A Simplified Method for the Evaluation of Floating-Body Motion Responses over a Sloping Bottom

Recently, many floating renewable energy platforms have been deployed in coastal regions, where sloping bottoms are an important factor when evaluating their safety. In this article, a simplified method coupling an eigenfunction matching method (EMM) and a finite-depth Green's function (FDGF) is developed to evaluate floating-body motion responses over a sloping bottom for which bathymetry is homogeneous in the longshore direction. We propose an extended EMM to create an incident wave model over the sloping bottom, thereby obtaining the Froude-Krylov (F-K) force and Neumann data on the wet surfaces of the floating body for the diffraction problem. An equivalent depth is introduced to account for the interaction between the sloping bottom and floating bodies when dealing with the diffraction and radiation problems. The accuracy of the present method is validated through a comprehensive comparison with numerical and/or experiment results for a liquefied natural gas (LNG) ship and a floating hemisphere from the literature. Generally, the present, simplified method can give predictions with sufficient accuracy.