Geodesic vortex detection on curved surfaces: Analyzing the 2002 austral stratospheric polar vortex warming event

Geodesic vortex detection is a tool in nonlinear dynamical systems to objectively identify transient vortices with flow-invariant boundaries that defy the typical deformation found in 2D turbulence. Initially formulated for flows on the Euclidean plane with Cartesian coordinates, we have extended this technique to flows on 2D Riemannian manifolds with arbitrary coordinates. This extension required further formulation of the concept of objectivity on manifolds. Moreover, a recently proposed birth-and-death vortex framing algorithm, based on geodesic detection, has been adapted to address the limited temporal validity of 2D motion in otherwise 3D flows, like those found in the Earth's stratosphere. With these adaptations, we focused on the Lagrangian, i.e., kinematic, aspects of the austral stratospheric polar vortex during the exceptional sudden warming event of 2002, which resulted in the splitting of the vortex. This study involved applying geodesic vortex detection to isentropic winds from reanalysis data. We provide a detailed analysis of the vortex's life cycle, covering its birth, splitting process, and eventual death. In addition, we offer new kinematic insights into ozone depletion within the vortex.