Correlation between skin friction and enstrophy convection velocity in near-wall turbulence

The enstrophy convection velocity (denoted by u?) in the evolution equation of the boundary enstrophy is proportional to skin friction (denoted by ?) in an incompressible viscous flow, which can be determined globally as an optical flow problem from a time sequence of the boundary enstrophy fields. The correlation coefficient between |u?| and |?| is evaluated in a turbulent channel flow at the friction Reynolds number Re? = 180, which is about 0.73 in the region of interest containing near-wall strong wall-normal velocity event associated with a sweep-ejection pair) and is approximately independent of the wall-normal coordinate in the viscous sublayer. This correlation coefficient is contributed mainly by strong near-wall coherent structures with high boundary enstrophy. The statistics of the difference between the normalized |u?| and |?| are discussed. The statistical correlation between u? and ? elucidates the connection between near-wall flow structures and skin friction.