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

Abstract

The enstrophy convection velocity (denoted by $u_{\Omega }$) in the evolution equation of the boundary enstrophy is proportional to skin friction (denoted by $\tau$) 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 $\left|u_{\Omega }\right|$ and $\left|\tau \right|$ is evaluated in a turbulent channel flow at the friction Reynolds number ${\mathrm{Re}}_{\tau }=180$, 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 $\left|u_{\Omega }\right|$ and $\left|\tau \right|$ are discussed. The statistical correlation between $u_{\Omega }$ and $\tau$ elucidates the connection between near-wall flow structures and skin friction.