Far-field representation for the vertical force on a floating structure

Equations are derived that relate the vertical hydrodynamic force on two- and threedimensional structures that are floating in a fluid of infinite depth to the far-field dipole coefficient in the velocity potential. By an application of Green’s theorem to the radiation or scattering potential and a suitable test potential, the heave added mass, the heave damping and the vertical exciting force are shown to be expressible in terms of the dipole coefficient in the relevant potential. The results add to the known reciprocity relations, which relate quantities such as the damping and the exciting force to the amplitude of the far-field radiated wave. The expressions are valid at all frequencies, and their high- and low-frequency asymptotics are investigated.