Alignment Trends of a Decomposed SGS Stress Tensor Determined From Holographic PIV Measurements

Based on the holographic PIV measurements in the core region of a square duct at Re_H ≈ 1.2×10⁵, the tensorial alignment of the deviatoric subgrid-scale (SGS) stress (τ_ij) is shown to have a bi-modal behavior (Tao et al., 2001, 2002). To gain further insight into the statistical geometry of τ_ij, we employ the Germano decomposition, τ_ij = L_ij + C_ij + R_ij (Leonard, 1974; Germano, 1986), and compute the decomposed stress elements directly from the velocity data. Their alignment trends are then investigated using joint probability density functions (pdf), similar to those in Tao et al. (2002). The alignment between the Leonard stress, L_ij, and the filtered strain-rate (S˜_ij) is found to exhibit a similar bi-modal trend, but the alignment angle between the corresponding eigenvectors is around 40° instead of 32°. The alignment between the SGS Reynolds stress, R_ij and S˜_ij, on the other hand, is found to be consistent with an eddy viscosity configuration. In contrast, the alignment between the cross stress, C_ij, and S˜_ij is more complicated and does not exhibit any significant trend. Furthermore, previously reported alignment trends of the vorticity vector, ω˜_i, relative to τ_ij, are primarily due to the contribution from L_ij. The orientation of ω˜_i relative to C_ij shows less robust alignment trends, and there is no clear trend in the alignment of ω˜_i relative to R_ij.