Interference effects on the Kelvin wake of a catamaran represented via a hull-surface distribution of sources

Abstract

Wave-interference effects on the far-field waves created by a catamaran, with identical twin hulls of length L at a lateral separation distance S, that advances at constant speed V along a straight path in calm water of large depth are considered. Systematic computations are performed for 125 Froude numbers Fs≡V/gS (where g denotes the acceleration of gravity) within the range 0.4≤Fs≤3.5, 25 hull spacings s≡S/L within the range 0.2≤s≤0.8, and seven simple mathematically-defined hulls that correspond to a broad range of main hull-shape parameters (beam/length, draft/length, beam/draft, waterline entrance angle), i.e. for 21,875 distinct cases in all. The two dominant wake angles ψi and ψo that correspond to the ray angles ψ=±ψi and ψ=±ψo where the largest divergent waves are found within the Kelvin wake −ψK≤ψ≤ψK with ψK≈19∘28′ are determined numerically via a realistic yet practical method. This practical method, used previously for monohull ships, is based on the numerical determination of the two major peaks of the amplitude function in the Fourier-Kochin representation of far-field ship waves, evaluated via the Hogner approximation and the stationary-phase approximation. The computations show that the hull shape only has a relatively small influence on the wake angles ψi and ψo associated with the dominant waves. A useful practical consequence of this numerical finding is that the two wake angles ψi and ψo can be estimated, without computations, for general catamarans in terms of the Froude number Fs and the hull spacing s via simple analytical approximations, obtained here via parametric computations. The computations also show that lateral interference effects are dominant if s and/or Fs are sufficiently large, i.e. for ‘wide’ and/or ‘fast’ catamarans. Moreover, the computations reported here for catamarans represented via hull-surface distributions of sources show that the basic two-point wavemaker model of interference between the waves created by the twin bows of a catamaran is realistic for wide and/or fast catamarans. However, wave-interference effects are more complicated if both s and Fs are small, i.e. for ‘narrow slow’ catamarans. The numerical analyses of dominant waves considered earlier for monohull ships and here for catamarans show that, although the amplitudes of the waves created by a ship are strongly influenced by the shape of the ship hull, the ray angles where the largest waves are found are mostly a kinematic feature that is only weakly influenced by the hull shape and the related wave amplitude.