Stability of filaments of uniform quasi-geostrophic potential vorticity

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.