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On the non-local geometry of turbulence

Bermejo-Moreno, Iván and Pullin, D. I. (2008) On the non-local geometry of turbulence. Journal of Fluid Mechanics, 603 . pp. 101-135. ISSN 0022-1120.

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A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed.

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Additional Information:Copyright © Cambridge University Press 2008. Reprinted with permission. (Received 12 July 2007 and in revised form 26 January 2008) The authors are grateful to P. O’Gorman for providing the numerical turbulence database, and to E. Candès and L. Ying for valuable discussions regarding the curvelet transform and for providing, along with L. Demanet, the Curvelab software on which our implementation of the multi-scale filtering in curvelet space is based. This work has been supported in part by the National Science Foundation under Grant DMS-0353838 and DMS-0714050.
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Deposited On:06 May 2008
Last Modified:03 Oct 2019 00:09

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