Study on rotating homogeneous turbulence

Abstract

The physics of rotating homogeneous turbulence is studied at various fields. They contain the study on the large-scale structure of rotating homogeneous turbulence to investigate the decay rate of final period of decay of rotating homogeneous turbulence, the velocity-derivative skewness to examine the reduction of spectral transfer by rotation and the turbulence model that can simulates proper decay rate of rotating homogeneous turbulence at high Reynolds number. In the study on large-scale structure of rotating homogeneous turbulence, the large-scale structure of rotating homogeneous turbulence is investigated with an asymptotic expansion method, and the corresponding final period of decay rate is studied. Extending the hypothesis of Batchelor and Proudman (1956) to rotating homogeneous turbulence, it is possible to determine the non-rotational part and the rotational one of the large-scale structure separately. For the non-rotational part, it is determined by the turbulence generation hypothesis only, and a further insight about spectral structures of the 2$^{nd}$ and the 3$^{rd}$ order velocity spectral tensors is obtained. For the rotational part, it is considered for two cases. The one, a general rotation rate, shows that combined with the results of non-rotational part, the asymptotic orders of velocity and vorticity spectral tensor are preserved as $O(\kappa^2)$ and $O(\kappa^4)$ with respect to non-rotating turbulence but their orders in physical space varies as $O(r^{-5})$ and $O(r^{-7})$, respectively. The other, a vanishing rotation rate, gives an exact representation of the large-scale structure of rotating homogeneous turbulence and verifies the results of general rotation rate. It is also found that the velocity and the voricity spectral tensors are even functions in rotation rate because of the invariant property of Navier-Stokes equation about inversion coordinate transform, and due to the homogeneity of turbulence, the helicity of large-scale...