On bounds for steady waves with negative vorticity

Abstract

AbstractWe prove that no two-dimensional Stokes and solitary waves exist when the vorticity function is negative and the Bernoulli constant is greater than a certain critical value given explicitly. In particular, we obtain an upper bound $$F \le \sqrt{2} + \epsilon $$ F ≤ 2 + ϵ for the Froude number of solitary waves with a negative constant vorticity, sufficiently large in absolute value.