Particle trajectories in the Serre equations

We present a numerical study of particle paths in an irrotational free surface flow over a flat bottom where the Serre equations are considered as the governing equations. For solitary surface waves, we obtain that the particle paths are parabolic with a large forward drift. Periodic solutions of the Serre equations feature nearly closed particle trajectories with a slight backward drift depending on the initial depth of the particles. This backward drift appears to be due to negative mean horizontal velocity in the periodic solutions.