Synthetic fibre ropes are preferable for taut moorings due to their low weight to strength ratio, which facilitates the reduction in cost. But the fibre ropes exhibit significant nonlinearity and viscoelasticity behaviour, which introduces difficulty in predicting the mooring dynamic response. The present study proposes a lumped mass method to simulate the dynamic response of mooring line. The elastic modulus of the fibre ropes is assumed to increase linearly with the instantaneous tension and a dashpot parallel to the spring is employed to represent the viscoelasticity. Six mooring configurations are employed and different types of motion are imposed to the fairlead. The energy dissipated by the hydrodynamic force and the viscoelastic force is calculated by the work done, which clarifies the damping characteristics of taut mooring lines.

The super-rogue wave solutions of the nonlinear Schrödinger equation (NLS) are numerically studied based on the weakly nonlinear hydrodynamic equation. The super-rogue wave solutions up to the 5th order, also known as the so-called super-rogue waves, are observed according to the results obtained by numerically solving the modified nonlinear Schrödinger equation which is also known as the Dysthe equation that has a higher accuracy along the wave evolution in space. By using the 4th order split-step pseudo-spectral method during the integral process, more accurate results with a smaller conservation error were obtained. It is found that the super-rogue waves can be generated when considering the higher order nonlinearity. The fourth-order terms in the mNLS equation should not be ignored in numerically simulating the evolution of the super-rogue wave formation. The bound wave components also play important roles in the wave evolution. The enhancement of wave amplitude becomes larger due to the influence of bound wave components