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

•Recent insights into the surf-riding of ships in irregular seas are reviewed.•Surf-riding in irregular seas is not equilibrium and it appears/disappears randomly.•A scheme for calculating instantaneous celerity of irregular waves is evaluated.•A point with zero sum of surge forces may not belong to a solution of motion equation.

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 surf-riding quasi-equilibrium at that instant. Further work includes studying the properties of the surf-riding phase plane in irregular waves and statistics of surf-riding occurrences.