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Do waveless ships exist? Results for single-cornered hulls

Published online by Cambridge University Press:  06 October 2011

Philippe H. Trinh ,
S. Jonathan Chapman  and
Jean-Marc Vanden-Broeck
Philippe H. Trinh*
Affiliation:
PACM, Princeton University, Washington Road, Princeton, NJ 08544, USA
S. Jonathan Chapman
Affiliation:
OCIAM, Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, UK
Jean-Marc Vanden-Broeck
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
*
†Email address for correspondence: [email protected]
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Abstract

Consider low-speed potential flow past a ship modelled as a semi-infinite two-dimensional body with constant draught. Is it possible to design the hull in such a way as to eliminate the waves produced downstream of the ship? In 1977, Vanden-Broeck & Tuck had conjectured that a single-cornered piecewise-linear hull will always generate a wake; in this paper, we show how recently developed tools in exponential asymptotics can be used to confirm this conjecture. In particular, we show how the formation of waves near a ship is a necessary consequence of singularities in the ship’s geometry (or its analytic continuation). Comprehensive numerical computations confirm the analytical predictions.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 413 - 439
Copyright
Copyright © Cambridge University Press 2011

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