Stability of filaments of uniform quasi-geostrophic potential vorticity

Abstract

We analyse the linear stability of filaments of uniform potential vorticity with a horizontal axis in a quasi-geostrophic flow. For a single filament, the situation corresponds to the simplest three-dimensional shear zone in a rapidly rotating, continuously stably stratified fluid. Yet, this has not been formally addressed to our knowledge. We show that the filament is sensitive to the Kelvin–Helmholtz instability for perturbations in a finite range of streamwise wavenumbers $0<k<k_c$, similarly to the classical situation of a two-dimensional strip of uniform vorticity. We also analyse the stability of a jet formed by two parallel filaments of opposite PV whose axes are located on the same horizontal plane as well as the stability of “hetonic” filaments. Hetonic filaments consist of a pair of opposite PV filaments located at different heights. These can be sensitive to baroclinic instabilities over a wide range of longitudinal wavenumbers.

Keywords:

• Vortex dynamics
• quasi-geostrophy

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Jean N. Reinaud https://orcid.org/0000-0001-5449-6628