不可压Hall MHD中的波turbulence
Wave turbulence in incompressible Hall MHD
摘要：
我们调查的陡峭的磁场波动幂律谱观察到的内太阳风的频率高于0.5赫兹。频谱的高频部分可归因于色散非线性过程。在这种情况下，弱相互作用波的长时间的行为进行检查的框架内的三维不可压缩霍尔MHD湍流。在标准的MHD方程中加入霍尔项，使阿尔文波具有色散和圆偏振。我们引入广义Elsässer变量，并使用复杂的螺旋度分解，我们推导出三波相互作用过程的一般波动力学方程，它们描述了在强均匀磁场$B_0 \ep$的存在下，阿尔文，哨声和离子回旋波湍流的非线性动力学。Hall MHD湍流的特征是具有不同强度的各向异性。我们证明了电子和标准MHD湍流可以看作是本理论的两个频率极限，但标准MHD极限是奇异的;此外，我们详细分析了离子MHD湍流极限。给出了主波动力学方程在小尺度和大尺度极限下的精确幂律解，分别给出了总能谱$E(\kpn,\kpa) \sim \kpn^{-5/2} |\kpa|^{-1/2}$和$E(\kpn,\kpa) \sim \kpn^{-2}$。一个各向异性的现象是开发来描述连续的能谱的不同的标度律，一个预测$E(\kpn,\kpa) \sim \kpn^{-2} |\kpa|^{-1/2} (1+\kpn^2d_i^2)^{-1/4}$。阿尔文，哨声和离子回旋波之间的非局部相互作用进行了研究;一个非平凡的动力学存在，只有当大尺度动能和磁能之间的均分发生差异。
英文摘要：
We investigate the steepening of the magnetic fluctuation power law spectra observed in the inner solar wind for frequencies higher than 0.5 Hz. This high frequency part of the spectrum may be attributed to dispersive nonlinear processes. In that context, the long-time behavior of weakly interacting waves is examined in the framework of 3D incompressible Hall MHD turbulence. The Hall term added to the standard MHD equations makes the Alfvén waves dispersive and circularly polarized. We introduce the generalized Elsässer variables and, using a complex helicity decomposition, we derive for three-wave interaction processes the general wave kinetic equations; they describe the nonlinear dynamics of Alfvén, whistler and ion cyclotron wave turbulence in the presence of a strong uniform magnetic field $B_0 \ep$. Hall MHD turbulence is characterized by anisotropies of different strength. We show that electron and standard MHD turbulence can be seen as two frequency limits of the present theory but the standard MHD limit is singular; additionally, we analyze in detail the ion MHD turbulence limit. Exact power law solutions of the master wave kinetic equations are given in the small and large scale limits for which we have, respectively, the total energy spectra $E(\kpn,\kpa) \sim \kpn^{-5/2} |\kpa|^{-1/2}$ and $E(\kpn,\kpa) \sim \kpn^{-2}$. An anisotropic phenomenology is developed to describe continuously the different scaling laws of the energy spectrum; one predicts $E(\kpn,\kpa) \sim \kpn^{-2} |\kpa|^{-1/2} (1+\kpn^2d_i^2)^{-1/4}$. Nonlocal interactions between Alfvén, whistler and ion cyclotron waves are investigated; a non trivial dynamics exists only when a discrepancy from the equipartition between the large scale kinetic and magnetic energies happens.
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