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The mean conformation tensor in viscoelastic turbulence

Published online by Cambridge University Press:  19 February 2019

Ismail Hameduddin Open the ORCID record for Ismail Hameduddin [Opens in a new window]  and
Tamer A. Zaki Open the ORCID record for Tamer A. Zaki [Opens in a new window]
Ismail Hameduddin
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T1Z2, Canada
Tamer A. Zaki*
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
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Abstract

This work demonstrates that the popular arithmetic mean conformation tensor frequently used in the analysis of turbulent viscoelastic flows is not a good representative of the ensemble. Alternative means based on recent developments in the literature are proposed, namely, the geometric and log-Euclidean means. These means are mathematically consistent with the Riemannian structure of the manifold of positive-definite tensors, on which the conformation tensor lives, and have useful properties that make them attractive alternatives to the arithmetic mean. Using a turbulent FENE-P channel flow dataset, it is shown that these two alternatives are physically representative of the ensemble. By definition, these means minimize the geodesic distance to realizations and exactly preserve the scalar geometric mean of the volume and of the principal stretches. The proposed geometric and log-Euclidean means have clear physical interpretations and are attractive quantities for turbulence modelling.

JFM classification

Waves/Free-surface Flows: Channel flow Turbulent Flows: Turbulent Flows Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 363 - 380
Copyright
© 2019 Cambridge University Press 

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