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Geometric study of Lagrangian and Eulerian structures in turbulent channel flow

Yang, Yue and Pullin, D. I. (2011) Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. Journal of Fluid Mechanics, 674 . pp. 67-92. ISSN 0022-1120.

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We report the detailed multi-scale and multi-directional geometric study of both evolving Lagrangian and instantaneous Eulerian structures in turbulent channel flow at low and moderate Reynolds numbers. The Lagrangian structures (material surfaces) are obtained by tracking the Lagrangian scalar field, and Eulerian structures are extracted from the swirling strength field at a time instant. The multi-scale and multi-directional geometric analysis, based on the mirror-extended curvelet transform, is developed to quantify the geometry, including the averaged inclination and sweep angles, of both structures at up to eight scales ranging from the half-height δ of the channel to several viscous length scales δ_ν. Here, the inclination angle is on the plane of the streamwise and wall-normal directions, and the sweep angle is on the plane of streamwise and spanwise directions. The results show that coherent quasi-streamwise structures in the near-wall region are composed of inclined objects with averaged inclination angle 35°–45°, averaged sweep angle 30°–40° and characteristic scale 20δ_ν, and 'curved legs' with averaged inclination angle 20°–30°, averaged sweep angle 15°–30° and length scale 5δ_ν–10δ_ν. The temporal evolution of Lagrangian structures shows increasing inclination and sweep angles with time, which may correspond to the lifting process of near-wall quasi-streamwise vortices. The large-scale structures that appear to be composed of a number of individual small-scale objects are detected using cross-correlations between Eulerian structures with large and small scales. These packets are located at the near-wall region with the typical height 0.25δ and may extend over 10δ in the streamwise direction in moderate-Reynolds-number, long channel flows. In addition, the effects of the Reynolds number and comparisons between Lagrangian and Eulerian structures are discussed.

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Additional Information:© 2011 Cambridge University Press. Received 9 August 2010; revised 7 December 2010; accepted 13 December 2010; first published online 2 March 2011. The authors are grateful to P. Koumoutsakos for providing generous access on the Brutus cluster at the ETH Zurich. The authors thank I. Bermejo-Moreno and D. Chung for helpful comments. This work has been supported in part by the National Science Foundation under grant DMS-1016111.
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Subject Keywords:boundary layer structure; turbulence theory; turbulent boundary layers
Record Number:CaltechAUTHORS:20110525-093417744
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Official Citation:YUE YANG and D. I. PULLIN (2011). Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. Journal of Fluid Mechanics, 674, pp 67-92 doi:10.1017/S0022112010006427
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23791
Deposited By: Tony Diaz
Deposited On:20 Jun 2011 16:16
Last Modified:21 Sep 2016 22:36

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