulent fluctuating kinetic energy reaches the peak and the turbulence burst is the most active. And then at different wall-normal locations, the time series of fluctuating longitudinal velocity component are unfolded into multi-scale components by wavelet analysis. It was found that the peak-scale with the maximum turbulent energy in the streamwise direction gradually varies from the 6th scale to the 9th scale as the wall-normal locations vary from the buffer layer to the logarithmic layer. Taking advantage of the autocorrelation function of wavelet coefficients at the maximum energy time-scale and the wavelet coefficients extremum detection criterion, The wavelet coefficient at maximum energy time-scale of longitudinal velocity component are point-by-point examined for the local positive maximum, which represents the center of sweep event and the negative minimum which represents a eject event center. According to the autocorrelation function of wavelet coefficients at the maximum energy time-scale, the average burst period of turbulence is determined, and the average phase waveform of the streamwise fluctuating velocity component, the normal-wall fluctuating velocity component and instantaneous Reynolds stress is obtained during eject event and sweep event occurs, and the results fit the features of eject event and sweep event well. Spatial multi-scale decomposition for the instantaneous velocity field is performed along the longitudinal direction at different normal positions. Eject and sweep are detected at four different normal positions of the fifth spatial scale, as well as the spatial phase-averaged modes of the streamline and vorticity are obtained around the detected points. It is found that in the logarithmic layer, there is a saddle-focal point dynamics system around the detection point, and the vorticity fields at the four corners of the saddle-focal point dynamics system show a quadrupole vortex structure, while in the buffer layer, the lower vortex-pair of the quadrupole disappears and the upper vortex-pair induces the ejection and sweep events. This study provides an experimental foundation for establishing the dynamics system model of multi-scale vortex structure in turbulent boundary layer.