Numerical study on breaking phenomena of ships’ waves in narrow and shallow waterways

The environmental impact of a ship’s waves, such as the risk of erosion of coasts and riverbanks, and unacceptable ship movements in a restricted waterway, is now a significant ship design criterion. Therefore, it is necessary to predict ship-wave phenomena accurately in a restricted waterway. In this study, a numerical investigation of the breaking phenomena of a ship’s waves in restricted waterways was carried out. Incompressible Navier–Stokes and continuity equations were employed. The equations are discretized by a finite-difference method in a curvilinear coordinate system. The interface capturing method was applied to simulation of a ship’s waves, including wave-breaking. A modification of the level-set method is proposed to find the free surface shape clearly and without difficulty of the implemation of the boundary conditions for the distance function. In order to obtain a high resolution of wave height, a constrained interpolated profile (CIP) algorithm is adopted. In order to check the advantage of the CIP method, computations by two numerical methods, the CIP and the 3rd-order up-wind scheme, were compared. The computations for a Wigley hull in restricted waterways were performed and compared with experiments. The phenomena of ships’ waves in restricted waterways are discussed in order to understand the mechanism of wave-breaking in relation to the change in water depth along a waterway.