The dynamics of the anisotropy of the Reynolds stress tensor and its behavior in decaying homogeneous turbulence subjected to system rotation are investigated in this study. Theoretical analysis shows that the anisotropy can be split into two parts: polarization and directional anisotropies. The former can be further separated into a linear part and a nonlinear part. The corresponding linear solution of the polarization anisotropy is derived in this paper. This solution is found to be equivalent to the linear solution of the anisotropy. While proposing a method to introduce the polarization anisotropy into an isotropic turbulence, direct numerical simulation (DNS) of the rotating turbulence with or without the initial anisotropy is carried out. The linear solution of the anisotropy agrees very well with the DNS result, showing that the evolution of the polarization anisotropy is mainly dominated by the linear effect of the system rotation. With an immediate rotation rate, the coupling effect between the system rotation and nonlinear interactions causes an energy transfer from the region near the pole to the region near the equator in wave space. This type of transfer causes an anisotropic distribution of the kinetic energy between the pole and equator, which relates closely to the directional anisotropy and the two-dimensionalization. In addition, we find that the presence of the initial polarization anisotropy does not affect the evolution of the directional anisotropy, while the presence of the initial directional anisotropy greatly influences the evolution of the polarization anisotropy.

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