Exploration of the Cusp Behavior of the RNG Eddy Viscosity Near the Cutoff Wavenumber.

摘要

The renormalization group (RNG) theory has been used to derive the cutoff-dependent subgrid eddy viscosity (Yakhot and Orszag, 1986). Here, the possibility of deriving the cusp for wavenumbers near the cutoff is investigated. It is explained why the cusp does not appear at lowest order in the RNG analysis of the Navier Stokes equations, and why previously proposed derivations of the cusp using RNG lead to mathematically or physically unreasonable results. However, the cusp may be derived from the lowest-order RNG equation for the energy spectrum using the RNG eddy damping. This energy equation is equivalent to the EDQNM model energy equation with a theoretically derived Kolmogorov constant. Renormalization group theory, Eddy viscosity, Vorticity equation.