Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

We perform a multi-scale non-local geometrical analysis of the structures extracted from the enstrophy and kinetic energy dissipation-rate, instantaneous fields of a numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in it periodic box. Three different resolutions are considered: 256(3), 512(3) and 1024(3) grid points, with k(max) (eta) over bar approximately 1, 2 and 4, respectively, the same initial conditions and Re-lambda approximate to 77, This allows it comparison or the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from blob-like and moderately stretched tube-like shapes at the large scales to highly stretched sheet-like structures at the small scales. The intermediate scales show a predominance of tube-like structures For both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency towards structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 256(3) grid resolution case (k(max) (eta) over bar approximate to 1)) was unable to detect the predominance of highly stretched sheet-like structures at the smaller scales in both fields. The same non-local methodology for the study of the geometry of structures, but without the multi-scale decomposition, is applied to two scalar fields used by existing local criteria for the eduction of tube- and sheet-like structures in turbulence, Q and [A(ij)](+), respectively, obtained from invariants of the velocity-gradient tensor and alike in the 1024(3) case. This adds the non-local geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally, we introduce a new methodology for the study of proximity issues among structures of different fields, based oil geometrical considerations and non-local analysis, by taking into account the spatial extent or the structures. We apply it to the Four fields previously studied. Tube-like structures of Q are predominantly surrounded by sheet-like structures of [Aij, which appear at closer distances. For the enstrophy, tube-like structures at,in intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented.