A Kinetic Perspective on k - ϵ Turbulence Model and Corresponding Entropy Production

In this paper, we present an alternative derivation of the entropy production in turbulent flows, based on a formal analogy with the kinetic theory of rarefied gas. This analogy allows for proving that the celebrated k - ϵ model for turbulent flows is nothing more than a set of coupled BGK (Bhatnagar–Gross–Krook)-like equations with a proper forcing. This opens a novel perspective on this model, which may help in sorting out the heuristic assumptions essential for its derivation, such as the balance between turbulent kinetic energy production and dissipation. The entropy production is an essential condition for the design and optimization of devices where turbulent flows are involved