Why can ship wakes appear narrower than Kelvin’s angle?

Abstract

An elementary analysis of interference between the divergent waves created by the bow and the stern of a monohull ship, of length Ls, that advances at constant speed Vs along a straight path in calm water of large depth shows that the largest waves created by the ship hull are found at an angle ψmax (measured from the path of the ship) that is smaller than the Kelvin wake angle ψK≈19∘28′ if the Froude number F≡Vs/gLs is larger than FK≈0.59. Interference between transverse and divergent waves created by the bow and the stern of a monohull ship also yields large waves at angles that can be significantly smaller than ψK for F<FK. A similar analysis of interference between the divergent waves created by the bows of the twin hulls of a catamaran shows that the largest waves created by the catamaran are found at an angle ψmaxcat that is smaller than the Kelvin angle ψK if the Froude number Fb≡Vs/gB based on the lateral separation distance B between the twin bows is larger than FKcat≈0.37. The angles ψmax and ψmaxcat are well approximated by the high-speed approximations ψmax≈0.14/F2 and ψmaxcat≈0.2/Fb. These theoretical predictions are consistent with reported observations of ‘unexpected’ narrow ship wakes, and thus suggest that these observations are merely the unsurprising result of interference between the waves created by main wave generators: the bow and the stern of a monohull, or the twin bows of a catamaran.