Hydrodynamic response of a submerged elliptic disc to surface water waves

Abstract

The impact of an elliptic disc submerged in water of infinite depth on radiation and scattering phenomena is analyzed employing linear water wave theory. The problem is tackled by reducing it into two-dimensional hypersingular integral equations over the surface of the disc. Utilizing a spectral method, where the hypersingularity is evaluated analytically, we obtain numerical solutions for the integral equations. This study presents numerical findings concerning various hydrodynamic parameters relevant to disc scattering and radiation. Initially it compares numerical outcomes with those of a circular disc, before conducting a comprehensive parametric investigation for the elliptic disc. The primary focus is on investigating how the submerged depth and the geometry of the disc impact physical quantities such as added mass, damping coefficient, surface elevation, differential cross-section, and exciting forces. The results reveal a noticeable change in the pressure field around the disc as it approaches the free surface, leading to resonance. Due to the geometry of the submerged rigid elliptic disc, notable alterations in wave profile are noted in the results for both radiation and scattering problems. Furthermore, the radiation problem results reveal significant variations in the added mass and the damping coefficient for non-circular bodies, particularly with a high ratio of the semi-major axis to the semi-minor axis. Overall, this investigation provides a significant benchmark and valuable insights into potential applications in ocean energy and indicates a new design idea of an elliptic base oscillator alongside the commonly used circular designs.