An elementary analytical theory of overturning ship bow waves

A fully-analytical theory that approximately predicts the size, shape and thickness of the overturning detached bow wave, and the width of the wavebreaking wake behind the plunging bow wave, generated by a ship with a fine bow that advances (at constant speed along a straight path) in calm water is reported. The theory yields simple analytical 'cause-and-effect' relations that provide useful physical insight and explicitly relate a ship's speed, draft, and main parameters characterizing the bow shape (entrance angles of the top and bottom waterlines, rake angle, flare) to the corresponding overturning bow wave and wavebreaking wake. Qualitative comparisons with experimental observations and CFD calculations show that while the elementary analysis underlying the theory cannot be expected to yield accurate predictions, the theory predicts trends correctly and provides practical estimates of the influence of basic ship design parameters (speed, draft, bow shape) on main characteristics of the overturning bow wave and the related wavebreaking wake created by a ship bow.