Estimating Wave Induced Kinematics Underneath Measured Time Histories of Surface Elevation

The present paper is concerned with the accurate prediction of nonlinear wave kinematics underneath measured time histories of surface elevation. It is desired to develop a method which is useful in analysis of offshore measurements close to wind turbine foundations. The method should therefore be robust in relatively shallow water and should be able to account for the presence of the foundation and the shortcrestedness of offshore seastates. The present method employs measurements of surface elevation time histories at one or a small number of locations and solves the associated velocity potential by minimizing the error in the free surface boundary conditions. The velocity potential satisfies exactly Laplace’s equation, the bed boundary condition and (optionally) the boundary condition on the wall of a uniform surface piercing column. This is achieved by associating one wavenumber with every wave frequency thereby sacrificing the possibility of following the nonlinear wave evolution but ensuring a good description of the wave properties locally. For shortcrested waves, the direction of wave component propagation is drawn from a known or assumed directional spectrum. No attempt is made to calculate the directional distribution of the wave field from the surface elevation measurements since this is usually not realistically possible with the available data. The method is set up for analysis with or without a uniform current, for shortcrested or longcrested waves and with or without a surface piercing column in the wave field. It has been compared with laboratory data for steep longcrested and shortcrested waves. The method is shown to be in good agreement with measurements. Since the method is based on a Fourier series of surface elevation, however, it cannot model overtopping breaking waves and associated wave impact loading. For problems where wave breaking is important, the method may serve as a screening analysis used to select wave events for detailed analysis using Computational Fluid Dynamics (CFD).