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

Keywords:

• homogeneous turbulence

Acknowledgements

We are grateful for ongoing discussions of this topic with Timothy Clark and Charles Zemach. We would also like to thank several colleagues who read and commented on various versions of this paper, including Joseph Morrison, Stephen Woodruff, and Tomasz Drozda of NASA Langley Research Center and Jackson Mayo of Sandia National Laboratory. SK acknowledges support from Malcolm Andrews (project leader for Mix and Burn project, ASC Physics and Engineering Models Program).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Work at the Los Alamos National Laboratory, through the ASC program, was performed under the auspices of the US DOE contract no. [DE-AC52-06NA25396].