Analytical and approximate solutions of the wave-current interaction problem are reviewed and the results on typical North Sea conditions are compared It is shown that the linear superposition method may give results which are in close agreement with analytical predictions when appropriate modifications are made. The wavelength and the kinematics under the crest below the still water level are best predicted when the apparent period is used and near the water surface when the actual period is used. The agreement is better when the current is evaluated at the particle mean position or the current profile is linearly stretched without maintaining flow rate


The problem of wave-current interaction has attracted the interest of a large number of researchers Peregrine and Jonsson (1983) and Srokosz (1985) presented comprehensive reviews of the Subject. In these papers the problem is very well described providing extensive theoretical backround and a concise list of references. This paper has a rather specialised scope, it deals with analytical and approximate solutions of predicting the cater particle kinematics in a wave-current environment a problem frequently encountered in the offshore engineering industry

The water particle kinematics in a wave-current regime are commonly predicted using the linear superposition method, the kinematics associated with a wave of the same period. In a zero current environment are added to the current This method does not take account of wave-current interaction effects.

Analytical solutions have recently been developed that solve the wavecurrent interaction problem for Stokes 5th order waves on a uniform current (Fenton 1985). Stokes 3rd order on all near shear current (Kishida and Sobey, 1988) and Stokes 5th order on a bilinear current (Eastwood and Watson. 1989) These solutions of wave-current interaction problems have not been validated by experimental results, mainly because of the difficulty involved in generating regular steep waves on a non-uniform current.

An internal research and development project within the Noble Denton Group aims to investigate the sensitivity of the environmental forces on marine structures to the method of predicting the water particle kinematics The analytical solutions described above have been implemented in FORTRAN Programs

In this paper the water particle kinematics as predicted from the analytical solutions are initially compared against one another, and then with those predicted from the linear superposition method. The sensitivity of the wave forces to the method of wave-current interaction has been assessed in research funded by the UK Department of Energy (1987) The sensitivity results are extended to Include the above listed recent analytical solutions and the approximate three-step kinematics method (Dalrymple and Heldeman. 1989


In this section, the main features of the various analytical solutions are highlighted for the common problem in which the wave height, wave period water depth and current profile are the given data and the wave kinematics are required.

Stokes 5th Waves - No Current

The solution derived by Skjelbreia and Hendrickson (1960) is widely used in the offshore industry. It has been used in numerous cases.

This content is only available via PDF.
You can access this article if you purchase or spend a download.