Average Turbulence Dynamics from a One-Parameter Kinetic Theory

We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with single free relaxation time depends on space and time. A proper equation is constructed from Klimontovich-type for fluid elements, which satisfies Navier–Stokes hydrodynamics exactly. In suitably averaged form, energy plays role of temperature in standard molecular thermodynamics. fluctuations resembles collision process asymptotically drives distribution towards Gaussian (Maxwell–Boltzmann) equilibrium form. Non-Gaussianity arises directly non-equilibrium shear effects. The present framework overcomes bane most conventional turbulence models theoretical frameworks arising lack scale separation between fluctuating scales Navier-Stokes an eddy viscous term. An flow behaves more like finite Knudsen number time, thus representation.