Kinetic closure of turbulence

Abstract

This letter presents a kinetic closure of the filtered Boltzmann--BGK equation, paving the way towards an alternative description of turbulence. The closure naturally incorporates the turbulent subfilter stress tensor without the need for explicit modeling, unlike in classical filtered Navier--Stokes closures. In contrast, it accounts for the subfilter turbulent diffusion in the nonconserved moments by generalizing the BGK collision operator. The model requires neither scale separation between resolved and unresolved scales nor a Smagorinsky-type ansatz for the subfilter stress tensor structure. The Chapman--Enskog analysis shows that its hydrodynamic limit converges exactly to the filtered Navier--Stokes equations, with velocity gradients isolating subfilter contributions. Validations through lattice Boltzmann simulations of the Taylor--Green vortex and the turbulent mixing layer demonstrate improved stability and reduced dissipation, benchmarked against the Smagorinsky model.