Hamiltonian Dysthe equation for hydroelastic waves in a compressed ice sheet
Apparaît dans la collection : 2026 - T2 - WS2 - Instabilities and transitions in geophysical flows
This study concerns the motion of nonlinear hydroelastic waves along a com- pressed ice sheet lying on top of a two-dimensional fluid of infinite depth. Applying tech- niques of Hamiltonian perturbation theory, a Hamiltonian Dysthe equation is derived for the slowly varying envelope of modulated wavetrains. The derivation is further complicated by the presence of cubic resonances. A Birkhoff normal form transformation is introduced to eliminate non-resonant triads while accommodating resonant ones. Numerical solutions constructed from the Dysthe equation are compared to direct simulations of the full Euler system, and very good agreement is observed.
Co-authors: Philippe Guyenne, Adilbek Kairzhan
