Direct numerical simulations of low-Rm MHD turbulence based on the least dissipative modes
Direct numerical simulations of low-Rm MHD turbulence based on the least dissipative modes
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DOI：
10.1017/s0022112010000807
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发表时间：
2010-02
影响因子：
3.7
通讯作者：
A. Poth'erat;V. Dymkou
中科院分区：
文献类型：
--
作者：
A. Poth'erat;V. Dymkou
本文提出了一种新的谱方法，用于低磁雷诺数下磁流体动力学湍流的直接数值模拟。我们的方法的独创性是，而不是使用传统的基地的功能，它依赖于本征模的基础上的耗散运营商，这代表粘性和焦耳耗散。我们应用这个想法的简单情况下，一个周期域在空间的三个方向上，在z方向上的均匀磁场。基仍然是傅立叶空间的子集，但是通过增长的线性衰减率来排序|λ|（即根据最小耗散模式）。我们表明，因为恒定能量的线倾向于遵循恒定能量的线，|λ|在傅立叶空间中，最小尺度的缩放|λmax|在强制流中，可以使用这个单一参数将其表示为雷诺数的函数，即$\（\sqrt{1\lambda^{max}|}/（2\upi k_f）\simeq 0.5\Rey^{1/2}\）$，其中kf是强迫波长，或作为Grashof数Gf的函数，Gf给出强迫的无量纲度量，如下|λmax| 1/2/（2πkf）<$0.47Gf0.20。还发现该缩放与由Alemany等人（J. Mec.，第18卷，1979年，第18页。277-313）和Pothérat & Alboussière（Phys. Fluids，第15卷，2003年，第15页）。3170-3180），并且我们能够数值量化为kzmax/kf <$0.5Re 1/2和kzmax/kf <$0.8kfRe/Ha。最后，我们表明，一组最少的耗散模式给出了一个相关的预测的规模的第一个三维结构出现在一个强制的，最初的二维湍流。这完成了我们的数值模拟，最小耗散模式可以用来模拟二维和三维低Rm磁流体动力学（MHD）流。
We present a new spectral method for the direct numerical simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number. The originality of our approach is that instead of using traditional bases of functions, it relies on the basis of eigenmodes of the dissipation operator, which represents viscous and Joule dissipation. We apply this idea to the simple case of a periodic domain in the three directions of space, with a homogeneous magnetic field in the ez direction. The basis is then still a subset of the Fourier space, but ordered by growing linear decay rate |λ| (i.e. according to the least dissipative modes). We show that because the lines of constant energy tend to follow those of constant |λ| in the Fourier space, the scaling for the smallest scales |λmax| in a forced flow can be expressed, using this single parameter, as a function of the Reynolds number as $\(\sqrt{1\lambda^{max}|}/(2\upi k_f)\simeq 0.5\Rey^{1/2}\)$, where kf is the forcing wavelength, or as a function of the Grashof number Gf, which gives a non-dimensional measure of the forcing, as |λmax|1/2/(2πkf) ≃ 0.47Gf0.20. This scaling is also found to be consistent with heuristic scalings derived by Alemany et al. (J. Mec., vol. 18, 1979, pp. 277–313) and Pothérat & Alboussière (Phys. Fluids, vol. 15, 2003, pp. 3170–3180) for interaction parameter S ≳ 1, and which we are able to numerically quantify as k⊥max/kf ≃ 0.5Re1/2 and kzmax/kf ≃ 0.8kfRe/Ha. Finally, we show that the set of least dissipative modes gives a relevant prediction for the scale of the first three-dimensional structure to appear in a forced, initially two-dimensional turbulent flow. This completes our numerical demonstration that the least dissipative modes can be used to simulate both two- and three-dimensional low-Rm magnetohydrodynamic (MHD) flows.