Large-amplitude steady downstream water waves

Adrian Constantin; Walter Strauss; Eugen Varvaruca

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arXiv · 1811.10353

Large-amplitude steady downstream water waves

Adrian Constantin·Walter Strauss·Eugen Varvaruca

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Abstract

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

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Adrian Constantin, Walter Strauss, Eugen Varvaruca. 2018-11-26. Large-amplitude steady downstream water waves. https://arxiv.org/abs/1811.10353

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