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

Yan Barabinot (1) , Jean N Reinaud (2) , Xavier J Carton (3) , Charly de Marez (3) , Thomas Meunier (3)

1 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)
2 University of St Andrews [Scotland]
3 LOPS - Laboratoire d'Océanographie Physique et Spatiale

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.

Mots clés: quasi-geostrophic flows vortex dynamics variational methods; quasi-geostrophic flows; vortex dynamics; variational methods; ODYSSEY

Domaines: Physique [physics]; Sciences de l'environnement

Yan Barabinot, Jean N Reinaud, Xavier J Carton, Charly de Marez, Thomas Meunier. A 3-D minimum-enstrophy vortex in stratified quasi-geostrophic flows. Journal of Fluid Mechanics, 2024, 986 (4), pp.R1. ⟨10.1017/jfm.2024.336⟩. ⟨hal-04841016⟩