Derivation of a PDF model for turbulent flows based on principles from statistical physics

Classical ideas from statistical physics are used to derive a PDF model for turbulent flows. The model is built by adopting a Lagrangian point of view and by considering separately the statistical effects of the viscous and of the pressure gradient forces which act on a fluid particle. Closures are developed alternatively in terms of the pdf itself and of the trajectories of the stochastic process. The viscous force is shown to manifest itself as an anti-diffusion in phase space while modeling of the fluctuating part of the pressure gradient force is based on linear laws for non-equilibrium thermodynamics along Onsager’s regression-to-equilibrium hypothesis. The final expression is identical to a Langevin equation proposed by Pope which is thus seen to be obtained from underlying principles.