shows the schematic diagram of the wave diffraction around a uniform surface-piercing cylinder, which is assumed to be rigid and mounted at the bottom of the seedbed. In the analysis, the origin of the coordinate system is set inside the cross section at the still water level (SWL). In polar coordinates, r and θ are defined in the horizontal plane, and the z -axis is perpendicular to the SWL and positive upward.
Under the action of gravity, the water wave is assumed to be an
ideal fluid with incompressible, inviscid and irrotational characteristics. Based on these conditions, the total velocity potentialof the fluid, Φ(r, θ, z, t ), can be written in a complex form as