论文标题
湍流螺旋发电机的饱和
Saturation of turbulent helical dynamos
论文作者
论文摘要
自然界中大型磁场的存在通常归因于由湍流螺旋发电机驱动的磁性螺旋性反向级联。在这项工作中，我们表明，在动荡的螺旋发电机中，磁性螺旋的逆通量向大尺度$π_ {\ Mathcal {h}} $界限为$ | |π_ {\ nathcal {h}耗散波数和$ c $一个订单一个常数。假设具有经典的各向同性湍流缩放，磁性螺旋性的逆通量$π_ {\ Mathcal {h}} $至少以$ -3/4 $ $ -3/4 $ power-law的速度，带有磁性雷诺数$ rm $ rm $ rm $：$ | wim | wim | wim | wim | wime |π_{\ Mathcal {\ Mathcal { \ lecε\ ell_f rm^{ - 3/4} \ max [pm，1]^{1/4} $，其中$ pm $ the Magnetic prandtl数字和$ \ ell_f $ the ofercing lengthscale。我们使用在中间尺度上强制的湍流发电机的直接数值模拟使用$ rm $的缩放。结果进一步表明，非线性饱和度是通过反向级联之间的平衡与域大小尺寸尺度尺度$ l $之间的平衡来实现的，在该域大小尺度尺度$ l $中，磁能的饱和值受$ {\ Mathcal {e}} _ \ text {m} _ \ text {m} {m} {m} rm^{1/4} \ max [1，pm]^{1/4} $。数值模拟还证明了这一结合。
The presence of large scale magnetic fields in nature is often attributed to the inverse cascade of magnetic helicity driven by turbulent helical dynamos. In this work we show that in turbulent helical dynamos, the inverse flux of magnetic helicity towards the large scales $Π_{\mathcal{H}}$ is bounded by $|Π_{\mathcal{H}}|\le c εk_η^{-1}$, where $ε$ is the energy injection rate, $k_η$ is the Kolmogorov magnetic dissipation wavenumber and $c$ an order one constant. Assuming the classical isotropic turbulence scaling, the inverse flux of magnetic helicity $Π_{\mathcal{H}}$ decreases at least as a $-3/4$ power-law with the magnetic Reynolds number $Rm$ : $|Π_{\mathcal{H}} | \le c ε\ell_f Rm^{-3/4}\max[Pm,1]^{1/4}$, where $Pm$ the magnetic Prandtl number and $\ell_f$ the forcing lengthscale. We demonstrate this scaling with $Rm$ using direct numerical simulations of turbulent dynamos forced at intermediate scales. The results further indicate that nonlinear saturation is achieved by a balance between the inverse cascade and dissipation at domain size scales $L$ for which the saturation value of the magnetic energy is bounded by ${\mathcal{E}}_\text{m}\leq c L (ε\ell_f)^{2/3} Rm^{1/4}\max[1,Pm]^{1/4}$. Numerical simulations also demonstrate this bound.
