Unstable Stokes waves in constant vorticity flows of finite depth

@misc{hsiao2026unstable,
  title = {{Unstable Stokes waves in constant vorticity flows of finite depth}},
  author = {Ting-Yang Hsiao and Vera Mikyoung Hur and Zhao Yang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04509},
  eprint = {2611.04509},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04509},
}

TY  - UNPB
TI  - Unstable Stokes waves in constant vorticity flows of finite depth
AU  - Ting-Yang Hsiao
AU  - Vera Mikyoung Hur
AU  - Zhao Yang
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04509
UR  - https://arxiv.org/abs/2611.04509
AB  - We study the spectral instability of small-amplitude Stokes waves in finite-depth flows with constant vorticity. A center-manifold reduction and the periodic Evans function give two explicit indices, one for long-wave instability near the origin and the other for an order-two resonance away from the origin. We prove instability when the low-frequency index is positive or the high-frequency index is nonzero, and obtain the leading expansions of the unstable spectral points. At low frequency, first- and second-order monodromy coefficients determine the leading figure-eight curve. At high frequency, we prove that the resonance exists uniquely and derive a limiting ellipse. An algebraic identity expresses the high-frequency index as a positive factor times the square of a real coupling coefficient. Thus every parameter pair with nonzero coupling gives high-frequency instability. The explicit formulas also permit a comparison of the two criteria in the parameter plane.
ER  -