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Geometry and interaction of structures in homogeneous isotropic turbulence

Published online by Cambridge University Press:  29 August 2012

T. Leung ,
N. Swaminathan  and
P. A. Davidson
T. Leung
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
N. Swaminathan*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
P. A. Davidson
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

A strategy to extract turbulence structures from direct numerical simulation (DNS) data is described along with a systematic analysis of geometry and spatial distribution of the educed structures. A DNS dataset of decaying homogeneous isotropic turbulence at Reynolds number is considered. A bandpass filtering procedure is shown to be effective in extracting enstrophy and dissipation structures with their smallest scales matching the filter width, . The geometry of these educed structures is characterized and classified through the use of two non-dimensional quantities, ‘planarity’ and ‘filamentarity’, obtained using the Minkowski functionals. The planarity increases gradually by a small amount as is decreased, and its narrow variation suggests a nearly circular cross-section for the educed structures. The filamentarity increases significantly as decreases demonstrating that the educed structures become progressively more tubular. An analysis of the preferential alignment between the filtered strain and vorticity fields reveals that vortical structures of a given scale are most likely to align with the largest extensional strain at a scale 3–5 times larger than . This is consistent with the classical energy cascade picture, in which vortices of a given scale are stretched by and absorb energy from structures of a somewhat larger scale. The spatial distribution of the educed structures shows that the enstrophy structures at the scale (where is the Kolmogorov scale) are more concentrated near the ones that are 3–5 times larger, which gives further support to the classical picture. Finally, it is shown by analysing the volume fraction of the educed enstrophy structures that there is a tendency for them to cluster around a larger structure or clusters of larger structures.

JFM classification

Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 710 , 10 November 2012 , pp. 453 - 481
Copyright
Copyright © Cambridge University Press 2012

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