Observations and computations of narrow Kelvin ship wakes

Computations of far-field ship waves, based on linear potential flow theory and the Hogner approximation, are reported for monohull ships and catamarans. Specifically, far-field ship waves are computed for six monohull ships at four Froude numbers F≡V/gL=0.58, 0.68, 0.86, 1.58 and for six catamarans with nondimensional hull spacing s≡S/L=0.25 at two Froude numbers Fs≡V/gS=1 and 2.5. Here, g is the gravitational acceleration, V and L denote the ship speed and length, and S is the separation distance between the twin hulls of a catamaran. The computations show that, although the amplitudes of the waves created by a ship are strongly influenced by the shape of the ship hull, as well known, the ray angles where the largest waves are found are only weakly influenced by the hull shape and indeed are mostly a kinematic feature of the flow around a ship hull. An important practical consequence of this flow feature is that the apparent wake angle of general monohull ships or catamarans (with arbitrarily-shaped hulls) can be estimated, without computations, by means of simple analytical relations; these relations, obtained elsewhere via parametric computations, are given here. Moreover, the influence of the two parameters Fs and s that largely determine the ray angles of the dominant waves created by a catamaran is illustrated via computations for three catamarans with hull spacings s=0.2, 0.35, 0.5 at four Froude numbers Fs=1, 1.5, 2, 2.5. These computations confirm that the largest waves created by wide and/or fast catamarans are found at ray angles that only depend on Fs (i.e. that do not depend on the hull spacing s) in agreement with an elementary analysis of lateral interference between the dominant waves created by the bows (or sterns) of the twin hulls of a catamaran. The dominant-waves ray angles predicted by the theory of wave-interference effects for monohull ships and catamarans are also compared with the observations of narrow Kelvin ship wakes reported by Rabaud and Moisy, and found to be consistent with these observations