Boltzmann kinetic equation for filtered fluid turbulence

We develop a kinetic Boltzmann equation for describing filtered fluid turbulence applicable for continuum and noncontinuum effects. The effect of unresolved turbulent motion on the resolved distribution function is elucidated and closure modeling issues of kinetic Boltzmann and Navier-Stokes descriptions are reconciled. This could pave the way for unifying turbulence modeling at kinetic and continuum levels and the development of numerical methods that are valid over a wide range of flow physics.