标题： 关于弱和强磁流体力学湍流 显示英文标题

标题： On weak and strong magnetohydrodynamic turbulence

摘要： 近期的数值研究和观测研究对磁流体力学湍流的谱给出了相互矛盾的报告。 为了阐明这一问题，我们研究了具有强引导场的各向异性不可压缩磁流体力学湍流$B_0$。 我们在一种特殊设定下进行约化磁流体力学方程组的数值模拟，这种设定使我们能够揭示弱湍流与强湍流之间的转变。 设$k_{\|}$和$k_\perp$分别为波动的场平行和场垂直波数特征值，$b_{\lambda}$为尺度为$\lambda\sim 1/k_{\perp}$的波动场。 我们发现当满足临界平衡条件$k_{\|}B_0\sim k_{\perp} b_{\lambda}$时，湍流是强的，并且能量谱为$E(k_{\perp})\propto k^{-3/2}_{\perp}$。 随着光谱的$k_{\|}$宽度增加，湍流迅速变弱，在极限情况下$k_{\|}B_0\gg k_{\perp} b_{\lambda}$，光谱接近$E(k_{\perp})\propto k_{\perp}^{-2}$。 光谱对线性与非线性相互作用平衡的敏感性可能会解释数值模拟和观测结果之间的矛盾，因为在这些研究中并未很好地控制这一平衡条件。 显示英文摘要

摘要： Recent numerical and observational studies contain conflicting reports on the spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue we investigate anisotropic incompressible magnetohydrodynamic turbulence with a strong guide field $B_0$. We perform numerical simulations of the reduced MHD equations in a special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote $k_{\|}$, $k_\perp$ characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and $b_{\lambda}$ the fluctuating field at the scale $\lambda\sim 1/k_{\perp}$. We find that when the critical balance condition, $k_{\|}B_0\sim k_{\perp} b_{\lambda}$, is satisfied, the turbulence is strong, and the energy spectrum is $E(k_{\perp})\propto k^{-3/2}_{\perp}$. As the $k_{\|}$ width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit $k_{\|}B_0\gg k_{\perp} b_{\lambda}$, the spectrum approaches $E(k_{\perp})\propto k_{\perp}^{-2}$. The observed sensitivity of the spectrum to the balance of linear and nonlinear interactions may explain the conflicting numerical and observational findings where this balance condition is not well controlled.