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SUMMARY:Moist potential vorticity inversion: a nonlinear PDE from atmosphe
 ric dynamics with free boundaries - Antoine Remond-Tiedrez (University of 
 Cambridge)
DTSTART:20221010T130000Z
DTEND:20221010T140000Z
UID:TALK178847@talks.cam.ac.uk
CONTACT:Daniel Boutros
DESCRIPTION:To describe the atmosphere on a synoptic scale (the scale at w
 hich high- and low-pressure systems are apparent on a weather map\, for ex
 ample) one may use the quasi-geostrophic equations\, which are derived as 
 a limit of the classical Boussinesq system under the assumptions of fast r
 otation and strong stratification. When incorporating the dynamics of wate
 r content in the atmosphere\, a.k.a. moisture\, one may then study the moi
 st Boussinesq equations and its limit\, the precipitating quasi-geostrophi
 c equations.\n\nThese models are important for atmospheric scientists in l
 ight of the role that the water cycle plays in atmospheric dynamics\, nota
 bly through energy budgeting (such as for example when atmospheric circula
 tions are diven by laten heat release in storms). Mathematically\, these m
 odels present interesting challenges due to the presence of boundaries\, w
 hose locations are a priori unknown\, between phases saturated and unsatur
 ated in water (schematically: boundaries between clouds and their surround
 ings).\n\nIn particular\, while the (dry) quasi-geostrophic equations rely
  on the inversion of a Laplacian\, this becomes a much trickier adversary 
 in the presence of free boundaries. In this talk we will discuss how this 
 nonlinear equation underpinning the precipitating quasi-geostrophic equati
 ons can be characterized using a variational formulation and we will descr
 ibe the many benefits one may derive from this formulation.
LOCATION:CMS\, MR13
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