  The broaching that follows the surf-riding is a dangerous phenomenon that can
lead to the capsizing of a vessel due to its violent yaw motion. Most of the
previous studies on surf-riding phenomena in irregular waves have been
conducted by replacing irregular waves with regular waves. In contrast, this
study provides suggestions on how to directly calculate nonlinear surge motion
in irregular seas. In this study, the statistical aspects of the surf-riding
phenomenon are first presented. Then, under several approximations, we show how
to calculate the probability density function theoretically. Although the
results obtained are based on strong approximations, it is found that the
nonlinear surge oscillations in irregular following seas can be explained from
a qualitative point of view.
