Transient free-surface hydrodynamics using rational approximation of the Green's function

Rational approximations in the frequency domain are developed for the sourc e function of linear free-surface hydrodynamics using the recently uncovere d fourth-order ordinary differential equation (ODE) satisfied by the time-d omain source function. The radiation problem for a floating body In deep wa ter is formulated using a source plus wave-free potential expansion for the fluid. The inherent rational dependence on frequency of the wave-free pote ntials as well as the source approximation are used to develop a system of constant-coefficient ODE's for the radiation impedance which can be used to develop the motion of the body in a simple manner. The technique is applie d to the heaving motion of a floating sphere with good results. The applica tion to more general body geometries is explored by formulating the frequen cy-domain problem using the variational principle of Chen and Mei and explo iting its polynomial dependence on frequency.