Characterization of velocity-gradient dynamics in incompressible turbulence using local streamline geometry

Abstract

This study develops a comprehensive description of local streamline geometry and uses the resulting shape features to characterize velocity gradient ( ) dynamics. The local streamline geometric shape parameters and scale factor (size) are extracted from by extending the linearized critical point analysis. In the present analysis, is factorized into its magnitude ( ) and normalized tensor . The geometric shape is shown to be determined exclusively by four parameters: second invariant, ( ); third invariant, ( ); intermediate strain rate eigenvalue, ; and vorticity component along intermediate strain rate eigenvector, . Velocity gradient magnitude, , plays a role only in determining the scale of the local streamline structure. Direct numerical simulation data of forced isotropic turbulence ( ) is used to establish streamline shape and scale distribution, and then to characterize velocity-gradient dynamics. Conditional mean trajectories (CMTs) in – space reveal important non-local features of pressure and viscous dynamics which are not evident from the -invariants. Two distinct types of – CMTs demarcated by a separatrix are identified. The inner trajectories are dominated by inertia–pressure interactions and the viscous effects play a significant role only in the outer trajectories. Dynamical system characterization of inertial, pressure and viscous effects in the – phase space is developed. Additionally, it is shown that the residence time of – CMTs through different topologies correlate well with the corresponding population fractions. These findings not only lead to improved understanding of non-local dynamics, but also provide an important foundation for developing Lagrangian velocity-gradient models.