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On the topology of the eigenframe of the subgrid-scale stress tensor

Published online by Cambridge University Press:  07 June 2016

Zixuan Yang  and
Bing-Chen Wang
Zixuan Yang
Affiliation:
Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada
Bing-Chen Wang*
Affiliation:
Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada
*
†Email address for correspondence: BingChen.Wang@umanitoba.ca
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Abstract

In this paper, the geometrical properties of the subgrid-scale (SGS) stress tensor are investigated through its eigenvalues and eigenvectors. The concepts of Euler rotation angle and axis are utilized to investigate the relative rotation of the eigenframe of the SGS stress tensor with respect to that of the resolved strain rate tensor. Both Euler rotation angle and axis are natural invariants of the rotation matrix, which uniquely describe the topological relation between the eigenframes of these two tensors. Different from the reference frame fixed to a rigid body, the eigenframe of a tensor consists of three orthonormal eigenvectors, which by their nature are subjected to directional aliasing. In order to describe the geometric relationship between the SGS stress and resolved strain rate tensors, an effective method is proposed to uniquely determine the topology of the eigenframes. The proposed method has been used for testing three SGS stress models in the context of homogeneous isotropic turbulence at three Reynolds numbers, using both a priori and a posteriori approaches.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , pp. 598 - 627
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Copyright
© 2016 Cambridge University Press 

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