Velocity-vorticity correlation structure in turbulent channel flow

We present a new definition of statistical structure - velocity-vorticity correlation structure (VVCS) - based on amplitude distributions of the tensor field of normalized velocity-vorticity correlation (u_iω _j), and show that it displays the geometry of the statistical structure relevant to a given reference point, and it effectively captures coherent motions in inhomogeneous shear flows. The variation of the extracted objects moving with the reference point y_r ⁺ then presents a full picture of statistical structures for the flow, which goes beyond the traditional view of searching for reference-independent structures. Application to turbulent channel flow simulation data at Re_τ=180 demonstrates that the VVCS successfully captures, qualitatively and quantitatively, the near-wall streaks, the streamwise vortices [1,2], and their extensions up to y_r ⁺=110 with variations of their length and inclination angle. More interestingly, the VVCS associated with the streamwise velocity component (particularly 〈uω_x〉 and 〈uω_z〉) displays topological change at four distances from the wall (with transitions at y_r ⁺≈20,40,60,110), giving rise to a geometrical interpretation of the multi-layer structure of wall-bounded turbulence. Specifically, we find that the VVCS of 〈uω_z〉 bifurcates at y_r ⁺=40 with one attached to the wall and the other near the reference location. The VVCS of 〈uω_x〉 is blob-like in the center region, quite different from a pair of elongated and inclined objects near the wall. The propagation speeds of the velocity components in the near-wall region, y ⁺ < 10, is found to be characterized by the same stream-wise correlation structures of 〈uω_x〉 and 〈uω_z〉, whose core is located at y⁺≈20. As a result, the convection of the velocity fluctuations always reveal the constant propagation speeds in the near-wall region. The coherent motions parallel to the wall plays an important role in determining the propagation of the velocity fluctuations. This study suggests that a variable set of geometrical structures should be invoked for the study of turbulence structures and for modeling mean flow properties in terms of structures. The method and the concept presented here are general for the study of other flow systems (like boundary or mixing layer), as long as ensemble averaging is well-defined.