Nonexistence of steady waves with negative vorticity

TL;DR

This paper proves the nonexistence of certain steady water waves with negative vorticity under specific conditions, providing explicit bounds on wave parameters and advancing theoretical understanding of fluid dynamics.

Contribution

It establishes the nonexistence of 2D steady waves with negative vorticity and derives explicit bounds on the Froude number for such waves.

Findings

No two-dimensional Stokes or solitary waves with negative vorticity exist above a critical Bernoulli constant.

An explicit upper bound of approximately √2 for the Froude number of such waves.

The results clarify conditions under which steady waves with negative vorticity cannot form.

Abstract

We 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 $F \lesssim \sqrt{2}$ for the Froude number of solitary waves with a negative constant vorticity, sufficiently large in absolute value.