Rossby and Drift Wave Turbulence and Zonal Flows: the Charney-Hasegawa-Mima model and its extensions
Rossby and Drift Wave Turbulence and Zonal Flows: the Charney-Hasegawa-Mima model and its extensions
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DOI：
10.1016/j.physrep.2015.10.009
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
C. Connaughton;S. Nazarenko;B. Quinn
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文献类型：
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作者：
C. Connaughton;S. Nazarenko;B. Quinn
详细研究了Charney-Hasegawa-Mima模型及其推广。对于大气中的Rossby波和磁约束等离子体中的漂移波，这些简单的非线性偏微分方程组表现出一些显著的和非平凡的性质，这些性质以定性的形式存在于更现实和更复杂的模型中。因此，它们构成了理解真实等离子体和地球物理系统中的湍流和纬向流动动力学的概念基础。探讨了小尺度湍流产生纬向流的两种理想情况：调制不稳定和湍流叶栅。对调制不稳定性产生纬向流的详细研究表明，这种纬向流产生机制的动力学随初始非线性程度的不同而有很大的不同。在强非线性情况下，喷流进一步卷曲进入涡街并饱和，而在较弱的非线性情况下，不稳定模的增长反转，系统在略微倾向于纬向的主导喷流和主导主波之间振荡。给出了Rossby和漂移波湍流纬向运动中的额外不变量的数值证明。虽然这个不变量的理论推导来自于假定弱波幅的波动动力学方程，但对于较高的非线性，它也是相对守恒的。与能量和拟能一起，这三个不变量级联成k空间中的各向异性扇区，正如Fjørtoft自变量所预测的那样。这些级联的特征是纬向地转将能量推向纬向尺度。应用于模式的小尺度不稳定强迫显示了众所周知的漂移波-纬向流反馈回路。漂移波湍流就是由这种初级不稳定性产生的。然后，纬向流被任一种产生机制激发，在漂移波增长时从漂移波中提取能量。最终湍流被完全抑制，纬向气流饱和。湍流谱以数学预测的方式扩散。从这个简单的模型中获得的见解可以为在更复杂的等离子体和地球物理流体动力学模型中进行等效研究提供基础，以努力全面理解等离子体和地球物理背景下的纬向流产生、湍流输送抑制和纬向流饱和过程，以及从混沌演化到秩序的其他波动和湍流系统。
A detailed study of the Charney–Hasegawa–Mima model and its extensions is presented. These simple nonlinear partial differential equations suggested for both Rossby waves in the atmosphere and drift waves in a magnetically-confined plasma, exhibit some remarkable and nontrivial properties, which in their qualitative form, survive in more realistic and complicated models. As such, they form a conceptual basis for understanding the turbulence and zonal flow dynamics in real plasma and geophysical systems. Two idealised scenarios of generation of zonal flows by small-scale turbulence are explored: a modulational instability and turbulent cascades. A detailed study of the generation of zonal flows by the modulational instability reveals that the dynamics of this zonal flow generation mechanism differ widely depending on the initial degree of nonlinearity. The jets in the strongly nonlinear case further roll up into vortex streets and saturate, while for the weaker nonlinearities, the growth of the unstable mode reverses and the system oscillates between a dominant jet, which is slightly inclined to the zonal direction, and a dominant primary wave. A numerical proof is provided for the extra invariant in Rossby and drift wave turbulence—zonostrophy. While the theoretical derivations of this invariant stem from the wave kinetic equation which assumes weak wave amplitudes, it is shown to be relatively well-conserved for higher nonlinearities also. Together with the energy and enstrophy, these three invariants cascade into anisotropic sectors in the k-space as predicted by the Fjørtoft argument. The cascades are characterised by the zonostrophy pushing the energy to the zonal scales. A small scale instability forcing applied to the model has demonstrated the well-known drift wave—zonal flow feedback loop. The drift wave turbulence is generated from this primary instability. The zonal flows are then excited by either one of the generation mechanisms, extracting energy from the drift waves as they grow. Eventually the turbulence is completely suppressed and the zonal flows saturate. The turbulence spectrum is shown to diffuse in a manner which has been mathematically predicted. The insights gained from this simple model could provide a basis for equivalent studies in more sophisticated plasma and geophysical fluid dynamics models in an effort to fully understand the zonal flow generation, the turbulent transport suppression and the zonal flow saturation processes in both the plasma and geophysical contexts as well as other wave and turbulence systems where order evolves from chaos.