Average Turbulence Dynamics from a One-Parameter Kinetic Theory

Hudong Chen, Ilya Staroselsky, Katepalli R. Sreenivasan, Victor Yakhot

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Article number1109
Issue number7
StatePublished - Jul 2023


  • finite Knudsen flows
  • kinetic theory
  • turbulence modeling

ASJC Scopus subject areas

  • Environmental Science (miscellaneous)


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