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

Abstract

For the problem describing steady, gravity waves with vorticity on a two-dimensional, unidirectional flow of finite depth the following results are obtained. (i) Bounds for the free-surface profile and for Bernoulli's constant. (ii) If only one parallel shear flow exists for a given value of Bernoulli's constant, then there are no wave solutions provided the vorticity distribution is subject to a certain condition.

13 pages

References in corpus (3)

• The Froude number for solitary water waves with vorticity
• Equivalence of weak formulations of the steady water waves equations
• No steady water waves of small amplitude are supported by a shear flow with still free surface

Cited by in corpus (6)

• Existence and qualitative theory for stratified solitary water waves
• The Froude number for solitary water waves with vorticity
• Nonexistence of subcritical solitary waves
• Solitary waves on rotational flows with an interior stagnation point
• Nonexistence of steady waves with negative vorticity
• On the amplitude of steady water waves with positive constant vorticity