The Motions of a Moored Ship in Waves

It is the intention of this thesis to formulate a mathematical model which can be used for computer simulations of the behaviour of a moored ship in waves. In order to achieve this, two problems must be solved. First, a set of equations of motion must be drawn up, which can describe adequately the behaviour in six degrees of freedom of a ship, moored by means of a non-linear mooring system in regular or irregular waves. Second, a method must be found for the computation of the wave forces and the hydrodynamic reaction forces acting on the ship. For the description of the motions, the six coupled equations of motion in the time-domain according to Cummins are used. These equations can bake into account non-linear and asymmetric restoring force characteristics of the mooring system, while the exciting forces may be arbitrary. The only restriction of these equations is that linearity is assumed of the hydrodynamic restoring forces. In general, mooring of ships occurs only in areas with a restricted water depth. In shallow water the flow around a ship has a three-dimensional character, and therefore the three-dimensional source technique is applied to obtain the wave loads and hydrodynamic reaction forces on the ship. Based on the linear potential theory, this technique supposes an ideal fluid and small amplitudes of waves and motions. The effect of a forward speed is not included in this method, but this is not of interest for moored ship problems. The influence of a restricted water depth and a quay parallel to the ship can be taken into account. An extensive experimental verification has been carried out by means of model tests, for a 200,000 tdw tanker in shallow water (the keel clearance amounted to 20 percent of the draft). Comparative computations and measurements of wave loads, hydrodynamic restoring forces and free floating ship motions have been carried out. Further, computer simulations have been made for the case that the ship is mooted in regular and irregular waves to a jetty, by means of mooring lines and fenders. The results of these computations are also compared with those of model experiments. An analysis of the results obtained shows that the typical behaviour of the moored ship, with subharmonic motion response, is represented adequately by the mathematical model. In conditions where the ship is pushed against the fenders by the waves, the subharmonic motions are caused mainly by the non-linear characteristics of the mooring system. When the angle between direction of wave propagation and the longitudinal axis of the ship is small, or in case the ship is pushed away from the fenders by the waves, it appears that the second order wave force has a dominant influence on the low frequency motions of the moored ship.