Soliton Dynamics over a Disordered Topography

TL;DR

This study experimentally investigates how solitons in a fluid surface are affected by disordered bottom topography, revealing localization effects, nonlinear influences, and complex wave dynamics with implications for coastal protection.

Contribution

First experimental observation of soliton localization due to disorder in a fluid system, demonstrating the impact of nonlinearity and topography on wave propagation.

Findings

Localization length matches linear theory at low amplitudes

Higher amplitudes enhance spatial attenuation

Distinct wave behaviors observed for periodic and random topographies

Abstract

We report on the dynamics of a soliton propagating on the surface of a fluid in a 4-m-long canal with a random or periodic bottom topography. Using a full space-and-time resolved wavefield measurement, we evidence, for the first time experimentally, how the soliton is affected by the disorder, in the context of Anderson localization, and how localization depends on nonlinearity. For weak soliton amplitudes, the localization length is found in quantitative agreement with a linear shallow-water theory. For higher amplitudes, this spatial attenuation of the soliton amplitude is found to be enhanced. Behind the leading soliton slowed down by the topography, different experimentally unreported dynamics occur: Fission into backward and forward nondispersive pulses for the periodic case, and scattering into dispersive waves for the random case. Our findings open doors to potential applications regarding ocean coastal protection against large-amplitude waves.