An extension of general identities for 3D water-wave diffraction with application to the Diffraction Transfer Matrix

Interaction theories are used in numerous branches of physics to efficiently evaluate wave scattering by multiple obstacles. An example of these interaction theories is the direct matrix method introduced by Kagemoto and Yue [1], which enables fast computation of three-dimensional water-wave multiple-scattering problems. The building block of interaction theories is a mathematical operator that encapsulates the mapping between incident and scattered waves. This operator is generally referred to as T-matrix and satisfies both reciprocity and energy identities. In some branches of physics, such as acoustics and electromagnetism, these identities are well established; in hydrodynamics, however, they have only been derived for a T-matrix that maps two-dimensional incident and scattered water waves. In three dimensions, water waves can be represented as a series expansion of cylindrical eigenfunctions. In this paper, we use this representation of water waves to derive the reciprocity and energy identities satisfied by the T-matrix of the direct matrix method, known as Diffraction Transfer Matrix (dtm). The identities derived herein represent an extension of existing general relations between two diffraction solutions. We show that this extension can be applied to verify the accuracy of the dtm entries, thereby increasing the reliability of existing schemes for computing the dtm. We present results for the dtm of two geometrically different isolated obstacles, as well as for the dtm of an asymmetric array. Finally, we demonstrate that the results presented herein can be extended to floating bodies found in a wide range of ocean engineering problems.     

Sea state characterisation of the test site of an offshore wave energy plant

The Archimedes Wave Swing (AWS) pilot plant, rated at 2 MW, was tested offshore at Póvoa de Varzim in northern Portugal in 2004, gathering a large team of engineers and scientists. The Mechanical Engineering Department of Instituto Superior Técnico was involved, following previous work done for the project. The present paper describes one of the studies conducted. It aims to characterise the sea state at the actual location of the pilot plant using the available pressure sensors. Two approaches were performed: a first one purely based in linear wave theory, neglecting the presence of the device, and a second one, based on the results from a Boundary Element Method (BEM) code named AQUADYN, originally developed at École Centrale de Nantes (France), which allowed a detailed quantification of the effects of the presence of the plant on the wave profile directly above it. Comparisons with a Datawell Waverider buoy located at a certain distance from the plant also played an important role in the current study.