Wave profile along a ship hull, short farfield waves, and broad inner Kelvin wake sans divergent waves

Abstract

The Neumann-Michell linear potential flow theory of the short farfield waves created by a ship that advances at a constant speed in calm water is coupled with nonlinear analytical relations for inviscid flow along the wave profile at the ship hull surface, i.e., the contact line between the ship hull surface and the free surface. This ad hoc coupling of linear farfield ship waves and a nonlinear nearfield flow along a ship waterline determines short farfield ship waves in terms of the free-surface elevation along the ship hull surface, and provides insight into the influence of nearfield nonlinearities (most significant at a ship waterline) on short farfield ship waves. For the Wigley parabolic ship model, nearfield nonlinearities are found to be relatively weak and to have a limited, although appreciable, influence on short farfield waves. The steepness of divergent ship waves is also analyzed. This analysis shows that, for a full-scale Wigley hull, divergent waves are too steep to exist inside a broad inner Kelvin wake with angle roughly equal to 13°, i.e., a third of Kelvin’s 39° ship wake angle.