Generation of zonal flows through symmetry breaking of statistical homogeneity
Generation of zonal flows through symmetry breaking of statistical homogeneity
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通过统计同质性的对称性破缺生成分区流
DOI：
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发表时间：
2014
期刊：
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通讯作者：
J. Krommes
中科院分区：
文献类型：
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作者：
J. Parker;J. Krommes
在地球物理和等离子体背景下，众所周知，纬向流（ZF）是由湍流引起的。我们阐明了从无ZFs的均匀湍流到有稳定ZFs的非均匀湍流的转变。从β平面上的正压气流方程出发，我们采用了准线性近似和统计平均两种方法，这两种方法保留了整个系统的大量定性行为。在由此产生的框架内被称为CE 2，我们扩展最近的理解的破坏臭氧层的不稳定性，并表明它是一个例子的类型是？>模式形成文献中的不稳定性。对称性破缺就是统计均匀性。在分叉点附近，CE 2的慢动力学由一个众所周知的振幅方程控制。这个振幅方程的重要特征是多重的，因此也是CE 2系统的重要特征。首先，ZF波长不是唯一的。在理想化的无限系统中，存在允许非线性平衡的ZF波长的连续带。其次，在这些波长中，只有那些在较小子带内的波长是稳定的。不稳定的波长必须演化到稳定的波长;这个过程表现为合并射流。这些行为的数值显示，在CE 2系统中。我们还得出结论，平衡点附近的稳定性，这是由Eckhaus不稳定性，是独立的Rayleigh-Kuo准则。
In geophysical and plasma contexts, zonal flows (ZFs) are well known to arise out of turbulence. We elucidate the transition from homogeneous turbulence without ZFs to inhomogeneous turbulence with steady ZFs. Starting from the equation for barotropic flow on a β plane, we employ both the quasilinear approximation and a statistical average, which retains a great deal of the qualitative behavior of the full system. Within the resulting framework known as CE2, we extend recent understanding of the symmetry-breaking zonostrophic instability and show that it is an example of a Type Is?> instability within the pattern formation literature. The broken symmetry is statistical homogeneity. Near the bifurcation point, the slow dynamics of CE2 are governed by a well-known amplitude equation. The important features of this amplitude equation, and therefore of the CE2 system, are multiple. First, the ZF wavelength is not unique. In an idealized, infinite system, there is a continuous band of ZF wavelengths that allow a nonlinear equilibrium. Second, of these wavelengths, only those within a smaller subband are stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets. These behaviors are shown numerically to hold in the CE2 system. We also conclude that the stability of the equilibria near the bifurcation point, which is governed by the Eckhaus instability, is independent of the Rayleigh–Kuo criterion.