On probability of surf-riding in irregular seas with a split-time formulation

Abstract

The paper reviews the status of a multi-year research effort for using the split-time method to calculate the probability of ship capsizing due to broaching-to in irregular waves. This required taking steps toward extending the existing theory of surf-riding and broaching-to, from regular waves to irregular waves and applying it to numerical simulation codes of ship motions. The extension of the theory for irregular waves leads to the formulation of a spatial-temporal framework for considering surf-riding where the celerity of irregular waves must be defined. An approximate metric for the likelihood of surf-riding in irregular waves has been proposed as the distance, in the phase plane, between the instantaneous position of a ship and the stable surfriding quasi-equilibrium at that instant. Further work includes studying the properties of the surfriding phase plane in irregular waves and statistics of surf-riding occurrences. This already complex setup becomes even more complex when, the ship motions are calculated with high accuracy, by using the more consistent, in ship hydrodynamics terms, formulation. Wave excitation can no longer be separated from stiffness while radiation and diffraction forces add a hydrodynamic memory effect. Furthermore, the irregularity of realistic ocean introduces new physical qualities to the phenomenon.The challenge to include surf-riding and broaching-to into a probabilistic assessment of stability based on advanced hydrodynamic codes has been taken up by the US Office of Naval Research (ONR) project "A Probabilistic Procedure for Evaluating the Dynamic Stability and

Theoretical estimation of joint probability density function of roll angle and angular acceleration in beam seas using PDF line integral method

“…From this figure, it can be seen that the change in the variance becomes smaller with the introduction of the approximation Eq. (18). Such changes in dynamics are basically not negligible.…”

“…Maki and Miyauchi [16] conducted free-running model experiments in a 247m-long towing tank at the Naval Systems Research Center of Acquisition, Technology & Logistics Agency and then attempted to define the surf-riding phenomenon in irregular waves based on the trend of the pitch angle of the ship model. Belenky et al [17,18] examined the reduction of overturning due to broaching and wave riding using a split-time method approach. Dostal and Kreuzer [19] used Melnikov's method [20] for irregular disturbances and conducted a theoretical study on the limits of surf-riding in irregular seas.…”

An overview of the current research on stability of ships and ocean vehicles: The STAB2018 perspective

“…Broaching zones are estimated, however the issue of their utilisation in real wave environment remains open. Belenky et al (2016aBelenky et al ( , 2016b use the concept of split-time method for the estimation of the probability of surf-riding and capsize due to pure loss of stability in irregular waves. By this concept, two problems are set: non-rare and rare, where a metric of the danger of the rare event is defined and computed utilising data from the non-rare problem (exceedances of an intermediate threshold) and statistical extrapolation techniques.…”

A Unified Numerical Method for Broaching and Loss of Stability in Astern Seas

“…It is also reported that surf-riding and broaching calculated by the code LAMP is used for evaluating probability with a split-time formulation, and its time-domain method of broaching is not published [14].…”