Leith diffusion model for homogeneous anisotropic turbulence
Abstract
Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the thirdorder 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 tracefree 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. Here, numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the nontrivial effects of spectral dependencies on the different returntoisotropy rates of the directional and polarization contributions.
 Authors:
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1419375
 Alternate Identifier(s):
 OSTI ID: 1338774
 Report Number(s):
 LAUR1621435
Journal ID: ISSN 00457930
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article: Publisher's Accepted Manuscript
 Journal Name:
 Computers and Fluids
 Additional Journal Information:
 Journal Volume: 151; Journal Issue: C; Journal ID: ISSN 00457930
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; spectral modeling; anisotropic diffusion; anisotropic turbulence
Citation Formats
Rubinstein, Robert, Clark, Timothy T., and Kurien, Susan. Leith diffusion model for homogeneous anisotropic turbulence. United States: N. p., 2017.
Web. doi:10.1016/j.compfluid.2016.07.009.
Rubinstein, Robert, Clark, Timothy T., & Kurien, Susan. Leith diffusion model for homogeneous anisotropic turbulence. United States. doi:10.1016/j.compfluid.2016.07.009.
Rubinstein, Robert, Clark, Timothy T., and Kurien, Susan. Thu .
"Leith diffusion model for homogeneous anisotropic turbulence". United States.
doi:10.1016/j.compfluid.2016.07.009.
@article{osti_1419375,
title = {Leith diffusion model for homogeneous anisotropic turbulence},
author = {Rubinstein, Robert and Clark, Timothy T. and Kurien, Susan},
abstractNote = {Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the thirdorder 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 tracefree 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. Here, numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the nontrivial effects of spectral dependencies on the different returntoisotropy rates of the directional and polarization contributions.},
doi = {10.1016/j.compfluid.2016.07.009},
journal = {Computers and Fluids},
number = C,
volume = 151,
place = {United States},
year = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
}
Web of Science

Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the thirdorder 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 tracefree 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. Here, numericalmore »Cited by 1

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