Free-surface hydrodynamics of a submerged prolate spheroid in finite water depth based on the method of multipole expansions

Abstract

Free-surface hydrodynamics of a submerged elongated (prolate) spheroid in water of finite depth is considered by employing spheroidal harmonics and the method of multipole expansions. In particular, we present semi-analytic solutions for both the wave making resistance and wave diffraction fundamental problems. Although these two cases are generally treated separately, it is demonstrated here that by using the present general methodology, the analytic procedures of these two problems are quite similar and thus the corresponding solutions can be obtained by using almost a single effort. The motion of the prolate spheroid is rectilinear and steady in a direction parallel to the undisturbed free surface and rigid planar bottom. The ambient wave field is assumed to be monochromatic with an arbitrary inclination angle with respect to the body's major axis. The Green's function based solution, employs Havelock's formula for the ultimate image singularity system which avoids redundant surface integrations and solving integral equations. Numerical simulations of the linearized Kelvin-Neumann problem for the hydrodynamic forces and moments exerted on the moving spheroid for different depths of submergence and flow parameters are presented and compared against the existing data, given mainly for spherical shapes. The present method is claimed to be simpler to implement and more versatile, yet more accurate with respect to existing codes. Aside from free surface hydrodynamics, it can be also extended to other harmonic practical problems involving interacting ellipsoidal geometries in confined domain.