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arXiv 1108.2264astro-ph.SR
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分层和/或旋转turbulence中的平均场输运

Mean-field transport in stratified and/or rotating turbulence

A. Brandenburg, K. -H. Rädler, K. Kemel

摘要:

我们调查的平均电动势的运动学框架中,也就是说,忽略反作用的磁场上的流体速度,轴对称湍流的假设下,由旋转,密度分层,或两者的存在下。我们使用一个类似的方法,平均被动标量通量。作为对流的替代,我们考虑等温层中的强迫湍流。当使用标准ansatzes时,平均磁输运由9个系数决定,平均被动标量输运由4个系数决定。我们给出了所有这些传输系数的结果。我们使用测试场方法和测试标量方法,其中输运系数通过求解具有适当选择的平均磁场或平均标量的方程组来确定。这些方法适用于可能依赖于所有三个空间坐标的平均场。我们发现湍流扩散的各向异性是温和的,尽管快速旋转或强密度分层。由平均磁场的梯度张量的对称部分决定的平均电动势的贡献,在以前的几次研究中被忽略了,结果证明是重要的。在分层旋转湍流中,$α$效应是强各向异性的,在大尺度上沿旋转轴被抑制,但在中等尺度上被强烈增强。此外,$\OO\times\meanJJ$效应在中等长度尺度下增强。湍流被动标量扩散率通常几乎是湍流磁扩散率的两倍。磁扩散和被动标量扩散沿旋转轴略有增强,但减少,如果有重力。

英文摘要:

We investigate the mean electromotive force in the kinematic framework, that is, ignoring the back-reaction of the magnetic field on the fluid velocity, under the assumption of axisymmetric turbulence determined by the presence of either rotation, density stratification, or both. We use an analogous approach for the mean passive scalar flux. As an alternative to convection, we consider forced turbulence in an isothermal layer. When using standard ansatzes, the mean magnetic transport is then determined by nine, and the mean passive scalar transport by four coefficients. We give results for all these transport coefficients. We use the test-field method and the test-scalar method, where transport coefficients are determined by solving sets of equations with properly chosen mean magnetic fields or mean scalars. These methods are adapted to mean fields which may depend on all three space coordinates. We find the anisotropy of turbulent diffusion to be moderate in spite of rapid rotation or strong density stratification. Contributions to the mean electromotive force determined by the symmetric part of the gradient tensor of the mean magnetic field, which were ignored in several earlier investigations, turn out to be important. In stratified rotating turbulence, the $α$ effect is strongly anisotropic, suppressed along the rotation axis on large length scales, but strongly enhanced at intermediate length scales. Also the $\OO\times\meanJJ$ effect is enhanced at intermediate length scales. The turbulent passive scalar diffusivity is typically almost twice as large as the turbulent magnetic diffusivity. Both magnetic and passive scalar diffusion are slightly enhanced along the rotation axis, but decreased if there is gravity.

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