Revisiting turbulence small-scale behavior using velocity gradient triple decomposition

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 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 ($A^2$). Especially, shear contribution is dominant in regions of intermittency (high values of $A^2$). It is also 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 absence of intermittency of the pressure-Laplacian, despite the strong intermittency of enstrophy and dissipation fields. Overall, it is demonstrated that triple decomposition offers unique and deeper understanding of velocity-gradient behavior in turbulence.

References in corpus (11)

• Rortex A New Vortex Vector Definition and Vorticity Tensor and Vector Decompositions
• A Definition of Vortex Vector and Vortex
• Extreme velocity gradients in turbulent flows
• Modeling the pressure Hessian and viscous Laplacian in Turbulence: comparisons with DNS and implications on velocity gradient dynamics
• Emergence of Multi-Scaling in a Random Force-Stirred Fluid
• Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence
• Statistics of Pressure Fluctuations in Decaying, Isotropic Turbulence
• Characterization of velocity-gradient dynamics in incompressible turbulence using local streamline geometry
• Anomalous Exponents in Strong Turbulence
• Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations
• Scaling of locally averaged energy dissipation and enstrophy density in isotropic turbulence

Cited by in corpus (4)

• Velocity gradient analysis of a head-on vortex ring collision
• Energy stability analysis of turbulent incompressible flow based on the triple decomposition of the velocity gradient tensor
• Velocity gradient partitioning in turbulent flows
• Normality-based analysis of multiscale velocity gradients and energy transfer in direct and large-eddy simulations of isotropic turbulence