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An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number

Published online by Cambridge University Press:  15 February 2007

MICHELE GUALA ,
ALEXANDER LIBERZON ,
ARKADY TSINOBER  and
WOLFGANG KINZELBACH
MICHELE GUALA
Affiliation:
Institute of Environmental Engineering, Swiss Federal Institute of Technology, ETH Zurich, CH-8093 Zurich, Switzerland
ALEXANDER LIBERZON
Affiliation:
Institute of Environmental Engineering, Swiss Federal Institute of Technology, ETH Zurich, CH-8093 Zurich, Switzerland Department of Fluid Mechanics and Heat Transfer, Tel Aviv University, 69978 Tel Aviv, Israel
ARKADY TSINOBER
Affiliation:
Marie Curie Chair in Fundamental and Conceptual Aspects of Turbulent Flows, Institute for Mathematical Sciences and Department of Aeronautics, Imperial College, London SW7 2AZ, UK
WOLFGANG KINZELBACH
Affiliation:
Institute of Environmental Engineering, Swiss Federal Institute of Technology, ETH Zurich, CH-8093 Zurich, Switzerland
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Abstract

Lagrangian auto- and cross-correlation functions of the rate of strain s2, enstrophy ω2, their respective production terms −sijsjkski and ωiωjsij, and material derivatives, Ds2/Dt and Dω2/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Reλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensor sij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2 to the relatively shorter time scales of s2, ωiωjsij and −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s2 and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkski and s2 and between −sijsjkski and Ds2/Dt, in addition to a marked anti-correlation between ωiωjsij and Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s2 and its production term, −sijsjkski.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 574 , 10 March 2007 , pp. 405 - 427
Copyright
Copyright © Cambridge University Press 2007

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