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On steady non-breaking downstream waves and the wave resistance

Published online by Cambridge University Press:  08 July 2015

Dmitri V. Maklakov  and
Alexander G. Petrov
Dmitri V. Maklakov*
Affiliation:
N.I. Lobachevsky Institute of Mathematics and Mechanics, Kazan (Volga region) Federal University, Kremlyovskaya 35, Kazan 420008, Russia
Alexander G. Petrov
Affiliation:
Institute for Problems in Mechanics of the Russian Academy of Sciences, prosp. Vernadskogo 101, block 1, Moscow 119526, Russia
*
†Email address for correspondence: dmaklak@kpfu.ru
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Abstract

In this work we have obtained exact analytical formulae expressing the wave resistance of a two-dimensional body by the parameters of the downstream non-breaking waves. The body moves horizontally at a constant speed $c$ in a channel of finite depth $h$. We have analysed the relationships between the parameters of the upstream flow and the downstream waves. Making use of some results by Keady & Norbury (J. Fluid Mech., vol. 70, 1975, pp. 663–671) and Benjamin (J. Fluid Mech., vol. 295, 1995, pp. 337–356), we have rigorously proved that realistic steady free-surface flows with a positive wave resistance exist only if the upstream flow is subcritical, i.e. the Froude number $\mathit{Fr}=c/\sqrt{gh}<1$. For all solutions with downstream waves obtained by a perturbation of a supercritical upstream uniform flow the wave resistance is negative. Applying a numerical technique, we have calculated accurate values of the wave resistance depending on the wavelength, amplitude and mean depth.

JFM classification

Waves/Free-surface Flows: Channel flow Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 776 , 10 August 2015 , pp. 290 - 315
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Copyright
© 2015 Cambridge University Press 

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