The cylindrical wave field of wave energy converters

Abstract

Knowledge of the wave field modification by a wave energy converter (WEC) is important to device and wave farm design. Cylindrical solutions to the linear wave field have long been used to analytically compute wave forces on circular-cylindrical geometries and have been the means of an important multi-body interaction theory. The cylindrical solutions are valid for an arbitrary geometry, but previous methods for computing the necessary coefficients were cumbersome. Herein, we present a new method for computing the cylindrical wave-field coefficients for an arbitrary geometry from a known circular-cylindrical section of the wave field. The method employs the Fourier transform and the orthogonality property of the depth dependence. The necessary circular-cylindrical section of the wave field is computed with the industry-standard boundary-element-method solver, WAMIT. Coefficients are computed for the radiated and scattered wave fields of four WECs, a heaving point absorber, a surging point absorber, a terminator, and an attenuator. The resulting cylindrical wave fields are compared over a large domain to wave fields computed completely by WAMIT and are found to be very accurate. The asymptotic representation of the cylindrical wave field is also considered and its range of accuracy is shown to depend the number of partial waves used to accurately represent the cylindrical wave field. Analytical solutions to the WEC wave field enable the use of interaction theories that accelerate WEC array computation and the integration with wave models that include additional physics.