Stability of a stratified tilted vortex
Résumé
The stability of a vortex tilted with respect to the stratification has been investigated theoretically and experimentally.The basic flow solution has been obtained analytically in the limit of small inclination angles. The inviscid approximation of the solution exhibits a singularity whereN = Ω(r), with N the Brunt-V¨aisala frequency and Ω(r) the angular velocity profile.This singularity can be smoothed by a viscous critical layer analysis. The solution corresponds to strong jets and strong density variations of order O(Re13 ) localized inthe critical layer of O(Re−13) width . PIV measurements and shadow graph visualization have been used to validate the theory (see figure 1a).The basic flow has been observed to be unstable. A shadowgraph picture reveals theemergence of co-rotating structures in two distinct strips arranged symmetrically oneither side of the vortex (see figure 1b). The evolution of the azimuthal vorticity has been obtained experimentally and show a reorganization of the vorticity from vertical homogeneous distribution toward ponctual and regularly spaced vortices. The unstable mode is not an helicoidal mode but instead localized on either side of the vortexas if it was due to a Kelvin-Helmholtz instability of the shear generated in the criticallayer. This interpretation is discussed and validated by simple models.The impact of this new and very general instability induced by tilting on mixing andinternal waves generation are also considered.