BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:The strange instability of the equatorial Kelvin wave - Stephen Gr
 iffiths (University of Leeds)
DTSTART:20221101T100000Z
DTEND:20221101T105000Z
UID:TALK185189@talks.cam.ac.uk
DESCRIPTION:The Kelvin wave is perhaps the most dynamically important of t
 he equatorially trapped waves in the terrestrial atmosphere and ocean. The
 oretically\, it can be understood from the linear dynamics of a rotating s
 tratified fluid\, which\, with simple assumptions about the disturbance st
 ructure\, leads to wavelike solutions propagating along the equator\, with
  exponential decay in latitude. However\, when the simplest possible backg
 round flow is added (with uniform latitudinal shear)\, the Kelvin wave bec
 omes unstable. This happens in an extremely unusual way: there is instabil
 ity for arbitrarily small nondimensional shear\, and the growth rate is ex
 ponentially small as the shear tends to zero.&nbsp\;\nThis Kelvin wave ins
 tability has been established numerically by Natarov and Boyd\, who also s
 peculated as to the underlying mathematical cause. Here we show how the gr
 owth rate and full spatial structure of the instability may be derived usi
 ng matched asymptotic expansions applied to the (linear) equations of moti
 on. This involves an adventure with confluent hypergeometric functions in 
 the exponentially-decaying tails of the Kelvin wave\, and a trick to revea
 l the exponentially small growth rate from a formulation that only uses re
 gular perturbation expansions. Numerical verification of the analysis is a
 lso interesting and challenging: it turns out that the growth rate scales 
 as p3 exp(-1/p2) in the limit of small nondimensional shear p\, meaning th
 at special high-precision calculations are required even when p is not tha
 t small (e.g.\, 0.2).&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR