Effects of nonlinearity on Anderson localization of surface gravity waves

TL;DR

This study demonstrates that nonlinearity enhances the localization of surface gravity waves in a disordered medium, providing new experimental insights into how nonlinearity affects wave localization.

Contribution

It provides the first experimental evidence of how nonlinearity influences Anderson localization of surface waves and reports the dependence of localization length on nonlinearity.

Findings

Nonlinearity strengthens wave localization.

Localization length varies with nonlinearity.

Disorder and finite size affect localization behavior.

Abstract

Anderson localization is a multiple-scattering phenomenon of linear waves propagating within a disordered medium. Discovered in the late 50s for electrons, it has since been observed experimentally with cold atoms and with classical waves (optics, microwaves, and acoustics), but whether wave localization is enhanced or weakened for nonlinear waves is a long-standing debate. Here, we show that the nonlinearity strengthens the localization of surface-gravity waves propagating in a canal with a random bottom. We also show experimentally how the localization length depends on the nonlinearity, which has never been reported previously with any type of wave. To do so, we use a full space-and-time-resolved wavefield measurement as well as numerical simulations. The effects of the disorder level and the system's finite size on localization are also reported. We also highlight the first experimental evidence of the macroscopic analog of Bloch's dispersion relation of linear hydrodynamic surface waves over periodic bathymetry.