剪切作用下螺旋turbulence中的α效应和扩散系数
Alpha effect and diffusivity in helical turbulence with shear
摘要：
我们研究了在螺旋强迫存在的情况下，湍流输运系数（例如$α$张量（$α_{ij}$）和湍流磁扩散系数张量（$η_{ij}$）的分量）对剪切和磁雷诺数的依赖性。我们使用三维直接数值模拟与周期性的边界条件和测量的湍流输运系数，使用运动学测试场方法。在所有情况下，磁普朗特数取为1。我们发现随着剪切的增加，$α_{ij}$淬灭的对角分量增加，而$η_{ij}$淬灭的对角分量增加。两个张量的反对称部分随着剪切的增加而增加。我们还提出了一个简单的表达式的湍流泵浦速度（或$γ$效果）。该抽吸速度与湍流的动力学螺旋度和平均流的涡度成比例。对于负螺旋度，即对于$α_{ij}$的正迹线，它指向平均涡度的方向，即垂直于切变流平面。我们的模拟支持低剪切和磁雷诺数的表达。输运系数与平均流的波数呈洛伦兹函数关系，这与非剪切湍流的情况相同。
英文摘要：
We study the dependence of turbulent transport coefficients, such as the components of the $α$ tensor ($α_{ij}$) and the turbulent magnetic diffusivity tensor ($η_{ij}$), on shear and magnetic Reynolds number in the presence of helical forcing. We use three-dimensional direct numerical simulations with periodic boundary conditions and measure the turbulent transport coefficients using the kinematic test field method. In all cases the magnetic Prandtl number is taken as unity. We find that with increasing shear the diagonal components of $α_{ij}$ quench, whereas those of $η_{ij}$ increase. The antisymmetric parts of both tensors increase with increasing shear. We also propose a simple expression for the turbulent pumping velocity (or $γ$ effect). This pumping velocity is proportional to the kinetic helicity of the turbulence and the vorticity of the mean flow. For negative helicity, i.e. for a positive trace of $α_{ij}$, it points in the direction of the mean vorticity, i.e. perpendicular to the plane of the shear flow. Our simulations support this expression for low shear and magnetic Reynolds number. The transport coefficients depend on the wavenumber of the mean flow in a Lorentzian fashion, just as for non-shearing turbulence.
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