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SUMMARY:Stokes waves in conformal plane: the Hamiltonian variables and ins
 tabilities - Sergey Dyachenko (University at Buffalo)
DTSTART:20221103T110000Z
DTEND:20221103T120000Z
UID:TALK192242@talks.cam.ac.uk
DESCRIPTION:The Stokes wave is a water wave that travels over a free surfa
 ce of water without changing shape. When a time-varying fluid domain is ma
 pped to a fixed geometry\, such as a periodic strip in the lower half-plan
 e\, the equation for the Stokes wave is a nonlinear integro-differential O
 DE whose solutions are found numerically to arbitrary precision. The spect
 ral stability of Stokes waves is studied by linearization of the equations
  of motion for the free surface around a Stokes wave\, and studying the sp
 ectrum of the associated Fourier-Floquet-Hill (FFH) eigenvalue problem. We
  developed a novel approach to studying the eigenvalue spectrum by combini
 ng the conformal Hamiltonian canonical variables\, the FFH technique built
  into a matrix-free Krylov-Schur eigenvalue solver. We report new results 
 for the Benjamin-Feir instability as well as the high-frequency\, and loca
 lized (superharmonic) instabilities of the waves close to the limiting Sto
 kes wave.
LOCATION:Seminar Room 2\, Newton Institute
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