A brief outline is given of the way in which waves and currents have traditionally been treated in the offshore design process. Emphasis is put on three unsatisfactory features:

  • the arbitrary selection of one of a range of mequivalent wave-kinematic theories

  • the lack of a sound theoretical basis for extension of the current velocity profile above the mean sea level up to the wave crest

  • the neglect of any interaction between the wave and current flows, both in the measurement of currents in the wave zone and in calculations of the total fluid flow

This chapter reports some developments in non-linear wave-current interaction theory which promise to help resolve these problems.


In the design of an offshore structure, a major input, which largely constrains the overall design, is the load due to extreme environmental forces, and in particular that due to waves and currents. Although in reality the fluid flow giving rise to such forces is a three-dimensional stochastic process, in the great majority of offshore designs this is modelled by a regular two-dimensional wave motion, superimposed on a one-dimensional current flow aligned along the direction of wave propagation, with a prescribed vertical profile. The parameters required to specify this flow- the wave height and period, the still-water depth, and the depth-average current-are supplied by an oceanographer, who may draw on local measurement or computer hindcast, and who will provide some elements of analysis and interpretation, including assessments of appropriate extreme value distributions, joint probabilities of extreme surge and tidal currents etc.

The present chapter is not concerned with the justification for his two-dimensional idealization of the three-dimensional reality, or with the process by which the ‘environmental design parameters’ are selected. Nor is it concerned with the use made of the two-dimensional fluid velocity profile in the design rather, it is concerned with the intermediate steps between these. In traditional design practice, these staps are:

  • to compute the wave velocity profile, using a suitably chosen non-linear wave theory, and ignoring the presence of the current

  • to establish the current profile up to the still-water level, using any available ‘engineering’ or ‘oceanographic’ insights

  • to extend the current profile up to the instantaneous sea surface, in particular up to the wave crest, using any available hydrodynamic insights

  • to superimpose the wave and current flows by liner addition of the velocity and acceleration vector fields, taking no account of any effect due to interaction of the wave and current

These four steps are considered in more detail in the following sections.

Non-linear Wave Kinematics

A range of non-linear wave theories is available, and there is a widespread belief that for any given set of environmental design parameters, one or more of these theories is applicable, and that if several are applicable they yield similar results.

The range of applicability of the different wave theories is considered in some detail by Sarpkaya and Isaacson (1981).

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