Toward improved consistency of a priori tests with a posteriori tests in large eddy simulation

It is well known that conventional a priori tests based on the instantaneous true subgrid scale (SGS) stress do not provide a useful diagnostic information on deterministic SGS models due to the stochastic nature of unresolved scales. In this study, the possibility of an alternative diagnostics based on the “best deterministic” model is investigated. The optimal SGS model [J. A. Langford and R. D. Moser, “Optimal LES formulation for isotropic turbulence,” J. Fluid Mech. 398, 321 (1999)] is considered as one of nearly best deterministic models. The validity of the optimal model is confirmed by a posteriori test, showing that the field from the optimal large eddy simulation can be regarded as one of the representative fields among all the possible realizations of filtered direct numerical simulation. Then, a priori and a posteriori tests for several SGS models are performed on the forced isotropic turbulence with a sharp cutoff filter. It is shown that a priori tests based on the optimal model are highly consistent with a posteriori tests. Also, dynamic eddy viscosity models are very close to the optimal model both in a priori and a posteriori senses, which implies that the accurate prediction of backward dissipation is not necessarily required for the deterministic model to predict accurate flow statistics at least for the isotropic turbulence. Therefore, the direct application of scale-invariance concept to the resolved field is shown to be unsuccessful for the spectral cutoff filter. The present study strongly suggests that this concept should be realized in terms of the dynamic constant(s) of dissipative models.