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arXiv · 2504.20221

Rigidity of symmetric doubly-periodic water waves near shear flows

Douglas Svensson Seth·Kristoffer Varholm·Erik Wahlén·Jörg Weber
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Abstract

We prove that symmetric, doubly periodic, capillary-gravity water waves in finite depth bifurcating from non-uniform non-stagnant shear flows are necessarily two-dimensional to leading order. This is in stark contrast to the case of uniform background flows, where the existence of truly three-dimensional bifurcating waves is well known. While this paper focuses on capillary-gravity water waves, our proof also applies to other suitable types of dynamic boundary conditions, such as hydroelastic waves.

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Douglas Svensson Seth, Kristoffer Varholm, Erik Wahlén, Jörg Weber. 2025-04-28. Rigidity of symmetric doubly-periodic water waves near shear flows. https://arxiv.org/abs/2504.20221

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