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. (C) 2013 Elsevier Inc. All rights reserved.