Normality-based analysis of multiscale velocity gradients and energy transfer in direct and large-eddy simulations of isotropic turbulence

Abstract

Symmetry-based analyses of multiscale velocity gradients highlight that strain self-amplification (SS) and vortex stretching (VS) drive forward energy transfer in turbulent flows. By contrast, a strain-vorticity covariance mechanism produces backscatter that contributes to the bottleneck effect in the subinertial range of the energy cascade. We extend these analyses by using a normality-based decomposition of filtered velocity gradients in forced isotropic turbulence to distinguish contributions from normal straining, pure shearing and rigid rotation at a given scale. Our analysis of direct numerical simulation (DNS) data illuminates the importance of shear layers in the inertial range and (especially) the subinertial range of the cascade. Shear layers contribute significantly to SS and VS and play a dominant role in the backscatter mechanism responsible for the bottleneck effect. Our concurrent analysis of large-eddy simulation (LES) data characterizes how different closure models affect the flow structure and energy transfer throughout the resolved scales. We thoroughly demonstrate that the multiscale flow features produced by a mixed model closely resemble those in a filtered DNS, whereas the features produced by an eddy viscosity model resemble those in an unfiltered DNS at a lower Reynolds number. This analysis helps explain how small-scale shear layers, whose imprint is mitigated upon filtering, amplify the artificial bottleneck effect produced by the eddy viscosity model in the inertial range of the cascade. Altogether, the present results provide a refined interpretation of the flow structures and mechanisms underlying the energy cascade and insight for designing and evaluating LES closure models.