Rigidity of symmetric doubly-periodic water waves near shear flows

2025/04/28 by Douglas Svensson Seth, Kristoffer Varholm, Seth, Douglas Svensson +5 · 1 citation
Earth and Planetary Sciences · Mathematics · #Ocean Waves and Remote Sensing #Navier-Stokes equation solutions #Coastal and Marine Dynamics

paper · pdf · doi:10.48550/arxiv.2504.20221

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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• Global bifurcation of doubly periodic gravity-capillary waves on Beltrami flows

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