Large-Amplitude Steady Downstream Water Waves

Abstract We study wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed. For large-amplitude periodic traveling gravity waves that propagate at the surface same direction as underlying current (downstream waves), we prove explicit uniform bounds for their amplitude. In particular, our estimates show maximum amplitude becomes vanishingly small increases without limit. also downstream on global bifurcating branch are never overhanging, and mass flux Bernoulli uniformly bounded.