Prediction of parametric rolling of ships in single frequency regular and triple frequency group waves

• Development of a nonlinear time domain 3D panel code based on impulse response function concept for the simulation of ship's 6 DoF motions.
• Validation of the developed code by comparison with tank tests.
• Correct prediction of the occurrence of parametric roll in all test cases, but less accurate prediction of roll amplitude.

A 3D nonlinear time domain simulation method based on the impulse response function concept is applied to the investigation of parametric rolling of the ITTC-A1 containership. In the numerical simulation, the hydrodynamic coefficients are determined beforehand by a 3D frequency domain panel code on the basis of linear potential theory, whereas the most nonlinear terms in the equations of motion are taken into account, such as the excitation by large amplitude waves (exact Froude–Krylov forces/moments), exact restoring forces/moments resulting from integration of the hydrostatic pressures over the actually wetted surface of the ship and the semi-empirical nonlinear viscous damping correction. In addition, all nonlinear inertia terms are retained when considering solution of large amplitude motions. The parametric rolling is predicted by solving the 6 degrees of freedom (DoF) nonlinear equations of ship motion in the time domain in response to single frequency regular waves and triple frequency group waves. The obtained numerical results are compared with corresponding experimental measurements and numerical predictions of an earlier conducted international benchmark study proving the good performance of the developed method in terms of the predictability of parametric roll phenomena and to a lesser degree to the accuracy of predicted roll amplitude values.