Subgrid-scale interactions in a numerically simulated planar turbulent jet and implications for modelling

Abstract

The dynamics of subgrid-scale energy transfer in turbulence is investigated in a database of a planar turbulent jet at Reλ ≈ 110, obtained by direct numerical simulation. In agreement with analytical predictions (Kraichnan 1976), subgrid-scale energy transfer is found to arise from two effects: one involving non-local interactions between the resolved scales and disparate subgrid scales, the other involving local interactions between the resolved and subgrid scales near the cutoff. The former gives rise to a positive, wavenumber-independent eddy-viscosity distribution in the spectral space, and is manifested as low-intensity, forward transfers of energy in the physical space. The latter gives rise to positive and negative cusps in the spectral eddy-viscosity distribution near the cutoff, and appears as intense and coherent regions of forward and reverse transfer of energy in the physical space. Only a narrow band of subgrid wavenumbers, on the order of a fraction of an octave, make the dominant contributions to the latter. A dynamic two-component subgrid-scale model (DTM), incorporating these effects, is proposed. In this model, the non-local forward transfers of energy are parameterized using an eddy-viscosity term, while the local interactions are modelled using the dynamics of the resolved scales near the cutoff. The model naturally accounts for backscatter and correctly predicts the breakdown of the net transfer into forward and reverse contributions in a priori tests. The inclusion of the local-interactions term in DTM significantly reduces the variability of the model coefficient compared to that in pure eddy-viscosity models. This eliminates the need for averaging the model coefficient, making DTM well-suited to computations of complex-geometry flows. The proposed model is evaluated in LES of transitional and turbulent jet and channel flows. The results show DTM provides more accurate predictions of the statistics, structure, and spectra than dynamic eddy-viscosity models and remains robust at marginal LES resolutions.