Lagrangian coherent structures have supported the description of transport processes in fluid dynamics. In this work we use the M function to provide new insights into the 3-D Lagrangian structure of the southern stratosphere. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied to describe the vertical extension of the stratospheric polar vortex and its evolution.

Our work shows that a simple kinematic model is able to retain the fundamental mechanisms responsible for complex fluid parcel evolution in the stratosphere. Our analysis justifies in a controlled manner the formation of filaments eroding the polar vortex and shows that the breaking and splitting of the polar vortex is explained by the sudden growth of a planetary wave and the decay of the axisymmetric flow.

The disappearance of Malaysia Airlines flight MH370 on 8 March 2014 is one of the great mysteries of our time. The most relevant aspect is that not a piece of debris was found during the intensive surface search carried out for roughly 2 months following the crash. By combining different ocean data with dynamical systems tools, we propose a revised search strategy by showing why debris could not have been expected in some targeted search areas and determining regions where debris could be.