Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence

Rubinstein, Robert; Kurien, Susan; Cambon, Claude

doi:10.1080/14685248.2015.1051184

Title: Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence

Abstract

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.

Authors:

Rubinstein, Robert ^[1]; Kurien, Susan ^[2]; Cambon, Claude ^[3]

NASA Langley Research Center, Hampton, VA (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Ecole Centrale de Lyon, Ecully Cedex (France)

Publication Date:: Mon Jun 22 00:00:00 EDT 2015

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1227460

Report Number(s):: LA-UR-15-20047
Journal ID: ISSN 1468-5248

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Turbulence (Online)

Additional Journal Information:: Journal Name: Journal of Turbulence (Online); Journal Volume: 16; Journal Issue: 11; Journal ID: ISSN 1468-5248

Country of Publication:: United States

Language:: English

Subject:: 99 GENERAL AND MISCELLANEOUS; 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Rubinstein, Robert, Kurien, Susan, and Cambon, Claude. Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence.  United States: N. p., 2015. 
Web.  doi:10.1080/14685248.2015.1051184.

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                    Rubinstein, Robert, Kurien, Susan, & Cambon, Claude. Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence.  United States.  https://doi.org/10.1080/14685248.2015.1051184

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                    Rubinstein, Robert, Kurien, Susan, and Cambon, Claude. Mon .  
"Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence".  United States.  https://doi.org/10.1080/14685248.2015.1051184.  https://www.osti.gov/servlets/purl/1227460.

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@article{osti_1227460,

  title        = {Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence},

  author       = {Rubinstein, Robert and Kurien, Susan and Cambon, Claude},

  abstractNote = {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.},

  doi          = {10.1080/14685248.2015.1051184},

  journal      = {Journal of Turbulence (Online)},

  number       = 11,

  volume       = 16,

  place        = {United States},

  year         = {Mon Jun 22 00:00:00 EDT 2015},

  month        = {Mon Jun 22 00:00:00 EDT 2015}

}

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Works referenced in this record:

The theory of axisymmetric turbulence
journal, September 1946

Batchelor, G. K.
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 186, Issue 1007, p. 480-502
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The theory of axisymmetric turbulence
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Chandrasekhar, Subrahmanyan
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Statistics of cosmic microwave background polarization
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Anisotropic developments for homogeneous shear flows
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Cambon, Claude; Rubinstein, Robert
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One-point turbulence structure tensors
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Waldmann, Ludwig
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Scaling exponents in anisotropic hydrodynamic turbulence
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L’vov, Victor S.; Procaccia, Itamar; Tiberkevich, Vasil
Physical Review E, Vol. 67, Issue 2
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Approach of axisymmetric turbulence to isotropy
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Rapid distortion of axisymmetric turbulence
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General second-rank correlation tensors for homogeneous magnetohydrodynamic turbulence
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Physical Review E, Vol. 56, Issue 3
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Third-order statistics and the dynamics of strongly anisotropic turbulent flows
journal, March 2013

Cambon, C.; Danaila, L.; Godeferd, F. S.
Journal of Turbulence, Vol. 14, Issue 3
DOI: 10.1080/14685248.2013.780128

Works referencing / citing this record:

Advanced spectral anisotropic modelling for shear flows
journal, June 2018

Briard, Antoine; Gréa, Benoît-Joseph; Mons, Vincent
Journal of Turbulence, Vol. 19, Issue 7
DOI: 10.1080/14685248.2018.1478092

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Similar Records

Title: Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence

Abstract

Citation Formats

The theory of axisymmetric turbulence journal, September 1946

The theory of axisymmetric turbulence journal, October 1950

Correlation functions in isotropic and anisotropic turbulence: The role of the symmetry group journal, June 1999

Group Theory and its Applications to Physical Problems journal, October 1962

Statistics of cosmic microwave background polarization journal, June 1997

Anisotropic developments for homogeneous shear flows journal, August 2006

One-point turbulence structure tensors journal, February 2001

Spectral transport model for turbulence journal, January 1996

Spectral approach to non-isotropic turbulence subjected to rotation journal, May 1989

Transporterscheinungen in Gasen von mittlerem Druck book, January 1958

Scaling exponents in anisotropic hydrodynamic turbulence journal, February 2003

Approach of axisymmetric turbulence to isotropy journal, January 1974

Rapid distortion of axisymmetric turbulence journal, February 1978

General second-rank correlation tensors for homogeneous magnetohydrodynamic turbulence journal, September 1997

Third-order statistics and the dynamics of strongly anisotropic turbulent flows journal, March 2013

Advanced spectral anisotropic modelling for shear flows journal, June 2018

The theory of axisymmetric turbulence
journal, September 1946

The theory of axisymmetric turbulence
journal, October 1950

Correlation functions in isotropic and anisotropic turbulence: The role of the symmetry group
journal, June 1999

Group Theory and its Applications to Physical Problems
journal, October 1962

Statistics of cosmic microwave background polarization
journal, June 1997

Anisotropic developments for homogeneous shear flows
journal, August 2006

One-point turbulence structure tensors
journal, February 2001

Spectral transport model for turbulence
journal, January 1996

Spectral approach to non-isotropic turbulence subjected to rotation
journal, May 1989

Transporterscheinungen in Gasen von mittlerem Druck
book, January 1958

Scaling exponents in anisotropic hydrodynamic turbulence
journal, February 2003

Approach of axisymmetric turbulence to isotropy
journal, January 1974

Rapid distortion of axisymmetric turbulence
journal, February 1978

General second-rank correlation tensors for homogeneous magnetohydrodynamic turbulence
journal, September 1997

Third-order statistics and the dynamics of strongly anisotropic turbulent flows
journal, March 2013

Advanced spectral anisotropic modelling for shear flows
journal, June 2018