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The Froude number for solitary water waves with vorticity

Published online by Cambridge University Press:  03 March 2015

Miles H. Wheeler
Miles H. Wheeler*
Affiliation:
Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
*
†Email address for correspondence: mwheeler@cims.nyu.edu
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Abstract

We consider two-dimensional solitary water waves on a shear flow with an arbitrary distribution of vorticity. Assuming that the horizontal velocity in the fluid never exceeds the wave speed and that the free surface lies everywhere above its asymptotic level, we give a very simple proof that a suitably defined Froude number $F$ must be strictly greater than the critical value $F=1$ . We also prove a related upper bound on  $F$ , and hence on the amplitude, under more restrictive assumptions on the vorticity.

JFM classification

Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows

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Papers
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Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 91 - 112
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© 2015 Cambridge University Press 

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