Revisiting turbulence small-scale behavior using velocity gradient triple decomposition

• Published in: New journal of physics Vol. 22; no. 6; pp. 63015 - 63030
• Main Authors: Das, Rishita, Girimaji, Sharath S
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01-06-2020
• Subjects: Computer simulation; Decomposition; Direct numerical simulation; Eigenvectors; Fluid flow; Intermittency; Isotropic turbulence; Mathematical analysis; Physics; Reynolds number; Rotating bodies; Rotation; Shear; Strain rate; Tensors; Topology; turbulence; Velocity; Velocity gradient; velocity gradient dynamics; Vorticity
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ab8ab2

Turbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor (Aij) into the symmetric strain-rate (Sij) and anti-symmetric rotation-rate (Wij) tensors. To develop further insight, we revisit some of the key studies using a triple decomposition of the velocity-gradient tensor. The additive triple decomposition formally segregates the contributions of normal-strain-rate (Nij), pure-shear (Hij) and rigid-body-rotation-rate (Rij). The decomposition not only highlights the key role of shear, but it also provides a more accurate account of the influence of normal-strain and pure rotation on important small-scale features. First, the local streamline topology and geometry are described in terms of the three constituent tensors in velocity-gradient invariants' space. Using direct numerical simulation (DNS) data sets of forced isotropic turbulence, the velocity-gradient and pressure field fluctuations are examined at different Reynolds numbers. At all Reynolds numbers, shear contributes the most and rigid-body-rotation the least toward the velocity-gradient magnitude (A2 ≡ AijAij). Especially, shear contribution is dominant in regions of high values of A2 (intermittency). It is shown that the high-degree of enstrophy intermittency reported in literature is due to the shear contribution toward vorticity rather than that of rigid-body-rotation. The study also provides an explanation for the non-intermittent nature of pressure-Laplacian, despite the strong intermittency of enstrophy and dissipation fields. The study further investigates the alignment of the rotation axis with normal strain-rate and pressure Hessian eigenvectors. Overall, it is demonstrated that triple decomposition offers unique and deeper understanding of velocity-gradient behavior in turbulence.