Dynamics of a stratified vortex under the complete Coriolis force: two-dimensional three-components evolution

We study the dynamics of an initially axisymmetric and vertical Lamb–Oseen vortex in a stratified-rotating fluid under complete Coriolis force on $f$ plane, i.e. presence background rotation both along horizontal directions. By combination direct numerical simulations asymptotic analyses for small rotation, we show that critical layer appears at radius where angular velocity is equal to buoyancy frequency when Froude number larger than unity. This generates invariant which first increases linearly with time then saturates amplitude scaling like $Re^{1/3}/\widetilde{Ro}$ , $Re$ Reynolds $\widetilde {Ro}$ non-traditional Rossby based component rotation. In turn, quasi-axisymmetric anomaly vorticity produced through force. Below depending Rayleigh's inflectional criterion satisfied shear instability subsequently triggered rendering fully non-axisymmetric. The decay enhanced until it everywhere lower frequency. A theoretical derived from Rayleigh condition predicts well instability. It shows this phenomenon can occur even large . Hence, might have much more impact geophysical vortices anticipated by considering order magnitude