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SUMMARY:A Hamiltonian Dysthe equation for  deep-water gravity waves with c
 onstant vorticity - Catherine Sulem (University of Toronto)
DTSTART:20220906T133000Z
DTEND:20220906T143000Z
UID:TALK177812@talks.cam.ac.uk
DESCRIPTION:This is study of the water wave problem in a two-dimensional d
 omain of infinite depth in the presence of nonzero constant vorticity.A go
 al is to describe the effects of uniform shear flow on the modulation of w
 eakly nonlinear quasi-monochromatic surface gravity waves.Starting from th
 e Hamiltonian formulation of this problem&nbsp\; due to Wahl&eacute\;n (20
 07) and using techniques from Hamiltonian transformation theory\, we deriv
 e a Hamiltonian Dysthe equation for the time evolution of the wave envelop
 e. Consistent with previous studies\, we observe that the uniform shear fl
 ow tends to enhance or weaken the modulational instability of Stokes waves
  depending on its direction and strength. Our method also provides a non-p
 erturbative procedure to reconstruct the surface elevation from the wave e
 nvelope\, based on the Birkhoff normal form transformation to eliminate al
 l non-resonant triads. This model is tested against direct numerical simul
 ations of the full Euler equations and against a related Dysthe equation r
 ecently derived by Curtis\, Carter and Kalisch (2018).
LOCATION:Seminar Room 1\, Newton Institute
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