Time-evolution of passive scalar structures in shock-turbulence interaction

A tracking algorithm is introduced to study the time evolution of isosurfaces of any scalar quantity in turbulent flows by relating the geometry of the surface with the underlying flow physics. At every instant in time each educed isosurface is represented as a point in a feature space of parameters that characterize the structures, including geometric and physical information. Correspondences between all structures educed in consecutive time instants are used to construct a graph in which each vertex represents an individual structure at a given time and the edges indicate the found correspondences between the structures over time.
Application of the methodology is presented to study structures of passive scalars (Sc ≈ 1) with well-defined initial shapes and sizes transported in a background turbulent flow (Re_λ≈ 40, M_t ≈ 0.3) passing through a nominally planar shock wave (M ≈ 1.5). Changes of the non-local geometry of the structures across the shock are related to changes of carried physical quantities, such as enstrophy, dissipation rates, and the alignment of strain-rate eigenvectors, vorticity and scalar gradient. Ensemble statistics for structures with common patterns of time evolution will be highlighted.