Speaker 2 :  Philippe Guyenne  (University of Delaware)
    Date & Time : June 17 (Fri.), 2022 / 10:00-11:30PM (Tokyo (JST))
                  (--> June 17 (Fri.), 2022 / 9:00-10:30AM (Newark (EDT)) )
    Title : Hamiltonian Dysthe equation for deep-water gravity waves
    Abstract : 
         A new Hamiltonian version of Dysthe's equation is derived for weakly modulated 
       gravity waves on deep water. A key ingredient in this derivation is a Birkhoff 
       normal form transformation that eliminates all non-resonant cubic terms and allows 
       for a refined reconstruction of the free surface. This modulational approximation 
       is tested against numerical solutions of the classical Dysthe's equation and 
       against direct numerical simulations of Euler's equations for nonlinear water waves. 
       Very good agreement is found in the context of Benjamin-Feir instability of Stokes 
       waves, for which an analysis is provided. An extension of our Hamiltonian model 
       incorporating exact linear dispersion as well as an alternate spatial form are also 
       proposed. Both the 2D and 3D problems are considered. Comparison with laboratory 
       experiments is also shown.