A 3D minimum enstrophy vortex in stratified quasi-geostrophic flows

Yan Barabinot*, Jean Noel Reinaud, Xavier Carton, Charly de Marez, Thomas Meunier

*Corresponding author for this work

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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.
Original languageEnglish
Article numberR1
Number of pages12
JournalJournal of Fluid Mechanics
Early online date3 May 2024
Publication statusPublished - 10 May 2024


  • Quasi-geostrophic flows
  • Vortex dynamics
  • Variational methods


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