The way in which the Boussinesq and Serre models deal with the internal kinematics of waves on mildly sloping beaches is examined. The equation normally used on the depth-averaged horizontal velocity to impose a parabolic profile vertically up through the wave is studied using experimentally and theoretically obtained values. In general, it is found that for near-bed regions the equation provides satisfactory comparisons, however, as one approaches the surface the theoretical values can substantially exceed the experimental ones, particularly in the crest of the wave.
