Stability and instability of Kelvin waves

نویسندگان

چکیده

The m-waves of Kelvin are uniformly rotating patch solutions the 2D Euler equations with m-fold rotational symmetry for \(m\ge 2\). For waves sufficiently close to disc, we prove a nonlinear stability result up an arbitrarily long time in \(L^1\) norm vorticity, symmetric perturbations. To obtain this result, first that wave is strict local maximizer energy functional some admissible class patches, which had been claimed by Wan 1986. This gives orbital support condition on evolution perturbations, but using Lagrangian bootstrap argument traces particle trajectories perturbation, able drop evolution. Based unconditional establish filamentation, or formation arms, occurs near waves, have observed various numerical simulations. Additionally, discuss annular patches same variational framework.

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ژورنال

عنوان ژورنال: Calculus of Variations and Partial Differential Equations

سال: 2022

ISSN: ['0944-2669', '1432-0835']

DOI: https://doi.org/10.1007/s00526-022-02334-0