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Title: 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 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. Here, 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.

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):
LA-UR-16-21435
Journal ID: ISSN 0045-7930
Grant/Contract Number:
AC52-06NA25396
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 0045-7930
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 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. Here, 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.},
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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.compfluid.2016.07.009

Citation Metrics:
Cited by: 1work
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  • Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. 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. Here, numericalmore » 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.« less
  • Homogeneous anisotropic turbulence consisting of a collection of straight vortex structures is considered, each with a cylindrically unidirectional, but otherwise arbitrary, internal vorticity field. The orientations of the structures are given by a distribution [ital P] of appropriate Euler angles describing the transformation from laboratory to structure-fixed axes. One-dimensional spectra of the velocity components are calculated in terms of [ital P], and the shell-summed energy spectrum. An exact kinematic relation is found in which volume-averaged Reynolds stresses are proportional to the turbulent kinetic energy of the vortex collection times a tensor moment of [ital P]. A class of large-eddy simulationmore » models for nonhomogeneous turbulence is proposed based on application of the present results to the calculation of subgrid Reynolds stresses. These are illustrated by the development of a simplified model using a rapid-distortion-like approximation.« less
  • The representation theory of the rotation group is applied to construct a series expansion of the correlation tensor in homogeneous anisotropic turbulence. The resolution of angular dependence is the main analytical difficulty posed by anisotropic turbulence; representation theory parametrises this dependence by a tensor analogue of the standard spherical harmonics expansion of a scalar. As a result, the series expansion is formulated in terms of explicitly constructed tensor bases with scalar coefficients determined by angular moments of the correlation tensor.
  • An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less
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