An efficient method for the numerical evaluation of the free-surface Green function for deep-water application was presented by Telste & Noblesse (1986) and again by Ponizy et al (1994). A FORTRAN code was include in their 1986 paper. The numerical method makes use of known mathematical functions. Numerical values of some of these mathematical functions were depicted, but no verification on the accuracy of the Green function routine in an application was given. The purpose of this paper is to compare their numerical values in the near-field and far-field regions with other similar computation for the infinite-depth Green function. The results of the infinite-depth Green function are also compared with the results from the finite-depth Green function that is more time consuming. Based on the accuracy of the various methods, the regions of application of the efficient deepwater Green function formulation and the effect of the water depth on the Green function are discussed. Any regions of inaccurate results are noted. Forces on submerged offshore structures and motions of the floating structures are determined using the lower-order panel method and these different Green function routines. The results on the motions of a semisubmersible in various water depths are compared and the accuracy of these routines in various regions is shown. The presented results will help the hydrodynamicist and designer to evaluate the suitable formulation and its regions of application for the accurate analysis and design of offshore structures.

The wave forces on a fixed two-dimensional object submerged in water of finite depth are obtained under the assumptions of linear wave theory. The far-field characteristics of the wave interaction with the object are also examined. The boundary-value problem for the wave potential is formulated in terms of Green's theorem, and the resulting integral equation is solved numerically. Results for a submerged and half-submerged circular cylinder and a bottom-seated half cylinder are presented. In the limiting case of infinite depth the numerical results compare quite well with known solutions.

In a recent paper, Raman et al (RJV) [1] 2 presented a second- order solution for the wave interaction with a large-diameter, bottom-mounted, surface-piercing, fixed vertical cylinder. Earlier, Chakrabarti [2,3] obtained an approximate solution for the vertical cylinder due to Stokes's fifth-order wave. Later, Yamaguchi and Tsuchiya (YT) [4] proposed a second-order solution in a closed form for the wave interaction problem with the vertical cylinder which was examined by Chakrabarti [5]. All these solutions are different due to the assumptions regarding the frequency of the scattered wave and the kinematic free-surface boundary condition. RJV [1] claim that their solution is superior to the earlier solutions because, according to them, it satisfies the nonlinear free-surface boundary conditions completely.

Dynamic effects due to waves on a large vertical circular cylinder were measured experimentally in a wave tank in the form of pressures, forces, and moments. The experimental data were compared with the wave diffraction theory following the classical analysis of Havelock on a fixed obstacle in waves. The viscous effects were neglected in the analysis on the assumption that for a cylinder of this size the inertia force is most predominant. The maximum horizontal force was found to correlate well with the theory. The pressure decay below the still water level followed the hyperbolic cosine law. Linear variation of pressure up to the free surface was found to be conservative.