| Abstract: |
| In this talk we consider nonlinear hydroelastic waves along a compressed ice sheet lying on top of a two-dimensional fluid of infinite depth. Based on a Hamiltonian formulation of this problem and by applying techniques from Hamiltonian perturbation theory, a Hamiltonian Dysthe equation is derived for the slowly varying envelope of modulated wavetrains. The derivation is complicated by the presence of cubic resonances. A Birkhoff normal form transformation is introduced to eliminate non-resonant triads while accommodating resonant ones. We also test the newly obtained Dysthe model against direct numerical simulations of the full Euler equations, and very good agreement is observed. |
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