Secondary vortices over surfaces with spanwise varying drag

A spanwise heterogeneity of streamwise drag is known to lead to the formation of large secondary motions of Prandtl's second kind. Based on the data sets extracted from direct numerical simulations (DNS) of fully developed turbulent channel flow where streamwise stripes of free-slip surface with varying spanwise extension are introduced, we investigate the topological structure of the secondary motions. We find a complex restructuring of the secondary motion with increasing extent of free-slip/no-slip region where the width of the free-slip region in viscous units appears to be one important governing parameter for the vortex formation. The most striking feature of this restructuring is a change in the rotational direction of the major vortex pair such that the related high- and low-momentum pathways are found at different locations. The present results reveal that the spanwise inhomogeneity of the Reynolds stress distribution is strongly related to the observed change of rotational direction. In addition, it is shown that the vorticity source remains largely unchanged and mainly restricted to a rather small region close to the discontinuity in the boundary condition, despite the fact that the topology of secondary motions substantially changes with variation of the spanwise length scale. This suggests a complex interplay between the vortices that are generated at the surface discontinuities and the surrounding flow.