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

Authors

Robert Rubinstein, Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VAFollow
Susan Kurien, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM
Claude Cambon, LMFA UMR 5509 CNRS - Ecole Centrale de Lyon, Université de Lyon, 69134 Ecully, France

Document Type

Article

Date of this Version

2015

Citation

Journal of Turbulence, 2015 Vol. 16, No. 11, 1058–1075

Comments

U.S. Government Work

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. The series expansion is formulated in terms of explicitly constructed tensor bases with scalar coefficients determined by angular moments of the correlation tensor.