Experimental study of breathers and rogue waves generated by random waves over non-uniform bathymetry

TL;DR

This experimental study investigates how random water waves over non-uniform bathymetry form stable coherent wave packages and rogue waves, with statistical analysis confirming their similarity to deep water breather solutions.

Contribution

The paper provides experimental evidence that stable wave packages and rogue waves over non-uniform bathymetry resemble deep water breather solutions and are characterized by specific statistical properties.

Findings

Stable wave packages travel with almost uniform group velocity.

Rogue waves form where BFI, kurtosis, and skewness are maximal.

Experimental data matches well with NLS equation solutions.

Abstract

Experimental results describing random, uni-directional, long crested, water waves over non-uniform bathymetry confirm the formation of stable coherent wave packages traveling with almost uniform group velocity. The waves are generated with JONSWAP spectrum for various steepness, height and constant period. A set of statistical procedures were applied to the experimental data, including the space and time variation of kurtosis, skewness, BFI, Fourier and moving Fourier spectra, and probability distribution of wave heights. Stable wave packages formed out of the random field and traveling over shoals, valleys and slopes were compared with exact solutions of the NLS equation resulting in good matches and demonstrating that these packages are very similar to deep water breathers solutions, surviving over the non-uniform bathymetry. We also present events of formation of rogue waves over those regions where the BFI, kurtosis and skewness coefficients have maximal values.