Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
- 1Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM. C/ Nicolás Cabrera 15, Campus de Cantoblanco UAM, 28049 Madrid, Spain
- 2Departamento de Matemáticas, Facultad de Ciencias, Universidad Autonóma de Madrid, 28049 Madrid, Spain
- 3Department of Atmospheric and Oceanic Sciences, University of California at Los Angeles, Los Angeles, California, USA
- 4School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
- 5Laboratoire de Physique de l'Atmosphere et de l'Ocean Simeon Fongang, Ecole Superieure Polytechnique, Universite Cheikh Anta Diop, 5085, Dakar-Fann, Senegal
Abstract. In this paper we study the three-dimensional (3-D) Lagrangian structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using Lagrangian descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of Lagrangian transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the Lagrangian structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex Lagrangian patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.