Tomographic TR-PIV measurement of coherent structure spatial topology utilizing an improved quadrant splitting method

Abstract

In this paper, we calculated the spatial local-averaged velocity strains along the streamwise direction at four spatial scales according to the concept of spatial local-averaged velocity structure function by using the three-dimensional three-component database of time series of velocity vector field in the turbulent boundary layer measured by tomographic time-resolved particle image velocimetry. An improved quadrant splitting method, based on the spatial local-averaged velocity strains together with a new conditional sampling phase average technique, was introduced as a criterion to detect the coherent structure topology. Furthermore, we used them to detect and extract the spatial topologies of fluctuating velocity and fluctuating vorticity whose center is a strong second-quadrant event (Q2) or a fourth-quadrant event (Q4). Results illustrate that a closer similarity of the multi-scale coherent structures is present in the wall-normal direction, compared to the one in the other two directions. The relationship among such topological coherent structures and Reynolds stress bursting events, as well as the fluctuating vorticity was discussed. When other burst events are surveyed (the first-quadrant event Q1 and the third-quadrant event Q3), a fascinating bursting period circularly occurs: Q4-S-Q2-Q3-Q2-Q1-Q4-S-Q2-Q3-Q2-Q1 in the center of such topological structures along the streamwise direction. In addition, the probability of the Q2 bursting event occurrence is slightly higher than that of the Q4 event occurrence. The spatial instable singularity that almost simultaneously appears together with typical Q2 or Q4 events has been observed, which is the main character of the mutual induction mechanism and vortex auto-generation mechanism explaining how the turbulence is produced and maintained.