  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.
