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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Moist potential vorticity inversion: a nonlinear P
DE from atmospheric dynamics with free boundaries
- Antoine Remond-Tiedrez (University of Cambridge)
DTSTART;TZID=Europe/London:20221010T140000
DTEND;TZID=Europe/London:20221010T150000
UID:TALK178847AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178847
DESCRIPTION:To describe the atmosphere on a synoptic scale (th
e scale at which high- and low-pressure systems ar
e apparent on a weather map\, for example) one may
use the quasi-geostrophic equations\, which are d
erived as a limit of the classical Boussinesq syst
em under the assumptions of fast rotation and stro
ng stratification. When incorporating the dynamics
of water content in the atmosphere\, a.k.a. moist
ure\, one may then study the moist Boussinesq equa
tions and its limit\, the precipitating quasi-geos
trophic equations.\n\nThese models are important f
or atmospheric scientists in light of the role tha
t the water cycle plays in atmospheric dynamics\,
notably through energy budgeting (such as for exam
ple when atmospheric circulations are diven by lat
en heat release in storms). Mathematically\, these
models present interesting challenges due to the
presence of boundaries\, whose locations are a pri
ori unknown\, between phases saturated and unsatur
ated in water (schematically: boundaries between c
louds and their surroundings).\n\nIn particular\,
while the (dry) quasi-geostrophic equations rely o
n the inversion of a Laplacian\, this becomes a mu
ch trickier adversary in the presence of free boun
daries. In this talk we will discuss how this nonl
inear equation underpinning the precipitating quas
i-geostrophic equations can be characterized using
a variational formulation and we will describe th
e many benefits one may derive from this formulati
on.
LOCATION:CMS\, MR13
CONTACT:Daniel Boutros
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