Velocities are measured using LDA within the bottom boundary layer for 10 oscillatory flow tunnel experiments involving regular and amplitude modulated oscillatory flows over a gravel-rough bed and a sand-rough bed. Corresponding regular and modulated flows were equivalent in terms of rms velocity, oscillatory flow period, skewness and asymmetry. The experimental results are compared with predictions based on a 1DV RANS model with turbulence closure. The effects of modulation on the hydrodynamics of individual flow half-cycles and on the time-averaged hydrodynamics are analysed. Turbulence is carried over from one half-cycle to the following half-cycle but the main hydrodynamic properties within a half-cycle (boundary layer thickness, peak turbulent kinetic energy, peak turbulent stress) show little or no dependence on prior half-cycle flow conditions. Turbulence propagation from the bed and vertical profiles of skewness, asymmetry, time-averaged turbulent kinetic energy and time-averaged turbulent stress show remarkably little effect of modulation. Modulation does not affect the shape of the time-averaged velocity profile generated by the non-symmetric flows, but it does reduce the magnitude. The RANS model shows generally good agreement with the measured hydrodynamics above about one grain diameter from the bed, but, because of its assumption of rough turbulent flow, poorly predicts the hydrodynamics of the low-velocity half-cycles of the modulated flows over the sand-rough bed