The Froude number for solitary water waves with vorticity

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.

arXiv comment19 pages

References in corpus (1)

• On bounds and non-existence in the problem of steady waves with vorticity

Cited by in corpus (8)

• Existence and qualitative theory for stratified solitary water waves
• Bound on the slope of steady water waves with favorable vorticity
• Continuous dependence on the density for stratified steady water waves
• Nonexistence of subcritical solitary waves
• On bounds and non-existence in the problem of steady waves with vorticity
• Solitary waves on rotational flows with an interior stagnation point
• Solitary water waves with discontinuous vorticity
• Nonexistence of steady waves with negative vorticity