Pré-Publication, Document De Travail Année : 2026

Do irrotational water waves remain irrotational in the limit of a vanishing viscosity?

Résumé

Theoretical results on water waves almost always start by assuming irrotationality of the flow in order to simplify the formulation. In this work, we investigate the well-foundedness of this hypothesis via numerical simulations of the free-surface Navier-Stokes equations. We show that, in the presence of a non-flat bathymetry, either angular or smooth, a gravity wave of finite amplitude can shed vortex pairs from the bottom boundary layer into the bulk of the flow. As these eddies approach the free surface they modify the shape of the wave. It is found that this perturbation does not vanish as the Reynolds number is increased. The vanishing viscosity limit of water waves is therefore singular when no-slip boundary conditions are enforced on the bottom.

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Est complété par 10.57745/N7QK7T Jeu de données RIQUIER, Alan; DORMY, Emmanuel, 2025, "Replication dataset associated with "Do irrotational water waves remain irrotational?"", https://doi.org/10.57745/N7QK7T, Recherche Data Gouv, V2

Dates et versions

hal-04782997 , version 1 (14-11-2024)
hal-04782997 , version 2 (20-11-2025)

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  • HAL Id : hal-04782997 , version 2

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Alan Riquier, Emmanuel Dormy. Do irrotational water waves remain irrotational in the limit of a vanishing viscosity?. 2026. ⟨hal-04782997v2⟩
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