Point vortices on a rotating sphere
Point vortices on a rotating sphere
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旋转球体上的点涡
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
F. Laurent
中科院分区：
文献类型：
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作者：
F. Laurent
研究了旋转球上$N$个点涡的动力学。由于科里奥利力的作用，使得哈密顿系统成为无穷维的。我们证明了非旋转球体的相同涡旋的纬向环形成的相对平衡在球体旋转时仍然是相对平衡。本文研究了旋转平面上平面点涡多边形的非线性稳定性，以便在环靠近极点时近似旋转球上相应的相对平衡。然后，我们对地转涡旋进行了同样的研究。最后，我们将我们的结果与南半球大气环流的观测结果进行比较。
We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of latitudinal rings of identical vortices for the non-rotating sphere persists to be a relative equilibrium when the sphere rotates. We study the nonlinear stability of a polygon of planar point vortices on a rotating plane in order to approximate the corresponding relative equilibrium on the rotating sphere when the ring is close to the pole. We then perform the same study for geostrophic vortices. To end, we compare our results to the observations on the southern hemisphere atmospheric circulation.