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SUMMARY:Dynamics of nearly isolated\, lenticular vortices: From waves to 
 bulk instabilities? - Jérémie Vidal (ENS Lyon)
DTSTART:20251020T150000Z
DTEND:20251020T160000Z
UID:TALK237598@talks.cam.ac.uk
CONTACT:Mattias Brynjell-Rahkola
DESCRIPTION:In geophysical and astrophysical settings\, rotating stratifie
 d flows often exhibit large-scale\, nearly isolated vortices. Examples inc
 lude the Mediterranean eddies in the Atlantic ocean\, or the Great Red Spo
 t (GRS) in Jupiter. These vortices have been widely studied using shallow-
 water or quasi-geostrophic models for decades. In particular\, these model
 s have successfully explained why these vortices maintain nearly lenticula
 r shapes through time. However\, prior reduced models have a blind spot wh
 en it comes to predicting the internal dynamics of such vortices\, despite
  the fact that they are far from being motionless in their bulk (e.g. as o
 bserved for the GRS). Various instabilities may sustain small-scale turbul
 ence and accelerate the decay of large-scale vortices on long time scales.
  \n\nHere\, I will present a reduced model accounting for the bulk dynamic
 s of large-scale pancake-like vortices. This model\, which is developed in
  the framework of an interdisciplinary collaboration between pure and appl
 ied mathematics\, is largely inspired by some ideas and methods pioneered 
 by astrophysicists (e.g. S. Chandrasekhar or N. Lebovitz). First\, I will 
 describe the properties of the normal modes\, because wave motions are oft
 en key to understanding the transition to turbulence in geophysical flows.
  As in the rotating non-stratified case\, it will be shown that the wave s
 pectrum solely consists of eigenvalues\, and that the eigenvectors are all
  smooth. Moreover\, it will be explained why some low-frequency waves/mode
 s\, which are governed by a mixed hyperbolic-elliptic problem for the velo
 city\, can exist below the usual cutoff frequency of inertia-gravity waves
 . Next\, by combining local and global stability methods\, I will discuss 
 whether some bulk instabilities could sustain small-scale bulk turbulence 
 in strongly deformed stratified vortices.
LOCATION:MR14 DAMTP and online
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