Numerical investigation on hopf bifurcation problem for nonlinear dynamics of a towed vessel in calm water and waves

Abstract

In this study, the Hopf bifurcation problem with regard to the nonlinear dynamics of a towed vessel was numerically investigated. A time-domain simulation method based on three degrees-of-freedom maneuvering equations of motion was applied to study the nonlinear dynamic responses of a towed vessel in calm water, wind and waves. In the towing operation, it is assumed that a vessel is passively towed by a tug via a towline with a constant towing speed following a straight line. In the case of wind or wave conditions, the steady wind or wave drift forces are considered as additional external force components. The hydrodynamic forces acting on the towed vessel are modeled as a modular-type hull force model, and the towline force is simply modeled as a linear spring. First, for the validation, the motion trajectories of the towed vessel were compared between the experimental data and numerical simulation results under the calm water condition. Discussions are provided on the effect of skegs on the dynamics of the towed vessel and related Hopf bifurcation according to the skeg size. Next, the wind speed was changed, and the resulting limit cycles were studied. It can be observed that the Hopf bifurcation can be delayed according to the wind speed and direction. Finally, the dynamic characteristics of the towed vessel in regular waves were investigated via numerical simulations. The stability of the towed vessel with no skegs increases owing to the mean wave drift forces for both the model test and numerical simulation. The effects of the wave height and period on the Hopf bifurcation were studied based on numerical simulations. It was found that the occurrence of Hopf bifurcation for nonlinear dynamics of a towed vessel is sensitive to the conditions of wave height and period.