Nonlinear Stability and Evolution of 3D Vortices in Rotating Stratified Flows

Coherent, long-lived vortices play an important role in mixing and transportation in many geophysical and astrophysical flows. To understand their dynamics, previous work explored the linear stability of 3D, axisymmetric, Gaussian vortices in rotating, stratified flow. Building on this, the finite-amplitude stability and nonlinear evolution of linearly unstable vortices is studied using an initial value code solving the Boussinesq equations. The vortices studied have exponential growth rates faster than 0.2x their turn-around time and are seeded with a range of small initial perturbations with different spatial symmetries and amplitudes. Although their linear instabilities have fast growth rates, in all but one case the initial finite-amplitude perturbation quickly plateaus and the vortex evolves to a final steady, non-axisymmetric vortex nearly indistinguishable from its initial form. Thus, despite their broken symmetry, for most practical purposes these vortices are effectively stable. Mathematically put, the vortices have large effective Landau constants that, despite their eigenmodes' large growth rates, damp their linear amplitudes quickly. The results open questions for further study and may be relevant to other long-lived vortex families (e.g., aircraft wake vortices). All vortices studied have the ratio of the Coriolis parameter to Brunt-Vaisala frequency of the far-field flow set to f/N=0.1 and exist in the Rossby–Burger number parameter space -0.5<Ro<0.5 and 0.07