To realistically simulate motions of a floating cylinder in waves, a fully nonlinear model that includes the effects of viscosity is developed. The equations of rigid-body motions are coupled with the Navier-Stokes equations, which are solved by the Free-Surface Random-Vortex Method (Yeung & Vaidhyanathan, 1994). Inviscid results that are of interest for comparison or validation purposes can be recovered by "shutting-off" viscosity in this tbrmulation. This nonlinear model is first applied to study the transient response of a body with initial displacements for pure heave or roll motion, for comparison with some existing inviscid results. Frequency-domain response in waves is obtained by simulating heave motions in the time domain over a range of frequency. For a freely-floating body in waves, the roll amplitude near resonance is observed to be reduced by viscosity by as much as 50%. The fully nonlinear model is validated by comparing the numerical results with those from the measured values of Sen (1993), revealing considerable improvement over existing predictions based on inviscid fluid.


Recent advancement in computational power and numerical algorithms encourage the development of time-domain solutions for body motions in waves. Time-domain analysis is preferable when transiedt response and large-amplitude motions of bodies are of concern. For motion involving substantial viscous effects, the time-domain formulation is the only logical approach. One of the first attempts to solve the time-dependent problem was given by Maskell & Ursell (1970), in which the transient response was calculated based on known frequency-domain hydrodynamic coefficients. Chapman (1979) obtained the transient response of a floating body by representing the radiated wave field in terms of a finite sum of harmonics. Yeung (1982) formulated the heave transient response of a floating body via the use of an unsteady Green function that satisfies the linearized free-surface boundary conditions.

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