Title: A Definition for Large-Eddy-Simulation Approximations of the Navier- Stokes Equations Running title: A definition of LES

This paper proposes a mathematical definition of Large-Eddy-Simulation (LES) for three-dimensional turbulent incompressible viscous flows. It is proposed to call LES approximation of the Navier–Stokes equations any sequence of finite-dimensional approximations of the velocity and pressure fields that converge (possibly up to subsequences) in the Leray class to a suitable weak solution. This definition introduces a discretization scale h and a cutoff scale for the large eddies ε. A significant byproduct of this definition is that it yields a mathematical rule to select the ratio h/ε. The relevance of the definition is demonstrated on several examples, where it yields results that are in agreement with the intuitive idea of LES.