# Fluid Mechanics and Acoustics Laboratory - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

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Article in J. Turbul. (2015)

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

Robert Rubinstein, Susan Kurien & Claude Cambon

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.