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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Analysis of a rotationally constrained convection
model - Yanqiu Guo ()
DTSTART;TZID=Europe/London:20220503T160000
DTEND;TZID=Europe/London:20220503T170000
UID:TALK172313AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/172313
DESCRIPTION:This talk is about the analysis of an asymptotical
ly reduced system for rotationally constrained con
vection. The presence of a dominant balance in equ
ations for fluid flow can be exploited to derive a
simpler set of governing equations that permits a
nalytical explorations. For rotation dominated flo
ws\, the geostrophic balance\noccurs: the pressure
gradient force is balanced by the Coriolis effect
.\nThe Taylor-Proudman constraint suggests that th
e dominant Coriolis force leads to flows that are
organized into vertical plumes or columns whose ho
rizontal scale is small compared to the layer heig
ht. Applying the asymptotic theory for small Rossb
y number and tall columnar structures\, Julien and
Knobloch derived a closed set of reduced equation
s from the three-dimensional Boussinesq equations.
Also\, Sprague et al. numerically simulated this
reduced model to study the equal populations of cy
clonic and anticyclonic structures in rapid rotati
ng convection. This reduced system is interesting
yet challenging for analytical study. On the one h
and\, the nonlinear convection term has a reduced
complexity since it contains only the horizontal g
radient. On the other hand\, the physical domain r
emains three dimensional\, while the regularizing
viscosity acts in the horizontal direction only\,
creating a major difficulty for establishing the g
lobal existence theory. Another difficulty arises
due to a linear term involving the vertical deriva
tive of the stream function\, reflecting the balan
ce of the Coriolis force by the pressure.\nI will
present some of our results motivated by the globa
l regularity problem. We show that the model is gl
obally well-posed if regularized by a very weak di
ssipation. I will also discuss the case of infinit
e Prandtl number convection\, and the situation wh
en both of the Prandtl and Rayleigh numbers approa
ch infinity. This is a joint project with Cao and
Titi.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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