Geometry dynamics of turbulent flow structures via tracking*

We present a methodology for the analysis of the temporal evolution of flow structures and their mutual interactions based on tracking. The structures, defined as closed surfaces from instantaneous snapshots of the flow, are characterized by area-based joint PDFs of differential geometry pointwise quantities (curvedness and shape index). A hybrid region- and attribute-based tracking algorithm finds realizable correspondences between structures at consecutive time frames, constructing a directed graph that describes the structure evolution and interaction events (e.g., merging and splitting). Common patterns of structure evolution are extracted by graph querying and subgraph mining conditioned on geometric attributes. Ensemble statistics for structures with common geometries are obtained to study their dynamics through trajectories in parameter spaces that combine geometry and flow physics. We show application of the methodology to numerical datasets obtained from direct numerical simulation of turbulent flows in several canonical configurations, including decaying homogeneous isotropic compressible turbulence and shock-turbulence interaction (at different Reynolds, shock and turbulence Mach numbers), compressible mixing layers (at different convective Mach numbers), and the multiphase flow interaction of a droplet breakup in homogeneous isotropic incompressible turbulence.