Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence

Abstract

Using results of direct numerical simulations of isotropic turbulence the subgrid-scale energy transfer in the physical space is calculated exactly employing a spectral decomposition of the velocity field into large (resolved) and small (unresolved) scales. Comparisons with large-scale quantities reveal large qualitative correlations between regions of subgrid transfer and the boundaries of regions of large vorticity production. This suggests a novel analysis of the nonlinear term, where it is decomposed into four components determined by four combinations of the resolved and unresolved velocity and vorticity fields. It is found that there is a 90% vector-correlation between the subgrid transfer and the component of the full transfer associated with the resolved velocity and unresolved vorticity, but that 90% of the total subgrid energy production is determined by the component associated with the unresolved velocity and resolved vorticity. These results suggest subgrid-scale models that have higher correlation values with the exact subgrid scale terms than a number of other physical quantities that are traditionally considered to govern the dynamics of the large scales of turbulence. The distinguishing feature of the new models is that they emphasize the nonlinear dynamics of the smallest resolved scales in the modeling procedures.