In many areas of mathematics and physics, understanding basic topological properties such as connectivity, cardinality, genus and winding of continuously deforming scalar, vector and tensor fields is beneficial, and often crucial. Topology is a powerful tool for analysing structural changes in complex, high-volume data. A prime example is a turbulent flow – e.g., one manifested during the evolution of an unstable vortex. These flows are critical for understanding fundamental astrophysical as well as geophysical phenomena.

Advances in computing now make it possible to detect topological changes directly using sophisticated algorithms. In addition, the persistence of a homology group across scales, as computed using persistent homology (PH), is particularly useful for studying the geometric and physical properties of structures directly. We utilise these algorithms to elucidate the structural evolution of a self-straining vortex at very high Reynolds number. Allowing the role of critical processes such as vorticity disconnections, reconnections, filamentations, intrusions and extrusions, on the surrounding flow field to be extracted and studied in detail. Further, we use a (2+1)-dimensional ‘space-time approach’ with PH to quantify the duration of these processes as the vortex evolves in time. This new method is particularly useful for studying flows of high spatial complexity, such as interacting planetary storms, vortex mergers and fluid mixing problems.