Experiment to Examine the Effect of Scale on a Breaking Bow Wave

An elementary analytical theory of overturning ship bow waves

“…2, the analytical bow wave profile given by the two complementary parabolic arcs (13) and the relations (11) are in good overall agreement with CFD bow wave profiles obtained via Euler-flow calculation methods [34]. Thus, the simple analytical relations (13) and (11), with the tables for the related functions ζ b , ξ b , ζ 0 , ξ 0 given in [34], provide a practical analytical approximation to the bow wave profile for x s ≤ x ≤ x 0 . This simple approximation is useful for a broad class of fine bows with rake and flare, common for fast ships that generate overturning bow waves of interest here.…”

“…2 is identical to the two-parameter (D, α) family of wedge-shaped bows considered in [1]. In this special case, (9) yields ϕ = 0, the functions ζ b , ξ b , ζ 0 in (11) are equal to 1 as shown in [33,34], and (11a)-(11c) are identical to the corresponding relations given in [1] as expected. The relations (11a)-(11c) and the related parabolic approximation (13a) to the bow wave front are shown in [1] to be in good overall agreement with experimental measurements for both wedgeshaped ship bows (Wigley hull and three sharp-ended strut-like hulls) with various entrance angles 2α and a rectangular flat plate at several incidence (yaw) angles α, i.e.…”

“…For the more general family of ship bows depicted in Fig. 2, the analytical bow wave profile given by the two complementary parabolic arcs (13) and the relations (11) are in good overall agreement with CFD bow wave profiles obtained via Euler-flow calculation methods [34]. Thus, the simple analytical relations (13) and (11), with the tables for the related functions ζ b , ξ b , ζ 0 , ξ 0 given in [34], provide a practical analytical approximation to the bow wave profile for x s ≤ x ≤ x 0 .…”

“…2 with β = 30 • and α ′ = α = 15 • at four draft-based Froude numbers F = 0.67, 1, 1.5 and 2.33. The corresponding analytical bow wave profiles defined by ( 13) and (11), and the bow stem line X = X s are also shown in Fig. 4.…”

“…Experimental investigations of ship bow waves, including overturning bow waves of interest here, have been reported in the literature; e.g. [5][6][7][8][9][10][11][12][13][14][15]. Overturning ship bow waves cannot be predicted using traditional theoretical methods, e.g.…”