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SUMMARY:Exponential asymptotics for the equatorial Kelvin wave and the hig
 her-order Stokes phenomenon - Josh Shelton (University of Bath)
DTSTART:20221101T145000Z
DTEND:20221101T152000Z
UID:TALK185198@talks.cam.ac.uk
DESCRIPTION:The equatorial Kelvin wave is a travelling atmospheric or ocea
 nographic wave that propagates easterly along the equator. It is known tha
 t this motion is destabilised with the inclusion of weak background shear\
 , which may be physically generated by zonal jets. Furthermore\, Natarov &
  Boyd (Dynam. Atmos. Oceans\, 2001) numerically demonstrated that this ins
 tability is exponentially small with respect to the small shear parameter.
  In this talk\, we demonstrate how this instability arises in connection w
 ith Stokes lines and the Stokes phenomenon. This problem includes various 
 subtitles\, such as an associated eigenvalue whose asymptotic expansion di
 verges\, and the higher-order Stokes phenomenon which is generated by Stok
 es switching in the late-terms of the asymptotic expansion of the solution
  itself. Techniques for the derivation of both of these features are discu
 ssed\, and an analytical result for the exponentially-small Kelvin wave in
 stability is obtained. This is joint work with S. Griffiths\, S. J. Chapma
 n\, and P. Trinh.
LOCATION:Seminar Room 1\, Newton Institute
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