Revisiting turbulence small-scale behavior using velocity gradient triple decomposition
Rishita Das, Sharath S Girimaji
Abstract
Abstract Turbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor ( A ij ) into the symmetric strain-rate ( S ij ) and anti-symmetric rotation-rate ( W ij ) 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 ( N ij ), pure-shear ( H ij ) and rigid-body-rotation-rate ( R ij ). 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 ( A 2 ≡ A ij A ij ). Especially, shear contribution is dominant in regions of high values of A 2 (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.