The Froude number for solitary water waves with vorticity

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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 onA F, and hence on the amplitude, under more restrictive assumptions on the vorticity.

Original languageEnglish
Pages (from-to)91-112
Number of pages22
JournalJournal of Fluid Mechanics
Early online date3 Mar 2015
Publication statusPublished - 10 Apr 2015


  • solitary waves
  • surface gravity waves
  • waves/free-surface flows

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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