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

Describing the time and spatial statistical characteristics of "eject" and "sweep" events in turbulent boundary layers is an important way to gain a deeper understanding of 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. Based on the maximum energy criterion of wavelet analysis and the statistical analysis method of conditional phase averaging, the fluctuating velocity was analyzed at multiple scales in time and space in the turbulent boundary layer of a flat plate, and the spatiotemporal multi-scale phase-averaged modes of the coherent structure of wall turbulence was carried out. The results show that 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 8th scale as the wall-normal locations vary from the buffer layer to the logarithmic layer. According to the autocorrelation function of wavelet coefficients at the maximum energy time-scale, 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 sixth 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.