Wavelengths of the highest waves created by fast monohull ships or catamarans

Abstract

Constructive interference among the divergent waves created by sources and sinks distributed over the hull surface of a ship that advances at high speed in calm water results in highest waves along ray angles located inside the cusps of the classical Kelvin wake. These highest waves are much shorter than the waves along the cusps of the Kelvin wake and are also significantly shorter than the ship length. The ray angles of the highest ship waves and their wavelengths are only weakly influenced by the hull shape, and indeed are kinematic flow features that are known for all monohull ships and catamarans; moreover, these angles and wavelengths are determined via simple analytical relations in terms of the Froude number and, for a catamaran, the distance between the twin bows of the catamaran. These simple general results about the highest waves created by a fast ship widely expand the classical results obtained by Kelvin in 1887 for a ship modeled as a one-point wavemaker.