In this paper the basic expressions for the computation of mean and low frequency second order wave drift forces on floating structures in directionally spread seas as can be derived from potential theory are discussed. The resultant expressions for the mean and slowly varying drift forces are applied to a specific form of the directional seas, i.e. cross seas which consist "of two irregular long-crested wave trains from different directions. The analysis shows under which conditions the drift forces in irregular cross seas may be calculated based on the superposition of the 'drift forces from the component long-crested irregular wave trains. Model tests were carried out with the model of a 200,000 DWT tanker moored in regular and irregular cross seas. The results of the model tests confirm theoretical predictions regarding the superposition of mean drift forces and the interaction effects present in slowly varying components of the drift forces in directional seas.


The analysis of the behaviour of vessels moored at sea is generally based on measurements from model tests in irregular uni-directional waves carried out in suitable model facilities.

Data obtained from such model tests has in the past proved to be indispensable in the design of offshore floating structures. Although, at all times, the conditions of the model tests represent a simplified reality, the on-site performance of full scale structures bears witness to the general validity of such model test data as a sound basis for judging the performance of a particular design with regard to both the motion behaviour and the loads on the structures.

Notwithstanding, however, the generally accepted validity of model testing under such simplified conditions, there is a need to investigate, in more detail, the effect of directional spreading of irregular waves, as it occurs in reality, on the loads and motions of floating offshore structures. See, for instance, ref. [1].

One method of obtaining such information is to conduct model tests in basins fitted with wave generators which have the capability to generate irregular directional waves. Such model tests will produce quantitative data, based on a physical reality, of the effects of directional waves. [1],[2] and [3].

Another method of obtaining data on the effects of multi-directional seas on the behaviour of floating structures is based on theoretical computations; [4]. It will be clear that efforts should be made to compare results of such computations with model test results. This is necessary since significant physical effects peculiar to directional seas may be present which are not accounted for in the theoretical approach.

For irregular uni-directional seas, computation methods exist which can, with reasonable accuracy, predict the behaviour of a moored vessel in both the frequency and the time domain; [5] and [6].

This type of computer program can be used to assess certain aspects associated with multi-directional seas provided a realistic formulation can be given for the wave loads, both oscillatory, first order wave loads and mean and low frequency second order drift forces in irregular directional waves, [7].

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