磁流体湍流能量传输的各向异性及时空关联

The classical turbulence theory suggests an energy cascade where energy is transferred from large to small scales at a constant rate, until at the smallest scales this energy is dissipated by viscous action. Two aspects of this energy transfer process are investigated: (i) Laws governing the behavior of statistical third-order structure functions in the inertial range, i.e., Politano-Pouquet law, are among the few rigorous results in homogeneous, isotropic magnetohydrodynamic(MHD) turbulence. The original Politano-Pouquet law, which relates the third-order structure functions to the energy cascade rate, requires assumptions of isotropy. In the past 10 years, this law has been widely used in estimating the heating rate of solar wind. However, in many applications, it is likely that the assumption of isotropy is not a particularly good one since numerical simulations and observations have clearly demonstrated the anisotropic nature of the energy cascade in the presence of a mean magnetic field. With this caveat in mind, a goal of the present proposal is to show how the anisotropy can be incorporated in the formulas of third-order structure functions. In this study, we will investigate the relationship between third-order structure functions and energy cascade (dissipation) rate, with a focus on the anisotropic effect, in a hope to clarify the key features of anisotropic energy transfer and to provide a feasible way to estimate the heating rate of solar wind. (ii) There are several vocabularies, arising from the energy transfer process, that are used to estimate local energy transfer (dissipation) rate, including the local energy transfer rate based on the third-order structure functions, the subgrid-scale energy flux based on spatial filters, and the viscous and Ohmic dissipation. The work done so far has not specifically emphasized the associations that exist among these quantities, yet a number of studies indicate that each of them exhibits intermittency and plays an important role in the energy transfer process. In this proposal we seek to describe their space-time correlations, which quantify how energy transfers at one location and one instant are correlated with those at another location and another instant. To take it further, it is promising to find some spatial and temporal scales that might be of great importance for understanding the energy transfer process in MHD turbulence. The proposal will be conducted via a series of numerical simulations and satellite observation data.

尺度间的能量传输过程是众多磁流体湍流理论和模型的关键。我们将从两个方面研究磁流体湍流的能量传输过程：（i）在惯性区，Politano-Pouquet定律将三阶结构函数和能量耗散率关联起来，因此在空间等离子体中，常依此定律，通过测量三阶结构函数得到能量耗散率，用以估算太阳风的加热率。Politano-Pouquet定律在各向同性的条件下成立，但如果有背景磁场的存在，磁流体湍流的能量传输将呈现各向异性。因此我们将研究各向异性的三阶结构函数标度律，以期更全面地了解磁流体湍流能量传输过程及太阳风的加热。（ii）为了定量给出局部的能量传输率，我们将采用基于三阶结构函数定义的局部能量传输率、滤波得到的亚格子能流以及粘性和磁阻耗散，研究它们之间的时空关联，即某一时刻某个位置的能量传输与另一个时刻另一个位置的能量传输之间的关联，以期找到其对应的特征时间尺度及特征空间尺度。

湍流普遍存在于空间等离子体中，其包含多尺度及多过程相互作用，使得等离子体湍流的物理过程非常丰富。本项目主要基于等离子体的磁流体模型，研究重点为磁流体湍流尺度间的能量传输过程，及驱动机制、压缩性、外加磁场导致的各向异性对能量传输过程的影响。研究结果揭示了各尺度主要的能量传输过程，并且发现各能量传输过程在空间分布上具有相似性；不同的驱动机制会影响尺度间的能量传输，仅需小部分的磁场加力，就可大大抑制对流项导致的动能尺度间传输；压缩性会引起胀压动能和热能的波动，而剪切动能和磁能之间的相互转化比其他能量转化过程更有效；背景磁场导致了能量传输呈现各向异性，因此为了定量给出能量传输率，需考虑各向异性的影响，采用多方向平均的方法。基于此研究，我们可以建立从大尺度到小尺度完整的能量传输过程，并可用于空间观测中得到更准确的太阳风加热率。