Boundary layers provide the main source of vorticity for turbulence as discussed in Sec. 6.4 . A boundary layer breaks away from the boundary when it reaches the end of the surface or by separation before reaching the end. Vorticity and turbulence are thereby swept into regions of ﬂuid away from solid boundaries.
Flow around a cylinder illustrates boundary layer separation, vorticity and turbulence. The ﬂuid ﬂows at uniform velocity upstream of the cylinder. It decelerates to stagnation, , at point A on the surface (in the -normal direction).
The ﬂow reaches a peak speed at B, then decelerates over the downstream side of the cylinder. The adverse pressure gradient causes to decrease. At some point C, the velocity gradient can reach . Beyond C, the boundary layer can separate such that along its proﬁle, see point D.
Boundary layer separation in a cylinder depends on Reynolds number , Eq. (2.68 ), using and . For , there is no separation, with the ﬂow exhibiting a pattern downstream that mirrors the upstream ﬂow.6
For , the boundary layer separates with its vorticity sustaining a pair of vortices attached to the rear of the cylinder.
At , the vorticity starts to become become chaotic, with turbulence beginning to appear in the vortices. At , the entire wake region becomes turbulent.
The frequency of vortex shedding is characterised by another dimensionless number from Eq. (2.68 ), the Strouhal number . For , experiments show7 , where is the period at which the vortex pattern repeats.