Nonlinear dynamics of water waves over nonuniformly periodic bottom

TL;DR

This paper uses numerical simulations to study nonlinear water wave behavior over nonuniformly periodic bottoms, revealing wave compression, formation of standing waves, and transient Bragg solitons near spectral gap edges.

Contribution

It introduces a detailed numerical analysis of nonlinear water wave dynamics over complex bottom profiles, highlighting phenomena like wave compression and transient soliton formation.

Findings

Wavepacket compression during Bragg reflection

Formation of standing waves with sharp crests

Transient Bragg solitons near spectral gap edges

Abstract

By numerical simulation of exact equations of motion (in terms of conformal variables) for planar non-stationary potential flows of an ideal fluid with a free surface over a strongly non-uniform bottom profile, the effect of nonlinear compression of a long wavepacket during its Bragg reflection from domain of gradually increasing, periodically placed barriers has been detected. In this case, a short and tall packet of standing waves with sharp crests is formed, and then it is transformed into the backward wave. It is essential that with variation of frequency of the incident wave, the effect is absent in the middle of the barrier-induced spectral gap, but it is quite prominent closely to the upper edge of the gap, when the forward wave penetrates deeply into the scattering domain and there, together with emerged backward wave, they form a semblance of Bragg soliton for some time interval.