Fluid flow in a straight duct with rectangular cross-section exhibits turbulence-induced secondary motion of small amplitude, but with a large effect on momentum, heat and mass transport. As an example, the wall shear-stress varies strongly along the wall-bounded perimeter, with possible consequences for sediment erosion. The mean secondary flow in a square duct bounded by four solid walls has the well-known 8-vortex pattern. At relatively low Reynolds number, the formation of the large-scale average vortices in the cross-section is due to statistically preferred locations of near-wall coherent structures in the vicinity of the corners [1,2]. The scaling with Reynolds number of this phenomenon is currently still an open question. When the duct cross-section has an aspect ratio other than unity and/or one of the boundaries is not a solid wall (e.g. a free surface), the shape of the pattern is even less well documented.
[1] M. Uhlmann, A. Pinelli, G. Kawahara, and A. Sekimoto. Marginally turbulent flow in a square duct. J. Fluid Mech., 588:153-162, 2007. DOI
[2] A. Pinelli, M. Uhlmann, A. Sekimoto, and G. Kawahara. Reynolds number dependence of mean flow structure in square duct turbulence. J. Fluid Mech., 644:107-122, 2010. DOI
