Reformulation of recursive-renormalization-group-based subgrid modeling of turbulence.

An alternative development of the recursive-renormalization-group (RNG) theory for the subgrid modeling of turbulence is presented which is now independent of the order in which the subgrid averaging is performed. The relevant approximations, perturbation ordering, and the averaging process are explicitly considered. In particular, it is shown that, of the higher-order nonlinearities introduced into the RNG Navier-Stokes equation, only the third-order nonlinearity appears at the desired level of the perturbation expansion. Moreover, these triple-velocity product terms appear at the same order as that of the eddy viscosity which is generated by the RNG subgrid-elimination procedure. These third-order nonlinearities also play a major role in the energy-balance equation with the corresponding energy-transfer process resulting in an analytic eddy-viscosity formulation which is in agreement with that from closure theories and the results of direct numerical simulations (DNS). This is also confirmed further here by a direct analysis of both large-eddy-simulation and DNS databases for the fluid velocity. Moreover, it is shown that these RNG-induced triple nonlinearities give rise to a backscatter in the energy from small scales to large spatial scales, in agreement with recent closure theories and numerical simulations.