Evolution and Statistical Analysis of Internal Random Wave Fields within the Benjamin–Ono Equation

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