Small-amplitude finite-depth Stokes waves are transversally unstable
Ziang Jiao, L. Miguel Rodrigues, Changzhen Sun, Zhao Yang
TL;DR
This paper proves that small-amplitude, irrotational, periodic water waves in finite-depth conditions are spectrally unstable when considering three-dimensional inviscid gravity water-waves equations.
Contribution
It establishes the spectral instability of small-amplitude finite-depth Stokes waves, a significant step in understanding their stability properties.
Findings
Small-amplitude Stokes waves are spectrally unstable in 3D.
Unconditional instability for all sufficiently small amplitudes.
Advances the theoretical understanding of water wave stability.
Abstract
We prove that all irrotational planar periodic traveling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravity water-waves equations.
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Taxonomy
TopicsOcean Waves and Remote Sensing · Coastal and Marine Dynamics · Navier-Stokes equation solutions