Flow in the spanwise symmetry plane

If the assumption of two-dimensionality is to be at all applicable to a three-dimensional flow in a tall cavity or duct, it is most likely to be so at the plane of spanwise symmetry ($Z=0$), since this is furthest from the end-walls. The flow in this plane is investigated here via the magnitude of the spanwise component of vorticity at the centre line $X=Z=0$ (the other components vanish there, by symmetry, for the sections considered in this chapter) and the profile of the vertical component of velocity along the line formed by the intersection of the plane and an arbitrary horizontal section $\{\mathbf{X}:-\mbox{$\frac{1}{2}$}<X<\mbox{$\frac{1}{2}$}, Z=0\}$.