Extended Velocity Potential Wave Kinematics

A double Fourier series expansion of the velocity potential for water waves was used to treat nonlinear single harmonic waves and irregular waves measured in the ocean test structure experiment. The (extended) velocity potential (EXVP) satisfies the governing hydrodynamic equations in the body of the water and matches the boundary conditions at the waves surface in the least-squares sense. The waves that are treatable with this velocity procedure can have a range of crest values for a specified wave height, period and water depth. In contrast, the common Stokes velocity procedures can treat only waves of fixed crest, for a given wave height, period and water depth. The water velocities measured for irregular waves in the ocean test structure experiment are in good agreement with the velocities predicted by this procedure; these correlations are significantly better than velocity correlations with the Stokes wave representation.