The Method of Image Singularities Employed for Oscillating Oblate Spheroids under a Free Surface

Abstract

The main objective of this study is to develop a semi-analytical formulation for the radiation problem of a fully immersed spheroid in a liquid field of infinite depth. The term “spheroid” refers herein to the oblate geometry of arbitrary eccentricity and to the axisymmetric case, where the axis of symmetry is normal to the free surface. The proposed numerical approach is based on the method of image singularities, and it enables the accurate and fast calculation of the hydrodynamic coefficients for the translational degrees of freedom of the oblate spheroid. The excellent agreement of the results, with those of other investigators for the limiting case of the sphere and with those obtained using a respected boundary integral equation code, demonstrates the accuracy of the proposed methodology. Finally, extensive calculations are presented, illustrating the direct impact of the immersion depth and the slenderness of the spheroid on the hydrodynamic coefficients.

Keywords

• image singularities
• Miloh’s theorem
• hydrodynamics
• radiation
• oblate spheroids