BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The strange instability of the equatorial Kelvin w
ave - Stephen Griffiths (University of Leeds)
DTSTART;TZID=Europe/London:20221101T100000
DTEND;TZID=Europe/London:20221101T105000
UID:TALK185189AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/185189
DESCRIPTION:The Kelvin wave is perhaps the most dynamically im
portant of the equatorially trapped waves in the t
errestrial atmosphere and ocean. Theoretically\, i
t can be understood from the linear dynamics of a
rotating stratified fluid\, which\, with simple as
sumptions about the disturbance structure\, leads
to wavelike solutions propagating along the equato
r\, with exponential decay in latitude. However\,
when the simplest possible background flow is adde
d (with uniform latitudinal shear)\, the Kelvin wa
ve becomes unstable. This happens in an extremely
unusual way: there is instability for arbitrarily
small nondimensional shear\, and the growth rate i
s exponentially small as the shear tends to zero.&
nbsp\;\nThis Kelvin wave instability has been esta
blished numerically by Natarov and Boyd\, who also
speculated as to the underlying mathematical caus
e. Here we show how the growth rate and full spati
al structure of the instability may be derived usi
ng matched asymptotic expansions applied to the (l
inear) equations of motion. This involves an adven
ture with confluent hypergeometric functions in th
e exponentially-decaying tails of the Kelvin wave\
, and a trick to reveal the exponentially small gr
owth rate from a formulation that only uses regula
r perturbation expansions. Numerical verification
of the analysis is also interesting and challengin
g: it turns out that the growth rate scales as p3
exp(-1/p2) in the limit of small nondimensional sh
ear p\, meaning that special high-precision calcul
ations are required even when p is not that small
(e.g.\, 0.2). \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
END:VEVENT
END:VCALENDAR