Statistical Closure to Derive a Subgrid-scale Modeling for Large Eddy Simulations of Three-dimensional Turbulence

The same method is extended to the passive scalar, deriving an eddy diffusivity from the transfer of scalar variance through a given wave number kc. Some specific terms of the transfers are used to determine the modifications that the eddy quantities undergo because of the closeness of kc to dissipative or large scales.

The eddy quantities can be split into two different contributions--an eddy viscosity (or diffusivity) and a higher-order dissipativity, the latter term corresponding to interactions between wave numbers in the neighborhood of the given wave number kc. Drastic differences between the dynamics of three- and two-dimensional turbulence are pointed out. The eddy quantities are used to parameterize the small scales of velocity and scalar fields, first in computations using the same two-point closure, then in direct numerical simulation of large scales.