Toward an equivalence criterion for Hybrid RANS/LES methods

•A criterion is established to assess the equivalence between hybrid RANS/LES methods.•It is based on the modeled energy of the unresolved scales.•Perturbation analyses about the equilibrium states are performed.•The equivalence between two particular hybrid methods is demonstrated, PITM and DES.•DES can thus be interpreted as a model for the temporally filtered Navier–Stokes equations. A criterion is established to assess the equivalence between hybrid RANS/LES methods, called H-equivalence, based on the modeled energy of the unresolved scales, which leads to similar low-order statistics of the resolved motion. Different equilibrium conditions are considered, and perturbation analyses about the equilibrium states are performed. The procedure is applied to demonstrate the equivalence between two particular hybrid methods, and leads to relationships between hybrid method parameters that control the partitioning of energy between the resolved and unresolved scales of motion. This equivalence is validated by numerical results obtained for the cases of plane and periodically constricted channel flows. This concept of H-equivalence makes it possible to view different hybrid methods as models for the same system of equations: as a consequence, detached-eddy simulation (DES), which is shown to be H-equivalent to the temporal partially integrated transport model (T-PITM) in inhomogeneous, stationary situations, can be interpreted as a model for the subfilter stress involved in the temporally filtered Navier–Stokes equations.