  In large eddy simulations, the Reynolds averages of nonlinear terms are not
directly computable in terms of the resolved variables and require a closure
hypothesis or model, known as a subgrid scale term. Inspired by the
renormalization group (RNG),we introduce an expansion for the unclosed terms,
carried out explicitly to all orders. In leading order, this expansion defines
subgrid scale unclosed terms, which we relate to the dynamic subgrid scale
closure models. The expansion, which generalizes the Leonard stress for closure
analysis, suggests a systematic higher order determination of the model
coefficients.
  The RNG point of view sheds light on the nonuniqueness of the infinite
Reynolds number limit. For the mixing of N species, we see an N+1 parameter
family of infinite Reynolds number solutions labeled by dimensionless
parameters of the limiting Euler equations, in a manner intrinsic to the RNG
itself. Large eddy simulations, with their Leonard stress and dynamic subgrid
models, break this nonuniqueness and predict unique model coefficients on the
basis of theory. In this sense large eddy simulations go beyond the RNG
methodology, which does not in general predict model coefficients.
