The laminar flow about a circular cylinder beneath a Stokes waves train is numerically investigated. An efficient grid free algorithm is developed by coupling an accurate boundary integral equation method for computing the velocity field with a viscous vortex method for solving the Navier Stokes equations near the body. The problem of generating the incident wave system is effectively circumvented by means of a perturbation formulation which assumes the Stokes wave solution as the base flow. Forβ ≈ 500 and Kc = Ο(1) the systematic comparison with the available experimental values for the Fourier components of the loading is presented. An overall good agreement is observed, even for the added inertia coefficient which is known to be largely affected by viscous effects.
The flow of an incompressible viscous fluid about a circular cylinder beneath a regular Stokes wave train is a typical problem of marine structures hydrodynamics. When the relevant wavelengths are comparable with the characteristic dimension of the body, the hydrodynamic loads are quantitatively dominated by the momentum exchange between the wave and the body. Consistently, it is widely accepted that the nonlinear potential flow theory effectively describes the force on the structure. In fact, the experimental analysis confirms that the vertical mean value of the hydrodynamic force and of both the second and third harmonics of the fluctuating components are well explained in terms of the inviscid wave diffraction in agreement with the predictions of weakly or fully nonlinear models (Ogilvie, 1963, Vada, 1987 and Liu et. al., 1992). However, the potential theory fails to capture exhaustively the entire phenomenon. Actually, a significant reduction in the amplitude of the fundamental harmonic of the loading is emphasized by Chaplin (1984), with respect to purely inviscid models.