Nonlinear Dynamics of Waves Over a Nonuniformly Periodic Bottom

The numerical simulation of exact equations of motion (in conformal variables) for unsteady plane potential flows of an ideal fluid with a free surface over a strongly nonuniform bottom profile has revealed the nonlinear compression of a long wave packet undergoing Bragg reflection from a section with a smoothly increasing height of periodically located barriers. In this case, a short high packet of standing waves with sharp crests is formed and is then transformed into a backward wave. It is essential that the effect as a function of the frequency of the incident wave is insignificant in the middle of the barrier-induced spectral gap, but is maximal closer to its upper edge, when the forward wave penetrates deeply into the scattering region and forms, together with the appearing backward wave, a semblance of a Bragg soliton for some time interval.