The aim of the present paper is to explain some of the differences between previously published analytical and numerical models of combined wave and current bottom boundary layer flow. To this end, the Grant and Madsen (1979) model for wave–current, rough turbulent flow is modified to include both first and second harmonic time variations in the eddy viscosity (K). The functional form of the coefficients controlling the amount of time variation is established by analysing the numerical model results of Davies (1990). The addition of time variation in K reduces the strong non-linearity exhibited by the mean stress in the original Grant and Madsen model for current dominated cases, and reproduces the veering of the current predicted by numerical turbulence closure models.