One of the continuing topics of interest in the field of design of offshore structures is that of wave-current interactions and their effects on structures. The standard approach to this problem appears to be to ignore any interaction between the waves and the current and simply to add the two together (vectorially), in order to calculate the forces on a structure. This approach carries with it certain difficulties; for example, it is not clear whether it will lead to an under or over-estimate of the forces. Additionally, as the current profile is usually only defined up to the mean level, it is necessary to make ad hoc assumptions about the form of the profile between the mean level and the wave crests. These assumptions are difficult to justify and are therefore unsatisfactory.

Beiboer (1984) has discussed wave-current interactions in relation to engineering design applications. He notes the need for a better understanding of the interactions and also the need for a better statistical description of the joint probability of occurrence of extreme wave and currents. We will not repeat his discussion her, instead, we will pursue only one aspect of the problem he identified. The aim of this chapter is to review the interaction of waves with a current which is steady and uniform in the horizontal plane, but varies with depth. The reasons for restricting our attention to this specific problem are two-fold: first, it is one that is of practical interest to those designing offshore structures; and secondly, to cover all aspects of wave-current interactions would require a much more comprehensive review than it is possible to give here.

For the benefit of readers who want to pursue aspects of the problem not considered here, we recommend the review papers by Peregrine (1976) and Peregrine and Jonsson (1983) Additionally, Peregrine et al. (1983) gave an annotated bibliography of papers on wave-current interaction, while Dalrymple (1973) describes various methods for calculating such interactions in more detail than it is possible to do here. Finally, for more general background information regarding wave kinematics and forces on structures, Carter et al (1986) and Sarpkaya and Isaacson (1981) may be consulted. It is perhaps worth nothing that most of the above references deal with deterministic aspects of the problem, much less is known about the statistics of wave-current interactions.

In this chapter, we will outline the mathematical models that are available for calculating the interaction of waves with a vertically varying current. These models will be considered in the light of such experimental evidence as exists presently, in order to assess their applicability. This will allow us to see where there are theoretical or practical difficulties in the application of the models. On the basis of our review we will give some indication as to which methods are suitable for practical application and also which aspects of the problem require further research. As we have restricted this review to only one are of the problem of wave-current interactions.

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