The irrotational motions induced by, but outside of, the selfpreserving turbulent wake and jet are examined. It is found that there is a mean flow towards the centre of the jet, although there is no such flow in the case of the wake. Phillips's (1955) results on the nature of fluctuating irrotational flows are found to be largely unaffected by the introduction of simple inhomogeneities into the boundary conditions, but another mode of fluctuation with movement along the lines of mean flow is also shown to be likely. It is pointed out that, contrary to a statement of Corrsin & Kistler (1954), it is possible for the vorticity-free fluid between bulges of turbulent fluid to partake of the mean velocity of the turbulent fluid.