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Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence

Yang, Yue and Pullin, D. I. and Bermejo-Moreno, Iván (2010) Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence. Journal of Fluid Mechanics, 654 . pp. 233-270. ISSN 0022-1120. https://resolver.caltech.edu/CaltechAUTHORS:20100805-083626186

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Abstract

We report the multi-scale geometric analysis of Lagrangian structures in forced isotropic turbulence and also with a frozen turbulent field. A particle backward-tracking method, which is stable and topology preserving, was applied to obtain the Lagrangian scalar field φ governed by the pure advection equation in the Eulerian form ∂_tφ + u · ∇φ = 0. The temporal evolution of Lagrangian structures was first obtained by extracting iso-surfaces of φ with resolution 1024^3 at different times, from t = 0 to t = T_e, where T_e is the eddy turnover time. The surface area growth rate of the Lagrangian structure was quantified and the formation of stretched and rolled-up structures was observed in straining regions and stretched vortex tubes, respectively. The multi-scale geometric analysis of Bermejo-Moreno & Pullin (J. Fluid Mech., vol. 603, 2008, p. 101) has been applied to the evolution of φ to extract structures at different length scales and to characterize their non-local geometry in a space of reduced geometrical parameters. In this multi-scale sense, we observe, for the evolving turbulent velocity field, an evolutionary breakdown of initially large-scale Lagrangian structures that first distort and then either themselves are broken down or stretched laterally into sheets. Moreover, after a finite time, this progression appears to be insensible to the form of the initially smooth Lagrangian field. In comparison with the statistical geometry of instantaneous passive scalar and enstrophy fields in turbulence obtained by Bermejo-Moreno & Pullin (2008) and Bermejo-Moreno et al. (J. Fluid Mech., vol. 620, 2009, p. 121), Lagrangian structures tend to exhibit more prevalent sheet-like shapes at intermediate and small scales. For the frozen flow, the Lagrangian field appears to be attracted onto a stream-surface field and it develops less complex multi-scale geometry than found for the turbulent velocity field. In the latter case, there appears to be a tendency for the Lagrangian field to move towards a vortex-surface field of the evolving turbulent flow but this is mitigated by cumulative viscous effects.


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http://dx.doi.org/10.1017/S0022112010000571 DOIArticle
Additional Information:© 2010 Cambridge University Press. Received 20 July 2009; revised 27 January 2010; accepted 28 January 2010; first published online 17 May 2010. This work has been supported in part by the National Science Foundation under grant DMS-0714050. D. I. Pullin benefited from support during a visit to the Center for Water Research at the University of Western Australia.
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NSFDMS-0714050
Record Number:CaltechAUTHORS:20100805-083626186
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100805-083626186
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19286
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Aug 2010 17:12
Last Modified:03 Oct 2019 01:54

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