The stability of a quasi-geostrophic ellipsoidal vortex in a background shear flow
The stability of a quasi-geostrophic ellipsoidal vortex in a background shear flow
复制标题
背景剪切流中准地转椭球涡的稳定性
DOI：
10.1017/s0022112006000462
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发表时间：
2006
影响因子：
3.7
通讯作者：
D. Dritschel
中科院分区：
文献类型：
--
作者：
W. McKiver;D. Dritschel
本文研究了一个具有均匀位涡的准地转椭球体在线性背景切变流作用下的平衡运动。这种运动取决于四个参数：涡的高宽比，$h/r$，以及表征背景剪切流的三个参数，即应变率，$\gamma$，背景旋转率与应变之比，$\beta$，以及剪切作用的角度，$\theta$。我们在这些参数的大范围内产生的平衡，并分析其线性稳定性。对于保持椭球形式的二阶（$m\，{=}\，2 $）模，我们能够导出本征模和增长率的方程。对于高阶模态，我们用数值方法来确定系统对一般扰动（$m\，{>}\，2 $）的完全线性稳定性。总的来说，我们发现，平衡是稳定的，在大多数的参数空间考虑，并发生不稳定的边缘不稳定性通常是椭球。从这些结果中，我们确定的参数值的旋涡是最稳定的，并推测这些是涡流特性，这将是最常见的湍流中观察到的。
We consider the motion of a single quasi-geostrophic ellipsoid of uniform potential vorticity in equilibrium with a linear background shear flow. This motion depends on four parameters: the height-to-width aspect ratio of the vortex, $h/r$, and three parameters characterizing the background shear flow, namely the strain rate, $\gamma$, the ratio of the background rotation rate to the strain, $\beta$, and the angle from which the shear is applied, $\theta$. We generate the equilibria over a large range of these parameters and analyse their linear stability. For the second-order ($m\,{=}\,2$) modes which preserve the ellipsoidal form, we are able to derive equations for the eigenmodes and growth rates. For the higher-order modes we use a numerical method to determine the full linear stability to general disturbances ($m\,{>}\,2$). Overall we find that the equilibria are stable over most of the parameter space considered, and where instability does occur the marginal instability is usually ellipsoidal. From these results, we determine the parameter values for which the vortex is most stable, and conjecture that these are the vortex characteristics which would be the most commonly observed in turbulent flows.