Study on parametric roll in oblique waves using a three-dimensional hybrid panel method

Providing a reliable numerical tool for the prediction of parametric roll is one of the main tasks in the development of the second generation intact stability criteria. The main difficulty for the prediction of parametric roll is due to significant coupling of roll with other motions, especially heave and pitch motions. In this paper, a numerical method for the calculation of parametric roll is studied and the results are benchmarked against model test data. Firstly, a 3 degrees-of-freedom (DOF) time domain hybrid panel method is presented and validated by experimental data in regular oblique waves and irregular head waves. Secondly, the verified 3DOF method is extended to a fully coupled 6 DOF with course control. Finally, taking the C11 containership as test case, parametric roll in oblique waves is computed, and the effects of surge, sway and yaw motions on parametric roll are evaluated with the developed mathematical models. The results show that the effects of surge and sway motions on parametric roll is insignificant, while the effects of yaw motion are more notable. The results of roll amplitudes and standard deviation of roll angles show that the model based on 3 DOF is relatively conservative, and can be directly used for the stability assessment of parametric roll.