Modeling return to isotropy using kinetic equations

Abstract

Kinetic equations modeling the behavior of the velocity probability density function (PDF) in homogeneous anisotropic decaying turbulence are hypothesized and their implications for return-to-isotropy are investigated. Anisotropic turbulent decay is a parametrically simple but theoretically complex turbulent flow that is dominated by nonlinear interactions. The physical implications of the Bhatnagar–Gross–Krook model, a relaxation model, and the Fokker–Planck model for the “collision” term in the PDF evolution equation are analyzed in detail. Using fairly general assumptions about the physics, three different parameter-free return-to-isotropy models are proposed. These models are compared with experimental data, classical models, and analytical limits. The final model expression is particularly interesting, and can easily be implemented in classic Reynolds stress transport models.