Dynamics of anisotropy on decaying homogeneous turbulence subjected to system rotation

Abstract

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.

Columnar eddy formation in freely decaying homogeneous rotating turbulence

“…These observations are in accordance with the argument that the nonlinear dynamics brings about energy transfer towards the plane k 3 = 0. Similar angulardependent spectra were obtained by EDQNM2 (Cambon & Jacquin 1989;Cambon et al 1997), LES (Cambon et al 1997), DNS (Morinishi et al 2001;Liechtenstein et al 2005) and AQNM (Bellet et al 2006). The results by Liechtenstein et al (2005) for the pure rotating turbulence are shown in figure 4.17 of Sagaut & Cambon (2008).…”

“…Waleffe (1993) showed the transfer towards the k 3 = 0 plane analytically on the basis of the instability assumption proposed by Waleffe (1992). The transfer was also confirmed for freely decaying turbulence by direct numerical simulation (DNS) (Morinishi, Nakabayashi & Ren 2001;Liechtenstein, Godeferd, & Cambon 2005), large eddy simulation (LES) (Cambon et al 1997) and wave turbulence theory developed in the limit of small Rossby number, Ro, asymptotic quasi-normal Markovian closure (AQNM) (Bellet et al 2006). Here Ro = U/(2ΩL), Ω is a constant rotation rate, U is the characteristic velocity and L is the characteristic length.…”

“…We use the helical decomposition (Cambon & Jacquin 1989;Waleffe 1992;Morinishi et al 2001;Sagaut & Cambon 2008) such aŝ…”

Large eddy simulations of decaying rotating turbulence

“…12 Following the idea of Cambon, Mansour, and Godeferd 4 they divided the influence of system rotation on turbulence into three effects: linear effect of the Coriolis term, a so-called scrambling effect, and a coupling effect. The linear effect is the linear viscous decay at high rotation rates which we already discussed.…”

“…[10][11][12][13] Among investigated flows in a rotating frame of reference were homogeneous turbulence, shear turbulence, and turbulent channel flow. 14,15,[17][18][19] To facilitate physical understanding and modeling, we need to isolate the effects of rotation from other effects.…”