On the consistency of the Rational Large Eddy Simulation model

In this paper we consider the Rational Large Eddy Simulation model for turbulent flows (RLES in the sequel), introduced by Galdi and Layton. We recall some analytical results regarding the RLES model and the main result we will prove is the convergence of the strong solutions to the RLES model to those of the Navier-Stokes (in some Sobolev spaces), as the averaging radius goes to zero. Estimates on the rates of convergence are also obtained. These results give more weight to the validity of the method in either computational or physical experiments. We also consider the error arising from the derivation of the model in presence of boundaries. In particular, the equations present an extra-term involving the boundary value of the stress tensor. By using some recent estimates on this ``commutation error'' we show that, with a Smagorinsky sub-grid scale term, the kinetic energy remains bounded.