Whitham and Benjamin predicted in 1967 that small-amplitude periodic traveling Stokes waves of the 2d-gravity water waves equations are linearly unstable with respect to long-wave perturbations, if the depth h is larger than a critical threshold hWB ≈ 1.363. In this paper, we completely describe, for any finite value of h > 0, the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent μ is turned on.
Benjamin–Feir Instability of Stokes Waves in Finite Depth / Berti, M.; Maspero, A.; Ventura, P.. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 247:(2023), pp. 1-54. [10.1007/s00205-023-01916-2]
Benjamin–Feir Instability of Stokes Waves in Finite Depth
Berti M.;Maspero A.;Ventura P.
2023-01-01
Abstract
Whitham and Benjamin predicted in 1967 that small-amplitude periodic traveling Stokes waves of the 2d-gravity water waves equations are linearly unstable with respect to long-wave perturbations, if the depth h is larger than a critical threshold hWB ≈ 1.363. In this paper, we completely describe, for any finite value of h > 0, the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent μ is turned on.| File | Dimensione | Formato | |
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