Kinetic theory of turbulence modeling: smallness parameter, scaling and microscopic derivation of Smagorinsky model

Ansumali, S., Karlin, I.V. and Succi, S. (2004) Kinetic theory of turbulence modeling: smallness parameter, scaling and microscopic derivation of Smagorinsky model. Physica A: Statistical Mechanics and its Applications, 338 (3-4), 379-394.

Abstract

A 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

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