Geometrical properties of the vorticity vector derived using large-eddy simulation

Abstract

In this paper, the geometrical properties of the resolved vorticity vector ω ¯ derived from large-eddy simulation are investigated using a statistical method. Numerical tests have been performed based on a turbulent Couette channel flow using three different dynamic linear and nonlinear subgrid-scale stress models. The geometrical properties of ω ¯ have a significant impact on various physical quantities and processes of the flow. To demonstrate, we examined helicity and helical structure, the attitude of ω ¯ with respect to the eigenframes of the resolved strain rate tensor S ¯ ij and negative subgrid-scale stress tensor - τ ij , enstrophy generation, and local vortex stretching and compression. It is observed that the presence of the wall has a strong anisotropic influence on the alignment patterns between ω ¯ and the eigenvectors of S ¯ ij , and between ω ¯ and the resolved vortex stretching vector. Some interesting wall-limiting geometrical alignment patterns and probability density distributions in the form of Dirac delta functions associated with these alignment patterns are reported. To quantify the subgrid-scale modelling effects, the attitude of ω ¯ with respect to the eigenframe of - τ ij is studied, and the geometrical alignment between ω ¯ and the Euler axis is also investigated. The Euler axis and angle for describing the relative rotation between the eigenframes of - τ ij and S ¯ ij are natural invariants of the rotation matrix, and are found to be effective for characterizing a subgrid-scale stress model and for quantifying the associated subgrid-scale modelling effects on the geometrical properties of ω ¯ .