Patterns of ship waves

Abstract

Patterns of water waves created by a moving disturbance representing a moving body, floating or submerged, can be found by applying (1) the principle of stationary phase, (2) the principle that the phase lines are normal to the wave-number vector, and (3) the perception that the local phase velocity of the waves must be equal to the component of the velocity of the disturbance normal to the phase line. The three equations thus obtained are solved, and formulas for the phase lines are derived, which depend explicitly on the dispersion equation, and on that equation only. These formulas are applied to deep-water surface waves, surface waves in water of finite depth, internal waves, and capillary waves in thin sheets to obtain the wave patterns sufficiently far from the moving disturbance.