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A numerical model has been developed to determine the large-amplitude motions of a steered vessel subjected to severe wave conditions, including those that may lead to capsizing. The model was used to identify different modes of capsizing, and to study relevant mechanisms and conditions. In this paper emphasis is placed on the theoretical aspects. The nonlinear model combines both potential and viscous flow effects, where integrations are carried out in the time domain over the instantaneous free surface; first-order memory effects are taken into account, and the free surface can be irregular, Some new results are presented concerning statistical properties relevant to the simulation of random following or quartering seas.

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The influence of wind, waves and current on the dynamic behavior of a single-point moored ship is investigated. Numerical simulations were used to compute the low-frequency motions of a tanker in the horizontal plane and the bow hawser force. Parameters varied comprised loading condition, hawser length and environment. A detailed overview is given of the theory for calculating the various force contributions in the numerical model. The onset of unstable motion behavior is described for both steady and unsteady wind, wave and current conditions. Unstable behavior tends to be more predominant for the lightly loaded condition. In the fully loaded condition the vessel behavior is generally very stable, except when the current direction is unsteady.