On the Amplitude of Steady Water Waves with Favorable Constant Vorticity

For two-dimensional steady pure-gravity water waves with a unidirectional flow of constant favorable 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.