论文标题
Zonosrothic不稳定性的几何解释
A geometric interpretation of zonostrophic instability
论文作者
论文摘要
通过涡流应激张量的几何分解，分析了ZonaLophic的不稳定性，从而导致Zonal射流出现。应力张量通过其特征与涡流特性相关的涡流椭圆形成可视化。椭圆形主轴的倾斜是相对于剪切的涡流的倾斜，椭圆的偏心率与涡流各向异性有关，而其大小与涡流动能有关。这些特征的变化与迫使平均流量的涡度通量直接相关。采用了二阶关闭的湍流的统计状态动力学，因为它为Zonosrotophic不稳定性和应力张量提供了分析表达。对于不稳定性的线性相，在稳定性边界上分析应力张量。对于不稳定性的非线性平衡，计算张量是在小小临界的极限下计算的，其中射流速度的振幅跟随金茨堡 - landau动力学。发现取决于强迫的特性，射流是加速的，因为它主要是对涡流的各向异性，以产生升级通量，或者因为它改变了涡流的倾斜度。不稳定性平衡，因为这些变化部分被非线性术语逆转。还讨论了椭圆特征的参数化。
The zonostrophic instability that leads to the emergence of zonal jets in barotropic beta-plane turbulence was analyzed through a geometric decomposition of the eddy stress tensor. The stress tensor is visualized by an eddy variance ellipse whose characteristics are related to eddy properties. The tilt of the ellipse principal axis is the tilt of the eddies with respect to the shear, the eccentricity of the ellipse is related to the eddy anisotropy, while its size is related to the eddy kinetic energy. Changes of these characteristics are directly related to the vorticity fluxes forcing the mean flow. The statistical state dynamics of the turbulent flow closed at second order was employed as it provides an analytic expression for both the zonostrophic instability and the stress tensor. For the linear phase of the instability, the stress tensor was analytically calculated at the stability boundary. For the non--linear equilibration of the instability the tensor was calculated in the limit of small supercriticality in which the amplitude of the jet velocity follows Ginzburg--Landau dynamics. It is found that dependent on the characteristics of the forcing, the jet is accelerated either because it primarily anisotropizes the eddies so as to produce upgradient fluxes or because it changes the eddy tilt. The instability equilibrates as these changes are partially reversed by the non--linear terms. Parameterizations of the ellipse characteristics are also discussed.
