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

Abstract

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.