Charney-Hasegawa-Mima方程中的非局域波turbulence
Nonlocal wave turbulence in the Charney-Hasegawa-Mima equation: a short review
摘要：
由Charney-Hasegawa-Mima（CHM）方程模拟的Rossby波湍流在尺度上是非局部的。因此，描述局部级联的Rossby波动力学方程的形式定态Kolmogorov-Zakharov解是无效的。相反，动力学方程的解主要由大尺度和小尺度之间的相互作用决定。这表明了一种替代的分析方法的基础上扩展的碰撞积分在一个小参数从尺度分离。这种扩展近似的积分碰撞算子的动力学方程的各向异性扩散算子在波数空间中，首先显示在一系列的论文由巴尔克，Nazarenko和Zakharov在20世纪90年代初。在这篇文章中，我们总结了这个理论的基础，并提供了原始论文中没有的技术细节。
英文摘要：
Rossby wave turbulence, as modelled by the Charney-Hasegawa-Mima (CHM) equation, is nonlocal in scale. As a result, the formal stationary Kolmogorov-Zakharov solutions of the Rossby wave kinetic equation, which describe local cascades, are not valid. Rather the solution of the kinetic equation is dominated by interactions between the large and small scales. This suggests an alternative analytic approach based on an expansion of the collision integral in a small parameter obtained from scale separation. This expansion approximates the integral collision operator in the kinetic equation by anisotropic diffusion operators in wavenumber space as first shown in a series of papers by Balk, Nazarenko and Zakharov in the early 1990's. In this note we summarize the foundations of this theory and provide the technical details which were absent from the original papers.
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