The kinematics under the crest of the highest waves in five two-dimensional two component wave groups are presented. The highest wave in each group had the same gross characteristics of wave height and period but each group has a different separation between the two fundamental components The measurement technique used, Particle Image Velocimetry, allowed velocity measurements to be made up to about 90% of the wave height.
The measured kinematics were compared with Linear Theory, its Wheeler Stretching derivative and Dean's Stream function (taken to 21st order) It was found that Linear & Dean's theory performed well at all depths for monochromatic waves and long groups but that all the theories underpredict crest kinematics in the shortest wave groups. Wheeler stretching did not perform well near the surface of any of the waves.
Over the years various approaches have been taken to the calculation of environmental forces. In the case of wave loading the prediction of the kinematics within the crest of extreme waves is vital. In determining the design criteria a statistical process is used to determine a design wave of given height and period. That wave is then modelled computationally using a high order wave theory - the choice of which depends on a number of factors (such as combinations of water depth, wave height and period) recently reviewed (Barltrop 1989). The design wave is assumed to be monochromatic and extending to infinity and the forces on a structure are predicted from the local velocities and accelerations calculated for the wave.
Much work has gone into attempts to verify or improve upon the methods used in these calculations For example Fenton (1985) published a correction to the Stokes Vth theory of Sk jelbreia and Hendrickson (1962). Cokelet (1977) derived an exact solution for waves of finite amplitude in any depth of water, although this is seldom applied in engineering design. Dean (1965) formulated his theory in terms of the stream function and published tables of coefficients to facilitate its use. Chaplin (1980) reformulated this solution by taking water depth, wave height and period as the independent parameters and using the surface elevations as the unknown. This theory can now be taken to any order without recourse to tables.
Linear or Airy theory is still used for many purposes because of its simplicity, its low computation time, its easy capacity for absorbing many components and its ability to model three dimensional sea-states. Wheeler (1970), Chakrabarti (1971), Cudmestad and Connor (1986) and Lo and Dean (1986) have all proposed stretching modifications to linear theory which reduce the errors in the free surface boundary conditions but which, in doing so violate the Laplace equation Wheeler's modification was proposed because of observed discrepancies between measurements and linear theory, in particular the high frequency contamination observed in the crests of waves.
