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

Bermejo-Moreno, Iván and Pullin, D. I. and Horiuti, Kiyoshi (2009) Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence. Journal of Fluid Mechanics, 620 . pp. 121-166. ISSN 0022-1120.

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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 a periodic box. Three different resolutions are considered: 256^3, 512^3 and 1024^3 grid points, with k_(max)η(overbar) approximately 1, 2 and 4, respectively, the same initial conditions and Re_λ ≈ 77. This allows a comparison of 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)η(overbar) ≈ 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 on geometrical considerations and non-local analysis, by taking into account the spatial extent of the structures. We apply it to the four fields previously studied. Tube-like structures of Q are predominantly surrounded by sheet-like structures of [A_ij]_+, which appear at closer distances. For the enstrophy, tube-like structures at an 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.

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Additional Information:© 2009 Cambridge University Press. Received 5 June 2008 and in revised form 20 October 2008; published online by Cambridge University Press 26 January 2009. This work has been supported in part by the National Science Foundation under Grant FRG DMS-0353838. K. H. is supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology, Japan (No. 18560156). Part of the computations were performed at Cybermedia Centre, Osaka University and National Institute for Fusion Science.
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NSFFRG DMS-0353838
Ministry of Education, Culture, Sports, Science and Technology, JapanNo. 18560156
Record Number:CaltechAUTHORS:20090603-165553557
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14361
Deposited By: Jason Perez
Deposited On:07 Aug 2009 17:45
Last Modified:03 Oct 2019 00:49

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