The stability and nonlinear evolution of quasi-geostrophic toroidal vortices
The stability and nonlinear evolution of quasi-geostrophic toroidal vortices
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准地转环形涡的稳定性和非线性演化
DOI：
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发表时间：
2019
影响因子：
3.7
通讯作者：
D. Dritschel
中科院分区：
文献类型：
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作者：
J. Reinaud;D. Dritschel
本文在准地转近似下研究了三维均匀位涡的环形涡旋的线性稳定性和非线性演化。环面可以经历一个主要的不稳定性，导致形成一个圆形阵列的漩涡，其半径大致相同的环面的主半径。这种情况发生的方位角不稳定模式数$m\geqslant 3$，足够薄的环面。涡的数目对应于在环面上生长的最不稳定模式的方位角模式数。这个值取决于环面的大半径与小半径的比值，薄的环面有利于高模值。当$m=4$和$m=5$时，所得到的阵列是稳定的，而当$m=3$和$m\geqslant 6$时，阵列是不稳定的。当$m=3$时，阵列几乎没有形成，然后随着无意识碎片的喷射而向中心坍塌。当$m=6$的旋涡表现出振荡的交错，当$m\geq倾斜7$，他们表现出不规则的交错后，大量的旋涡迁移，例如，一个旋涡的中心时，$m=7$。我们还研究了位于环面中心的附加涡的影响。这种涡改变了环面的稳定性以及由主环面不稳定性形成的圆形涡阵的稳定性。我们表明，一个喜欢签署的中心涡可以稳定一个圆形的$m$涡阵列与$m\geqslant 6$。
We investigate the linear stability and nonlinear evolution of a three-dimensional toroidal vortex of uniform potential vorticity under the quasi-geostrophic approximation. The torus can undergo a primary instability leading to the formation of a circular array of vortices, whose radius is approximately the same as the major radius of the torus. This occurs for azimuthal instability mode numbers $m\geqslant 3$ , on sufficiently thin tori. The number of vortices corresponds to the azimuthal mode number of the most unstable mode growing on the torus. This value of $m$ depends on the ratio of the torus’ major radius to its minor radius, with thin tori favouring high mode $m$ values. The resulting array is stable when $m=4$ and $m=5$ and unstable when $m=3$ and $m\geqslant 6$ . When $m=3$ the array has barely formed before it collapses towards its centre with the ejection of filamentary debris. When $m=6$ the vortices exhibit oscillatory staggering, and when $m\geqslant 7$ they exhibit irregular staggering followed by substantial vortex migration, e.g. of one vortex to the centre when $m=7$ . We also investigate the effect of an additional vortex located at the centre of the torus. This vortex alters the stability properties of the torus as well as the stability properties of the circular vortex array formed from the primary toroidal instability. We show that a like-signed central vortex may stabilise a circular $m$ -vortex array with $m\geqslant 6$ .