Mean streamwise vorticity in turbulent flow is shown to arise both from mean flow skewing and from the inhomogeneity of anisotropic wall turbulence. The structure of the Reynolds stress tensor is examined in several flows where the latter mechanism predominates. On the basis of a simple model for the anisotropy, the direction of the secondary currents is deduced for the corner boundary layer, the salient edge flow, and in the non-uniform nominally two-dimensional boundary layer.