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 onA F, and hence on the amplitude, under more restrictive assumptions on the vorticity.
Original language | English |
---|---|
Pages (from-to) | 91-112 |
Number of pages | 22 |
Journal | Journal of Fluid Mechanics |
Volume | 768 |
Early online date | 3 Mar 2015 |
DOIs | |
Publication status | Published - 10 Apr 2015 |
Keywords
- solitary waves
- surface gravity waves
- waves/free-surface flows
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering