Towards a self-consistent Boltzmann's kinetic model of fluid turbulence

A closure for the effective relaxation time of the Boltzmann-BGK kinetic equation for fluid turbulence is presented, based on a double-averaging procedure over both kinetic and turbulent fluctuations. The resulting effective relaxation time appears to agree with values obtained via a renormalization group treatment of the Navier-Stokes equation only at low values of $k/T$, the ratio of turbulent kinetic energy to fluid temperature. For $k/T>0.1$ the kinetic treatment delivers a significantly longer effective relaxation time.

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