Leith diffusion model for homogeneous anisotropic turbulence. (27th June 2017)

• Record Type: Journal Article
• Authors: Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan
• Is Part Of: Computers & fluids. Volume 151(2017)
• Page Start: 108
• Page End: 114
• Publication Date: 2017-06-27
• Subjects: Spectral modeling -- Anisotropic diffusion -- Anisotropic turbulence; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2016.07.009
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Generalization of Leith diffusion model to anisotropic turbulence. Expansion using irreducible representations of the S0(3) symmetry group. Decomposition into directional and polarization anisotropy. Truncation at second order for directional and polarization components. Numerical simulations used to test new model equations. Abstract: A new spectral closure model for homogeneous anisotropic turbulence is proposed. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.