Constrained Euler system for Navier-Stokes turbulence

We propose a model system based on the Euler equations with integral constraints to describe high-Reynolds-number Navier-Stokes turbulence. This system is Galilean invariant. It is demonstrated computationally that the system, under appropriate constraints, evolves to a quasiequilibrium state which reproduces accurately both low- and high-order statistical measures of turbulence observed in laboratory experiments and direct numerical simulations. A large-eddy simulation model based on the constrained Euler system is formulated and computationally validated. The theoretical interest of the proposed system in the context of nonequilibrium statistical mechanics is briefly discussed.