Roles of non-aligned eigenvectors of strain-rate and subgrid-scale stress tensors in turbulence generation

Abstract

Alignment of the eigenvectors for strain-rate tensors and subgrid-scale (SGS) stress tensors in large-eddy simulation (LES) is studied in homogeneous isotropic turbulence. Non-alignment of these two eigenvectors was shown in Tao, Katz & Meneveau (2002). In the present study, the specific term in the decomposition of the SGS stress tensor, which is primarily responsible for causing this non-alignment, is identified using the nonlinear model. The bimodal behaviour of the alignment configuration reported in Tao et al. (2002) was eliminated by reordering the eigenvalues according to the degree of alignment of the corresponding eigenvectors with the vorticity vector. The preferred relative orientation of the eigenvectors was ${\approx}\,42^\circ$. The alignment trends were conditionally sampled based on the relative dominance of strain and vorticity. The effect of the identified term on the alignment was the largest in the region in which the magnitudes of strain and vorticity were comparable and large (flat sheet). The most probable alignment configuration in the flat-sheet region was different from those in the strain-dominated and vorticity-dominated regions. The relative orientation of the eigenvectors was dependent on the degree of resolution for the flat sheet region yielded on the LES mesh. When the alignment was conditionally sampled on the events with the backward scatter of the SGS energy into the grid scale, the interchange of the alignment of the eigenvectors took place. Relevance of the identified term for the generation of turbulence is investigated. It is shown that the identified term makes no contribution to the production of the total SGS energy, but contributes significantly to the generation of the SGS enstrophy. The identified term causes a time-lag in the evolution of the turbulent energy and enstrophy. It is shown that generation of vorticity is markedly attenuated when the magnitude of the identified term is modified, and the original nonlinear model yielded the results which are in the closest agreement with the direct numerical simulation data.