Here we consider the mean velocity profile in the core region of a uni
directional turbulent flow, that is, a flow in which the turbulent mot
ion is superposed upon parallel time-averaged streamlines. A kinematic
al variational principle, originally developed for three-dimensional f
ree-turbulent motions, is shown to be applicable to significant parts
of the velocity profiles for flows of both Couette and Poiseuille type
s. In addition to pure plane Couette and pure plane Poiseuille flows,
the motions considered include a variety of admixtures produced by blo
wing through a wide flat channel one of whose walls comprises a belt w
hich moves either in the direction of the blowing or counter to it.