Application of the Free-Surface Random-Vortex Method (FSRVM, Yeung, 2002) is made to investigate two types of forced motion problems with the effects of viscosity considered. A submerged body undergoing periodic swaying oscillation is considered and compared with results of the vorticity-diffusion theory of Yeung and Wu (1991), the latter with the convective terms of the Navier-Stokes equations neglected. A practical shape consisting of a rectangular cylinder with horizontal and vertical keels or baffle-plates is used to study the roll inertia and damping characteristics. Comparison with some recent experimental results are made to illustrate the efficacy and accuracy of the theory.
With an increase in the variety of design solutions for offshore drilling and operation systems, such as FPSOs, truss-spar systems, multi-hull support, among other unconventional shapes, it is helpful that a scientifically rational and fast method be available to estimate and evaluate the hydrodynamic characteristics of these systems. Hydrodynamic properties affect exciting wave loads, stability and amplitude of motion repsonse, structural integrity, safety and hazards of operations. In this paper, we have undertaken a special study of applying a recently developed viscous-flow computational method to two specific problems related to cylindrical sections. The method of analysis called Free-Surface Random-Vortex Method (FSRVM) was outlined in Yeung et al. (1998) with an overivew of its wide-ranging capabilities given in the review article of Yeung (2002). This is a considerable improvement over the solution of the linearized Navier-Stokes flow developed in the 90's by Yeung & Wu (1991). This work provided the necessary Green-function expressions for viscous flow by neglecting the convective terms in the Navier-Stokes equations, yet allowing the inclusion of free-surface effects. This was essentially a free-surface "Vorticity-Diffusion" theory, which marked the beginning of the many recent efforts to model viscous effects on free-surface flows.
