A 3D minimum enstrophy vortex in stratified quasi-geostrophic flows
Date
10/05/2024Metadata
Show full item recordAbstract
Applying a variational analysis, a minimum-enstrophy vortex in three-dimensional (3-D) fluids with continuous stratification is found, under the quasi-geostrophic hypothesis. The buoyancy frequency is held constant. This vortex is an ideal limiting state in a flow with an enstrophy decay while energy and generalized angular momentum remain fixed. The variational method used to obtain two-dimensional (2-D) minimum-enstrophy vortices is applied here to 3-D integral quantities. The solution from the first-order variation is expanded on a basis of orthogonal spherical Bessel functions. By computing second-order variations, the solution is found to be a true minimum in enstrophy. This solution is weakly unstable when inserted in a numerical code of the quasi-geostrophic equations. After a stage of linear instability, nonlinear wave interaction leads to the reorganization of this vortex into a tripolar vortex. Further work will relate our solution with maximal entropy 3-D vortices.
Citation
Barabinot , Y , Reinaud , J N , Carton , X , de Marez , C & Meunier , T 2024 , ' A 3D minimum enstrophy vortex in stratified quasi-geostrophic flows ' , Journal of Fluid Mechanics , vol. 986 , R1 . https://doi.org/10.1017/jfm.2024.336
Publication
Journal of Fluid Mechanics
Status
Peer reviewed
ISSN
0022-1120Type
Journal article
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