2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/22544A mean-field approach (filtering out subgrid scales) is applied to the Boltzmann equation in order to derive a subgrid turbulence model based on kinetic theory. It is demonstrated that the only Smagorinsky type model which survives in the hydrodynamic limit on the viscosity time scale is the so-called tensor-diffusivity model. Scaling of the filter-width with Reynolds number and Knudsen number is established. This sets the first rigorous step in deriving turbulence models from kinetic theory.18 pages, Minor corrections, Accepted in Physica AStatistical MechanicsMathematical PhysicsChaotic DynamicsFluid Dynamicstext