Theoretical prediction of broaching in the light of local and global bifurcation analyses

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.