Elementary ship models and farfield waves

Kelvin's classical 1-point ship model, the basic 2-point models of a monohull ship and a catamaran previously studied via elementary geometrical considerations, optimal versions of these two basic 2-point models, and a 4-point model of a catamaran (not considered previously) are analyzed within a common theoretical approach based on potential flow theory, the Green function associated with the Kelvin-Michell linear boundary condition at the free surface, the related Fourier representation of farfield ship waves, and the farfield stationary-phase approximation. The analysis shows that the apparent wake angle associated with the highest waves found inside the cusps of the Kelvin wake as a result of interferences among the divergent waves created by a ship at a high Froude number can be realistically predicted via elementary ship models. In particular, the apparent wake angles for monohull ships and catamarans can be predicted very well via a 2-point model or a 4-point model. Moreover, these models provide basic insight into main features of the farfield waves created by fast ships. Notably, differences between the amplitudes of the bow and stern waves are shown to have no influence on the occurrence of constructive or destructive interferences, although they affect the intensity of wave-interference effects (strong if the amplitudes of the bow and stern waves are commensurate, weak otherwise). Another notable conclusion is that lateral interference effects become more important as the Froude number increases. Indeed, lateral interferences between the twin hulls of a catamaran dominate longitudinal interferences between the fore and aft of the ship at Froude numbers greater than about 1. However, longitudinal interferences between the bow and the stern waves remain dominant for common fast monohull ships.