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SUMMARY:Stokes waves are unstable - Vera Mikyoung Hur (University of Illin
 ois at Urbana-Champaign)
DTSTART:20220718T123000Z
DTEND:20220718T133000Z
UID:TALK176084@talks.cam.ac.uk
DESCRIPTION:I will discuss a new periodic Evans function approach for cyli
 ndrical domains\, and its application to the spectral instability of Stoke
 s waves in the finite depth. Numerical evidence suggests instability whene
 ver the unperturbed wave is 'resonant' with its infinitesimal perturbation
  waves. This has not been studied analytically except the Benjamin-Feir in
 stability\, near the origin of the spectral plane\, when (wave number)x(de
 pth)>1.3627... for small amplitude. I will discuss an alternative proof of
  the Benjamin-Feir instability and\, also\, the first proof of spectral in
 stability away from the origin\, when (wave number)x(depth) is not 1.8494.
 ..\, thereby all Stokes waves are unstable. Joint work with Z. Yang.
LOCATION:Seminar Room 1\, Newton Institute
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