Interference effects on the Kelvin wake of a monohull ship represented via a continuous distribution of sources

Wave-interference effects on the wave pattern of a monohull ship that advances at constant speed along a straight path in calm water are considered. The flow around the ship is represented via a continuous distribution of sources over the hull surface, rather than via a point source at the bow and a point sink at the stern. A practical and realistic numerical method for determining the apparent wake angle ψmax, where the largest waves are found at high Froude numbers, for general ship hulls (including multihulls and/or distributions of pressure at the free surface) is considered. The method only involves elementary numerical computations that can be performed simply and efficiently. The method is therefore used here to perform systematic computations for seven ship hulls that correspond to broad ranges of main hull-shape parameters (beam/length, draft/length, beam/draft, waterline entrance angle) at ten Froude numbers. This numerical study shows that the apparent wake angle ψmax is only weakly influenced by the shape of the ship hull. A useful practical consequence of this numerical finding is that the wake angle ψmax can be estimated for general monohull ships via simple analytical relations. These relations provide relatively-accurate practical estimates (without computations) of the apparent wake angle ψmax(F) for arbitrary ship hull forms and Froude numbers. The explicit approximations for the wake angle ψmax(F) obtained here account for both longitudinal interference between the divergent waves created by the fore and aft regions of a monohull ship and lateral   interference between the divergent waves created by the port and starboard sides of the hull. As expected, these relations yield an estimate of the wake angle ψmax(F) for a monohull ship that is more precise than the analytical estimate given by an elementary analysis of interference between the dominant waves created by the bow and the stern of a ship, which corresponds to a 2-point wavemaker approximation of the continuous hull-surface distribution of sources considered here.