Added Mass of an Oscillating Hemisphere at Very-Low and Very-High Frequencies

Abstract

A floating hemisphere under forced harmonic oscillation at very-low and very-high frequencies is considered. The problem is reduced to an elliptic one, that is, the Laplace operator in the exterior domain with Dirichlet and Neumann boundary conditions. Asymptotic values of the added mass are found with an analytic prolongation for the surge mode, and with a seminumerical computation with spherical harmonics for the heave one. The general procedure is based on the use of spherical harmonics and its derivation is based on a physical insight rather than a mathematical one. This case can be used to test the accuracy achieved by numerical codes based on other formulations as finite or boundary elements.