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 perform ed. The relevant approximations, perturbation ordering, and the averag ing process are explicitly considered. In particular, it is shown that , of the higher-order nonlinearities introduced into the RNG Navier-St okes equation, only the third-order nonlinearity appears at the desire d 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 thi rd-order nonlinearities also play a major role in the energy-balance e quation with the corresponding energy-transfer process resulting in an analytic eddy-viscosity formulation which is in agreement with that f rom 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. Moreo ver, it is shown that these RNG-induced triple nonlinearities give ris e to a backscatter in the energy from small scales to large spatial sc ales, in agreement with recent closure theories and numerical simulati ons.