Basic models of farfield ship waves in shallow water

Abstract

Basic models of the farfield waves created by a monohull ship or a catamaran that travels at a constant speed in calm water of uniform finite depth are considered. A classical basic model is the 1-point ship model introduced by Kelvin in 1887 for deep water and extended to uniform finite water depth by Havelock in 1908. Another basic model is the 2-point ship model, which considers the two dominant waves created by the bow and the stern of a monohull ship or by the twin bows of a catamaran, and therefore accounts for main wave interference effects. These 2-point ship models contain information that cannot be found in the classical patterns for the 1-point ship model commonly used since Kelvin. In particular, whereas Havelock’s classical wave patterns for the 1-point model only depend on the Froude number based on the water depth, the farfield waves for the 2-point models of a monohull ship or a catamaran also depend on the Froude number associated with the length of the monohull ship or the spacing between the twin hulls of the catamaran. Moreover, the ‘apparent wake angles’ associated with the highest waves that result from constructive wave interferences can greatly differ from the cusp or asymptote angles of Havelock’s wave patterns.