Nonlinear hydrodynamic forces on an accelerated body in waves

Wave-drift added mass results from nonlinear interactions between waves and low-frequency oscillatory motions of a floating body, in the presence of incident waves. In previous works, wave-drift damping which is the component of wave-drift force in phase with the velocity of low-frequency oscillations was investigated mainly based on a quasi-steady analysis. However, investigations related to wave-drift added mass, the component in phase with acceleration, were very few. In this paper wave-drift added mass is derived directly from a perturbation analysis with two small parameters and two time scales, using a Cartesian coordinate system that follows the low-frequency oscillations, dynamic oscillation model has been used. Especially, the method to solve higher-order potentials, which are necessary for evaluation of wave-drift added mass, is presented. Analytical solutions and calculated results of wave-drift added mass, and far field radiation conditions for each order of potentials are obtained. Also, wave-drift added mass of floating bodies has been systematically measured from a slowly forced oscillation test or a free decay test in waves. Experimental results are compared with calculated results. Then, for a supplement, the secular behavior that some velocity potentials show is discussed. Applying a multiple scale perturbation analysis to one of these problems, a nonsecular solution is obtained.