Ultimate Image Singularities in Oblate Spheroidal Coordinates with Applications in Hydrodynamics

Abstract

This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamical applications. The theorem provides explicit relations that express the oblate spheroidal harmonics, given in terms of the fundamental solutions of the Laplace equation. Here, the theorem is employed to transform the underlying Green’s function into the relevant coordinate system and, consequently, to formulate the diffraction potential. The case considered refers to the axisymmetric placement of the spheroid, namely, symmetrical axis perpendicular to the free surface. The mathematical formulations have been implemented numerically providing exceptionally accurate computations, which manifests the consistency and robustness of the relevant formulas.

Keywords

• image singularities
• miloh theorem
• oblate spheroids
• green’s function
• sources
• multipoles
• hydrodynamics