Turbulence in a skewed three‐dimensional wall‐bounded shear flow: effect of mean vorticity on structure modification

Mean‐flow three‐dimensionalities affect both the turbulence level and the coherent flow structures in wall‐bounded shear flows. A tailor‐made flow configuration was designed to enable a thorough investigation of moderately and severely skewed channel flows. A unidirectional shear‐driven plane Couette flow was skewed by means of an imposed spanwise pressure gradient. Three different cases with 8°, 34°and 52°skewing were simulated numerically and the results compared with data from a purely two‐dimensional plane Couette flow. The resulting three‐dimensional flow field became statistically stationary and homogeneous in the streamwise and spanwise directions while the mean velocity vector V and the mean vorticity vector Ω remained parallel with the walls. Mean flow profiles were presented together with all components of the Reynolds stress tensor. The mean shear rate in the core region gradually increased with increasing skewing whereas the velocity fluctuations were enhanced in the spanwise direction and reduced in the streamwise direction. The Reynolds shear stress is known to be closely related to the coherent flow structures in the near‐wall region. The instantaneous and ensemble‐averaged flow structures were turned by the skewed mean flow. We demonstrated for the medium‐skewed case that the coherent structures should be examined in a coordinate system aligned with V to enable a sound interpretation of 3D effects. The conventional symmetry between Case 1 and Case 2 vortices was broken and Case 1 vortices turned out to be stronger than Case 2. This observation is in conflict with the common understanding on the basis of the spanwise (secondary) mean shear rate. A refined model was proposed to interpret the structure modifications in three‐dimensional wall‐flows. What matters is the orientation of the mean vorticity vector Ω relative to the vortex vorticity vector ω _v, that is, the sign of Ω · ω _v. In the present situation, Ω · ω _v > 0 for the Case 1 vortices causing a strengthening relative to the Case 2 vortices. Copyright © 2011 John Wiley & Sons, Ltd.