The equations governing the oscillatory flow in a turbulent shear wave boundary layer are integrated numerically. By representing the Reynolds stress by Prandtl's mixing length hypothesis it is found that the velocity profile can be well approximated by a logarithmic profile. The depth of this depends upon the phase, the amplitude, and the frequency of the wave. It is shown further that the profile cannot be identified with a constant stress profile and that an attempt to do so will lead to an underestimate of the bottom stress.