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SUMMARY:Frequency Downshifting: A Dispersive Whitham Perspective - Daniel 
 Ratliff (Northumbria University)
DTSTART:20220711T103000Z
DTEND:20220711T110000Z
UID:TALK175826@talks.cam.ac.uk
DESCRIPTION:For many decades\, the Benjamin-Feir instability of water wave
 s has long attracted interest for its many dynamical intricacies. One such
  phenomenon is frequency downshifting\, where the spectral peak of the wav
 etrain permanently decreases during the evolution of the instability. Long
  thought to be a viscously driven effect\, a growing amount of evidence su
 ggests that such phenomenon does not require dissipation. Is it possible t
 o explain how permanent conservative downshifting is possible?&nbsp\;\nThi
 s talk revisits Whitham&rsquo\;s seminal work on the water wave problem fr
 om a phase dynamics perspective to answer this question. In doing so\, we 
 uncover that the role of the bulk mode is fundamental in the evolution of 
 the Stokes waves. Further\, we demonstrate that the Benjamin-Feir transiti
 on causes a point-wise linear degeneracy\, which is the mechanism for freq
 uency downshifting to be supported by the system. Such a conclusion is sho
 wn to be universal for Stokes waves with mean flow effects\, providing an 
 interesting outlook for the Benjamin-Feir instability in a menagerie of ot
 her systems\, both hydrodynamic and beyond.&nbsp\;\nThis talk is joint wor
 k with Tom Bridges (U. Surrey) and Olga Tritchenko (U. Western Ontario)
LOCATION:Seminar Room 1\, Newton Institute
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