On the non-local geometry of turbulence

A multi-scale methodology for the study of the non-local geometry of structures in turbulence is applied to a passive-scalar field and the square of the vorticity field of a $5123$ periodic cube DNS of homogeneous isotropic turbulence. Results of its application to the vorticity field of a set of DNS with identical initial conditions and increasing grid resolutions ($256,512,10243$, with $k_{max}\eta\approx 1$,$2$,$4$) are also discussed. The methodology consists of three main steps: extraction, characterization and classification, starting from a 3D scalar field. Extraction is done via the curvelet transform (allowing a multi-scale decomposition), followed by isosurfacing of the set of scalar fields obtained by filtering in curvelet space. Characterization is based on the area-based probability density function of two differential-geometry properties, shape index and curvedness, complemented with global invariants of the surface, thus defining its signature. Classification uses a feature space of parameters obtained from the signature of each structure,where clustering techniques are applied searching for groups of structures with common geometry.