Hybrid surging and surf-riding motions of a ship in steep Bi-chromatic following seas

In the present paper are reported unconventional nonlinear ship motion patterns that were found during nu-merical investigations of ship motions when an extra wave component, with different frequency, was introduced to an initially harmonic wave excitation. The specific focus of the work is on the surge dynamics of a ship operating in long following waves. Asymmetric large amplitude surging and surf-riding are well-known types of nonlinear ship behaviour exhibited in simple harmonic waves. By the inclusion of a second frequency in the excitation, surf-riding is rendered oscillatory. Moreover, as the excitation is intensified, hybrid motions, involving intensive surge fluctuations combining features of surging and surf-riding, emerge. Moreover, a quite robust irregular version of hybrid surging was identified. The mathematical model includes three degrees of freedom (surge-pitch-heave) and it accounts for hydrodynamic memory effects. It was combined with the steady -state continuation technique, in order to determine, in parameters' space, the boundaries separating the different types of behaviour and the associated underlying bifurcations.