Study on nonlinear wave motions and wave forces on ship sections against vertical quay in a harbor

A two-dimensional time-domain coupled numerical model isdeveloped to calculate the nonlinear wave forces acting on a ship sectionagainst vertical quay in a harbor. The fluid domain is divided into an innerdomain and an outer domain. The outer domain is the area between the leftside of the ship section and the incident boundary, where the flow canbe expressed byBoussinesq equations. The rest area is the inner domain, which is the domainbeneath the ship section plus the domain between the right side of the shipsection and the vertical quay wall. The flow in the inner domain can be expressed byNewton's Second Law. Matching conditions on the interface between the innerdomain and the outer domain are the continuation of volume flux and theequality of pressures. The numerical results of the coupled model agree wellwith the experimental data for wave elevations and wave forces. The naturalfrequency of the fluid motions in the gap between a ship section, seabed andvertical quay wall is derived. It is shown from the experimental data andnumerical results that the resonance waves in the gap are induced by the first orhigher harmonics of incident waves, and the first or higher order horizontalwave forces on the ship section against vertical quay wall increasegreatly whenthe frequency of the harmonics of incident waves is close to the naturalfrequency of fluid motions in the gap.