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 semi-numerical computation with spherical harmonics
for the heave mode. 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. [To appear in Journal Fluids Engineering ASME]