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Kelvin wake pattern at large Froude numbers

Published online by Cambridge University Press:  05 December 2013

Alexandre Darmon ,
Michael Benzaquen  and
Elie Raphaël
Alexandre Darmon
Affiliation:
PCT, UMR CNRS 7083 Gulliver, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France EC2M, UMR CNRS 7083 Gulliver, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France
Michael Benzaquen
Affiliation:
PCT, UMR CNRS 7083 Gulliver, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France
Elie Raphaël*
Affiliation:
PCT, UMR CNRS 7083 Gulliver, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France
*
†Email address for correspondence: elie.raphael@espci.fr
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Abstract

Gravity waves generated by an object moving at constant speed at the water surface form a specific pattern commonly known as the Kelvin wake. It was proved by Lord Kelvin that such a wake is delimited by a constant angle ${\simeq }19. 4{7}^{\circ } $. However a recent study by Rabaud and Moisy based on the observation of airborne images showed that the wake angle seems to decrease as the Froude number $Fr$ increases, scaling as $F{r}^{- 1} $ for large Froude numbers. To explain such observations they make the strong hypothesis that an object of size $b$ cannot generate wavelengths larger than $b$. Without the need of such an assumption and modelling the moving object by an axisymmetric pressure field, we analytically show that the angle corresponding to the maximum amplitude of the waves scales as $F{r}^{- 1} $ for large Froude numbers, whereas the angle delimiting the wake region outside which the surface is essentially flat remains constant and equal to the Kelvin angle for all $Fr$.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Wakes/Jets: Wakes/Jets Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 738 , 10 January 2014 , R3
Copyright
©2013 Cambridge University Press 

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