Velocity-vorticity correlation structure in turbulent channel flow

A statistical structure -- velocity-vorticity correlation structure (VVCS) -- is defined by the amplitude distribution of a tensor field of correlation coefficicents. Applied to turbulent channel flow DNS database (at $Re_{\tau}=180$), it captures most relevant features -- qualitative and quantitative -- of coherent structures near the wall, including streaks (Kline et al. 1967, JFM), inclined streamwise vortices (Jeong et al. 1997, JFM), and transverse vorticity (Jimenez \& Moin 1991, JFM), etc. Associated with the streamwise velocity component (particularly $\langle u \omega_x \rangle$), VVCS reveals a change of topology with increasing $y_r^+$, providing a physical interpretation of multiple layers of wall-bounded turbulence. The statistical structure of $\langle u \omega_x \rangle$ depends on the $y_r^+$-location of $u$ detection. When $y_r^+$ is near the wall, the structure resembles streamwise vortices. But when $y_r^+$ is close to the center, it becomes a blob-like structure, quite different from streamwise vortices in the near-wall region. We propose that the statistical structure is adequate in modeling of the mean flow field. This study raises some doubt about unique structures in turbulent flows: consideration of a set of statistical structures is unavoidable.