On the amplitude of steady water waves with positive constant vorticity

TL;DR

This paper establishes an explicit bound on the amplitude of steady water waves with positive constant vorticity, showing it diminishes as vorticity increases, applicable to all wave types without symmetry restrictions.

Contribution

It provides a universal amplitude bound for steady water waves with positive vorticity, regardless of wave type or symmetry, extending previous results.

Findings

Amplitude bound decreases with increasing vorticity

Result applies to all wave types, not just periodic or symmetric

Amplitude tends to zero as vorticity tends to infinity

Abstract

For two-dimensional steady pure-gravity water waves with a unidirectional flow of constant favourable vorticity, we prove an explicit bound on the amplitude of the wave, which decays to zero as the vorticity tends to infinity. Notably, our result holds true for arbitrary water waves, that is, we do not have to restrict ourselves to periodic or solitary or symmetric waves.