Boundary between unsteady and overturning ship bow wave regimes

Abstract

Measurements of the bow waves generated by a rectangular flat plate, immersed at a draughtD= 0.2 m, towed at constant speedU= 1.75 m s−1in calm water and held at a heel angle 10° and a series of nine yaw angles α = 10°, 15°, 20°, 25°, 30°, 45°, 60°, 75° and 90° are reported. The measurements show that bow wave unsteadiness is significantly larger for the flat plate towed at yaw angles 30° ≤ α ≤ 90° than at 10° ≤ α ≤ 20°, which are associated with the unsteady and overturning bow wave regimes, respectively, separated by the boundary$U\hspace{-0.05em}/\hspace{-0.1em}\sqrt{g\hspace{0.05em}D}\,{=}\, 4.4\hspace{0.1em}\tan\hspace{-0.1em}\alpha\hspace{0.1em}/ \hspace{-0.1em}\cos\hspace{-0.1em}\alpha-\hspace{-0.1em}1$with g ≡ acceleration of gravity. These measurements of bow wave unsteadiness provide preliminary experimental validation of the foregoing simple theoretical relation for the boundary between the unsteady and overturning bow wave regimes for non-bulbous wedge-shaped ship bows with insignificant rake and flare. Extension of this relation to more complicated ship bows, notably bows with rake and flare, is also considered.