Velocity–vorticity correlation structure in turbulent channel flow

Abstract

AbstractA new statistical coherent structure (CS), the velocity–vorticity correlation structure (VVCS), using the two-point cross-correlation coefficient $R_{ij}$ of velocity and vorticity components, $u_i$ and $\omega _j~ (i, j = 1, 2, 3)$, is proposed as a useful descriptor of CS. For turbulent channel flow with the wall-normal direction $y$, a VVCS study consists of using $u_i$ at a fixed reference location $y_r$, and using $|R_{ij} (y_r; x, y, z)|\geqslant R_0$ to define a topologically invariant high-correlation region, called $\mathit{VVCS}_{ij}$. The method is applied to direct numerical simulation (DNS) data, and it is shown that the $\mathit{VVCS}_{ij}$ qualitatively and quantitatively captures all known geometrical features of near-wall CS, including spanwise spacing, streamwise length and inclination angle of the quasi-streamwise vortices and streaks. A distinct feature of the VVCS is that its geometry continuously varies with $y_r$. A topological change of $\mathit{VVCS}_{11}$ from quadrupole (for smaller $y_r$) to dipole (for larger $y_r$) occurs at $y^{+}_r=110$, giving a geometrical interpretation of the multilayer nature of wall-bounded turbulent shear flows. In conclusion, the VVCS provides a new robust method to quantify CS in wall-bounded flows, and is particularly suitable for extracting statistical geometrical measures using two-point simultaneous data from hotwire, particle image velocimetry/laser Doppler anemometry measurements or DNS/large eddy simulation data.