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Simple analytical relations for ship bow waves

Published online by Cambridge University Press:  26 March 2008

FRANCIS NOBLESSE ,
GÉRARD DELHOMMEAU ,
MICHEL GUILBAUD ,
DANE HENDRIX  and
CHI YANG
FRANCIS NOBLESSE
Affiliation:
David Taylor Model Basin, NSWCCD, West Bethesda, MD, USA
GÉRARD DELHOMMEAU
Affiliation:
Laboratoire de Mécanique des Fluides (UMR CNRS n6598), École Centrale, Nantes, France
MICHEL GUILBAUD
Affiliation:
Laboratoire d'Études Aérodynamiques (UMR CNRS n6609), Univ. de Poitiers, France
DANE HENDRIX
Affiliation:
David Taylor Model Basin, NSWCCD, West Bethesda, MD, USA
CHI YANG
Affiliation:
College of Science, George Mason University, Fairfax, VA, USA
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Abstract

Simple analytical relations for the bow wave generated by a ship in steady motion are given. Specifically, simple expressions that define the height of a ship bow wave, the distance between the ship stem and the crest of the bow wave, the rise of water at the stem, and the bow wave profile, explicitly and without calculations, in terms of the ship speed, draught, and waterline entrance angle, are given. Another result is a simple criterion that predicts, also directly and without calculations, when a ship in steady motion cannot generate a steady bow wave. This unsteady-flow criterion predicts that a ship with a sufficiently fine waterline, specifically with waterline entrance angle 2αE smaller than approximately 25°, may generate a steady bow wave at any speed. However, a ship with a fuller waterline (25°<2αE) can only generate a steady bow wave if the ship speed is higher than a critical speed, defined in terms of αE by a simple relation. No alternative criterion for predicting when a ship in steady motion does not generate a steady bow wave appears to exist. A simple expression for the height of an unsteady ship bow wave is also given. In spite of their remarkable simplicity, the relations for ship bow waves obtained in the study (using only rudimentary physical and mathematical considerations) are consistent with experimental measurements for a number of hull forms having non-bulbous wedge-shaped bows with small flare angle, and with the authors' measurements and observations for a rectangular flat plate towed at a yaw angle.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 600 , 10 April 2008 , pp. 105 - 132
Copyright
Copyright © Cambridge University Press 2008

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