Annali di Matematica Pura ed Applicata (1923 -)· 2026Q1
On the short-wavelength stability and the Kelvin–Helmholtz instability of some explicit solutions to the two-layer nonlinear three-dimensional water wave problem
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- Q1SCImago
- 2026year
Short summary
Researchers derived explicit radial solutions for steady, three-dimensional, nonlinear water waves with a free surface and a density-stratified interface, proving their short-wavelength stability and Kelvin–Helmholtz instability.
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Key points
- Derived explicit radial solutions for steady, 3D nonlinear water waves with a free surface and density interface.
- Proved short-wavelength stability for these solutions using WKB ansatz and Lyapunov criterion.
- Demonstrated Kelvin–Helmholtz instability for the derived exact solutions.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract This study is concerned with explicit solutions in the Eulerian framework to the three-dimensional nonlinear Euler equations with a free surface and an interface. Starting with a depth-dependent density, continuous within the fluid domain, except across the interface, we present exact radial solutions to the steady water wave problem. While the velocity field and the pressure are given explicitly, the free surface and the interface are determined implicitly by a functional analytic approach. We also prove short-wavelength stability results for these explicit solutions by means of a Wentzel–Kramers–Brillouin ansatz together with a Lyapunov-type stability criterion. We conclude the analysis by proving the Kelvin–Helmholtz instability of the exact solutions.
The authors' abstract, as published at the source. Annali di Matematica Pura ed Applicata (1923 -), 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics