Euler Angle and Axis—“Fingerprints” of a Subgrid-Scale Stress Model

  • Zixuan Yang
  • Bing-Chen WangEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 165)


The concepts of Euler angle and axis are utilized to investigate the relative rotation between the eigenframes of the deviatoric subgrid-scale (SGS) stress tensor \(-\tau _{ij}^d\) and the resolved strain rate tensor \(\bar{S}_{ij}\). Both Euler angle and axis are “natural invariants” of fluid tensors, which uniquely describe the relative rotation between eigenframes of two tensors. The Euler angle and axis can be regarded as “fingerprints” of a SGS stress model and have a profound implication for structural modeling of the SGS stress tensor. As an application, three SGS models are tested in the context of turbulent channel flows. The proposed Euler angle and axis are proven to be effective for demonstrating geometrical properties of a SGS stress model.


Large Eddy Simulation Direct Numerical Simulation Euler Angle Viscous Sublayer Turbulent Channel Flow 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of ManitobaWinnipegCanada

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