A hidden mechanism of dynamic LES models

The dynamic model is one of the most successful inventions in subgrid-scale (SGS) modeling as it alleviates many drawbacks of the static coefficient SGS stress models. The model coefficient is dynamically calculated through the minimization of the Germano-identity error (GIE). However, the driving mechanism behind the dynamic model's success is still not well understood. In the present work, we show that the essence of the dynamic procedure is contained in special low-dimensional subspaces of the resolved velocity field. Specifically, we find that minimization of the GIE along only the principal direction(s) of the resolved strain-rate tensor, in lieu of its nine components in its original formulation, produces equally comparable results as the original dynamic model when examined in canonical turbulent channel flow, a three-dimensional turbulent boundary layer, and a separating flow over periodic hills. On the other hand, when only the non-principal components are considered in the GIE, the model performs as bad as no SGS model case. This suggests that not all components of the Germano identity are equally important for the success of the dynamic model, and that there might be dynamically more important directions for modeling the subgrid dynamics. A potential extension of this idea to a tensorial coefficient Smagorinsky model will also be discussed.