Abstract
For developing design and operational criteria to be used at the International Maritime Organization (IMO), critical conditions for broaching are explored in the light of bifurcation analysis. Since surf-riding, which is a prerequisite to broaching, can be regarded as a heteroclinic bifurcation, one of global bifurcations, of a surge–sway–yaw–roll model in quartering waves, the relevant bifurcation condition was mathematically formulated and then a numerical procedure for obtaining its solution was presented with successful example. This identified bifurcation condition was compared with direct numerical simulation in time domain. As a result, it was confirmed that the heteroclinic bifurcation provides a boundary between motions periodically overtaken by waves and non-periodic motions such as surf-riding, broaching and so on. Then a local bifurcation analysis was applied to the surf-riding equilibria. This results could explain a boundary between stable surf-riding and oscillatory surf-riding as a Hopf bifurcation. Furthermore, comparison with free-running model experiments shows some discrepancies and an improvement with an aid of nonlinearity in wave-induced surge force is presented.