The magnetohydrodynamic (MHD) turbulence appears in engineering laboratory flows and is a common phenomenon in natural systems, e.g. stellar and planetary interiors and atmospheres and the interstellar medium. The applications in engineering are particularly interesting due to the recent advancement of tokamak devices, reaching very high plasma temperatures, thus giving hope for the production of thermonuclear fusion power. In the case of astrophysical applications, perhaps the main feature of the MHD turbulence is its ability to generate and sustain large-scale and small-scale magnetic fields. However, a crucial effect of the MHD turbulence is also the enhancement of large-scale diffusion via interactions of small-scale pulsations, i.e. the generation of the so-called turbulent viscosity and turbulent magnetic diffusivity, which typically exceed by orders of magnitude their molecular counterparts. The enhanced resistivity plays an important role in the turbulent dynamo process. Estimates of the turbulent electromotive force (EMF), including the so-called $\alpha$ -effect responsible for amplification of the magnetic energy and the turbulent magnetic diffusion are desired. Here, we apply the renormalization group technique to extract the final expression for the turbulent EMF from the fully nonlinear dynamical equations (Navier–Stokes, induction equation). The simplified renormalized set of dynamical equations, including the equations for the means and fluctuations, is derived and the effective turbulent coefficients such as the viscosity, resistivity, the $\alpha$ -coefficient and the Lorentz-force coefficients are explicitly calculated. The results are also used to demonstrate the influence of magnetic fields on energy and helicity spectra of strongly turbulent flows, in particular the magnetic energy spectrum.

中文翻译：

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磁流体动力湍流和发电机的重整化群分析

磁流体动力学 (MHD) 湍流出现在工程实验室流动中，并且是自然系统中的常见现象，例如恒星和行星内部、大气层和星际介质。由于托卡马克装置的最新进展，其在工程中的应用特别有趣，达到了非常高的等离子体温度，从而为生产热核聚变能带来了希望。在天体物理学应用的情况下，MHD 湍流的主要特征可能是它产生和维持大尺度和小尺度磁场的能力。然而，MHD 湍流的一个关键作用也是通过小尺度脉动的相互作用增强大规模扩散，即产生所谓的湍流粘度和湍流磁扩散率，通常比它们的分子对应物高出几个数量级。提高的电阻率在湍流发电机过程中起着重要作用。湍流电动势 (EMF) 的估计，包括所谓的 $\阿尔法$ 需要负责磁能放大和湍流磁扩散的效应。在这里，我们应用重整化群技术从完全非线性动力学方程（Navier-Stokes，感应方程）中提取湍流 EMF 的最终表达式。导出了简化的重整化动力学方程组，包括均值方程和波动方程，以及有效湍流系数，如粘度、电阻率、 $\阿尔法$ -系数和洛伦兹力系数是明确计算的。结果还用于证明磁场对强湍流的能量和螺旋度谱的影响，特别是磁能谱。