Approximate probability density function for nonlinear surging in irregular following seas

Abstract

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.

Figures (7)

• Figure 1: Body plan of the subject ship (DTMB5415). Here, ship length is $L_{\mathrm{PP}}=2.75~\mathrm{m}$. The detailed description of this ship can be found in the literature maki2016surfridingmaki2024NOLTA.
• Figure 2: Phase portraits for DTMB5415 with $H/\lambda =0.04$ and $\lambda/L_{\mathrm{S}} =1.0$
• Figure 3: Phase portraits for DTMB5415 with $H/\lambda =0.04$ and $\lambda/L_{\mathrm{S}} =2.0$
• Figure 4: Statistical analysis for several Froude numbers for the equation of motion \ref{['eq:equation_of_motion_before_approximation']}
• Figure 5: Statistical analysis for several Froude numbers for the approximated equation of motion (\ref{['eq:euqation_of_motion_approximated']})