The effect of subgrid-scale models on the vortices computed from large-eddy simulations

Abstract

Direct numerical and large-eddy simulations (DNS/LES) of temporal plane jets are carried out in order to analyze the effect of the subgrid-scale (SGS) models on the vortices obtained from LES. The dynamics of the filtered vorticity norm (or filtered enstrophy) is analyzed through the application of a box filter to temporal DNS of turbulent plane jets (Reλ≈100), using a methodology similar to da Silva and Métais [J. Fluid Mech. 473, 103 (2002)]. Special emphasis is placed on the enstrophy SGS dissipation term, which represents the effect of the SGS models on the vortices computed from LES. When the filter is placed in the inertial range region the evolution of the vorticity norm is governed by the enstrophy production and enstrophy SGS dissipation, which represents, in the mean, a sink of resolved enstrophy. Thus the coherent vortices obtained from LES are subjected to an additional (nonviscous) dissipation mechanism. Locally, however, the enstrophy SGS dissipation can be either a sink or a source of resolved vorticity (forward/backward enstrophy cascade), but the forward cascade dominates, in analogy with what happens with the resolved kinetic energy equation. A priori tests are conducted using several SGS models in order to analyze their ability to represent the enstrophy SGS dissipation. The models analyzed are the Smagorinsky, structure function, filtered structure function, dynamic Smagorinsky, gradient, scale similarity, and mixed. It turns out that in terms of spatial localization all the models lead to a good correlation between the “real” and “modeled” enstrophy SGS dissipation. Moreover, all the SGS models, even of eddy-viscosity type, are able to provide enstrophy SGS backscatter. However, in terms of statistical behavior the eddy-viscosity models do not provide enough enstrophy backscatter as the non-eddy-viscosity models. LES are carried out and show that the Smagorinsky, structure function, and mixed models cause excessive vorticity dissipation compared to the other models, and although the enstrophy SGS dissipation affects mainly the smallest resolved scales, it may affect also some low-wave numbers. An estimation of the “vorticity error” and its wave number dependence is given, for each SGS model. Both a priori tests and LES show that the dynamic Smagorinsky and filtered structure function models seem to be the best suited to a correct prediction of the resolved vorticity field.