A numerical model is described which allows to simulate the slow-drift motion of moored tankers, in waves, wind, and current. Emphasis is put on the physical problems for which a better knowledge is required in order to improve the model. Some numerical applications are presented.


For the past years IFP has been carrying out a thorough research program on wave-drift forces and slow-drift motion of moored tankers. In a previous OTC paper I it has been described how wave drift forces in regular waves could be obtained from potential theory, through diffraction-radiation codes. In irregular waves the drift force varies according to the wave envelope squared, and induces slow-drift motion of moored structures. Wind and current also play an appreciable role, and in some cases may cause dynamic instabilities of the system 1.

So far the only tools for designs of SPM systems have been model testing and rules of thumb based on previous experience and the calculation of mean wind and current loads 2. In most cases model testing remains the only alternative for the final design of a system however the need is felt for more handy and less expensive tools for preliminary designs or parametric studies.

In the recent past different attempts at solving this problem numerically have been proposed. Due to the many occurring non-linearities, simulation models are usually preferred ',4, eventhough they present some disadvantages regarding the statistical interpretation of the results. Models dealing directly with the statistics 5 or working in the frequency domain are so far restricted to academic cases.

The main difficulty in elaborating a simulation model for slow-drift motion consists in formulating properly the hydrodynamic exciting loads and damping terms. Since one is dealing with a resonant system the latter ones are as important as the former ones, even- though they have been kind of overlooked in many instances. The first paragraph consists in a short presentation of the simulation model. In the second one some considerations are given on the problem of properly formulating the hydrodynamic loads and damping. They aim more at pointing out where the problems are than at providing solutions. Last the third paragraph presents some results obtained with the model, and discusses their validity.


Figure 1 schematically illustrates the problem that is considered: a tanker moored by a hawser to a buoy anchored in 0, and exposed to waves, wind, and current coming from different directions in the horizontal plane. The wave-system, defined by its power spectrum S(w), is assumed to be mono directional, while the wind and current may be time varying.

The position of the tanker is referenced by the horizontal coordinates (xG,YG) of its center of gravity G, its heading, together with its vertical coordinate ZG.

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