Surface Particle Orbits in Uniform Waves

A numerical method is developed for calculating free-surface particle velocities in steady-state gravity waves of known profile. The method generates a unique solution for the orbit of a particle in the free surface, such that its motion is compatible with the observed wave profile, wavelength and surface mass transport velocity, and satisfies the dynamic free-surface boundary condition. Velocities of all free-surface particles may be derived from the geometry of the orbit. Velocities computed from the profile of a wave generated in the laboratory are shown to be compatible with simultaneous subsurface velocity measurements by the Laser Doppler Anemometer. The method has proved valuable in calculating impact velocities in wave slamming experiments. In view of the scatter apparent in almost all experimental evaluations of wave force coefficients, it is suggested that the method be applied to check the validity, at the free surface, of wave theories used in deriving coefficients from measured forces.