TY - JOUR

T1 - On the topology of the eigenframe of the subgrid-scale stress tensor

AU - Yang, Zixuan

AU - Wang, Bing Chen

N1 - Publisher Copyright:
© 2016 Cambridge University Press.

PY - 2016/7/10

Y1 - 2016/7/10

N2 - 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.

AB - 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.

KW - isotropic turbulence

KW - turbulence modelling

KW - turbulence simulation

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U2 - 10.1017/jfm.2016.336

DO - 10.1017/jfm.2016.336

M3 - Article

AN - SCOPUS:84973325747

SN - 0022-1120

VL - 798

SP - 598

EP - 627

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -