Evolution and statistical analysis of random wave fields within the Benjamin-Ono equation

TL;DR

This paper explores the evolution of random internal wave fields governed by the Benjamin-Ono equation, analyzing their statistical properties, spectral convergence, and rogue wave formation through numerical simulations.

Contribution

It provides new insights into the statistical behavior and rogue wave phenomena of BO random waves, including deviations from Gaussianity and the identification of distinct rogue wave types.

Findings

Spectra converge to a stationary state with non-Gaussian characteristics

Increased Ursell parameter leads to higher skewness and kurtosis

Identified rogue wave types: 'two sisters' and 'three sisters'

Abstract

This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using the Benjamin-Ono (BO) equation. The research focuses on analyzing various properties associated with the BO random wave field, including the transition to a steady state of the spectra, statistical moments, and the distribution functions of wave amplitudes. Numerical simulations are conducted across different Ursell parameters, revealing intriguing findings. Notably, it is observed that the spectra of the wave field converges to a stationary state in a statistical sense, while exhibiting statistical characteristics that deviate from a Gaussian distribution. Moreover, as the Ursell parameter increases, the positive skewness of the wave field intensifies, and the kurtosis increases. The investigation also involves the computation of the probability of rogue wave formation, revealing deviations from the Rayleigh distribution. Notably, the study uncovers distinct types of rogue waves, specifically referred to as "two sisters" and "three sisters" phenomena.