Lagrangian-based spatial-temporal topological study on the evolution and migration of coherent structures in wall turbulence

In this work, we study the development, evolution, and migration of turbulent coherent structures in the turbulent boundary layer at Re-tau = 630 using time-resolved particle image velocimetry (TR-PIV). Multiple techniques, including multi-scale analysis, conditional averaging, cross-correlation, and spatial-temporal topological analysis are applied to extract the evolution principle, migration trajectory, and convection velocity vector of the targeted coherent structures from a Lagrangian perspective. The spanwise vortex structures with larger scale and intensity at a certain wall-normal height y were the main focus of the present study. In the statistical sense, spanwise vortex structures move away from the wall with the shape changing from a bulge to an ellipse, and finally to a circle. Two straight lines emerge from the mean transfer trajectory curve of the spanwise vortex, in which the horizontal one is located at the viscous sublayer (y(+) < 10), the other is a logarithmic straight line existing in the range of 50 < y(+) < 120, and the inclination angle of the tangential migration path is fixed at around 12 degrees. The streamwise convection velocity U-c of scaled spanwise vortex structures satisfies U-c/U-infinity = 0.5-0.6 below y = 0.03 delta (i.e., U-c(+) = 11-13 under y(+) = 20). In particular, in the region of 50 < y(+) < 120, the velocity growth curves of U-c and wall-normal convection velocity V-c follow the log-law distribution very well, and the slopes are consistent with that of the log-law region of the turbulent boundary layer. Our observations provide microscopic evidences of the logarithmic-linear distribution of the migration trajectory of spanwise vortex structures.