The invariant theory of isotropic turbulence in magneto-hydrodynamics
The invariant theory of isotropic turbulence in magneto-hydrodynamics
复制标题
磁流体动力学各向同性湍流不变理论
DOI：
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发表时间：
1951
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通讯作者：
S. Chandrasekhar
中科院分区：
文献类型：
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作者：
S. Chandrasekhar
本文在Batchelor最近导出的运动方程的基础上，建立了磁流体力学中各向同性湍流的不变理论，用以描述不可压缩流体的流体力学，而流体又是良好的电导体。当没有外部施加的电场或磁场时，该理论允许电磁场与湍流运动之间的相互作用。定义了涉及速度和磁场强度分量的各种双重和三重相关张量，并推导了三个控制这些张量的标量的方程；后一种方程承认洛伊茨扬斯基型积分。导出了由黏度和电导率决定能量耗散的方程；它们展示了能量在速度和磁场之间交换的方式。最后，得到了外部外力以恒定速率向系统提供动能且系统处于平稳状态时的方程；他们认为，磁场中的能量主要包含在具有大波数的涡流中。
In this paper the invariant theory of isotropic turbulence in magneto-hydrodynamics is developed on the basis of the equations of motion recently derived by Batchelor to describe the hydrodynamics of an incompressible fluid which is also a good electrical conductor. The theory allows for the interaction between the electromagnetic field and the turbulent motion when there is no externally imposed electric or magnetic field. Various double and triple correlation tensors involving the components of the velocity and the magnetic field intensity are defined, and three equations governing the scalars defining these tensors are derived; these latter equations admit integrals of Loitsiansky’s type. The equations governing the dissipation of energy by viscosity and conductivity are also derived; they exhibit the manner in which energy is exchanged between the velocity and the magnetic fields. Finally, the equations appropriate for the case, when an external agency supplies kinetic energy to the system at a constant rate and a stationary condition prevails, are obtained; they suggest that the energy in the magnetic field is contained, principally, in the eddies with large wave numbers.