Turbulence in a three‐dimensional wall‐bounded shear flow

Abstract

Abstract A new turbulent flow with distinct three‐dimensional characteristics has been designed in order to study the impact of mean‐flow skewing on the turbulent coherent vortices and Reynolds‐averaged statistics. The skewing of a unidirectional plane Couette flow was achieved by means of a spanwise pressure gradient. Direct numerical simulations of the statistically steady Couette–Poiseuille flow enabled in‐depth explorations of the turbulence field in the skewed flow. The imposition of a modest spanwise gradient turned the mean flow about 8° away from the original Couette flow direction and this turning angle remained nearly the same over the entire cross section. Nevertheless, a substantial non‐alignment between the turbulent shear stress angle and the mean velocity gradient angle was observed. The structure parameter turned out to slightly exceed that in the pure Couette flow, contrary to the observations made in some other three‐dimensional shear flows. Coherent flow structures, which are known to be associated with the Reynolds shear stress in near‐wall regions, were identified by the λ 2 ‐criterion. Instantaneous and ensemble‐averaged vortices resembled those found in the unidirectional Couette flow. In the skewed flow, however, the vortex structures were turned to align with the local mean‐flow direction. The conventional symmetry between Case 1 and Case 2 vortices was broken due to the mean‐flow three‐dimensionality. The turning of the coherent vortices and the accompanying symmetry‐breaking gave rise to secondary and tertiary turbulent shear stress components. By averaging the already ensemble‐averaged shear stresses associated with Case 1 and Case 2 vortices in the homogeneous directions, a direct link between the educed near‐wall structures and the Reynolds‐averaged turbulent stresses was established. These observations provide evidence in support of the hypothesis that the structural model proposed for two‐dimensional turbulent boundary layers remains valid also in flows with moderate mean three‐dimensionality. Copyright © 2009 John Wiley & Sons, Ltd.