In this paper, we study the stability of a barotropic polar vortex cap on a rotating sphere. We present the linear stability analysis of the polar vortex cap, approximating the piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. We investigate the dependence of the flow stability on the location of the vortex cap, modes of perturbation and rotation speed. The linear stability analysis shows that the polar vortex cap is always stable when the angular speed of the rotating body and the vorticity constant of the north are of the same sign, but is unstable when they are of different signs, regardless of the location of the cap boundary. We also compute the nonlinear evolution of the vortex cap on the rotating sphere for the unstable cases and compare it with the linear stability analysis. The flow away from the boundary of the vortex cap is the most unstable, which is in accordance with the eigenvector corresponding to the unstable eigenvalue. It is found that the solid body rotation has stabilizing effects on the evolution of the polar vortex cap.

在本文中，我们研究了旋转球上正压极涡旋盖的稳定性。我们提出了极涡旋盖的线性稳定性分析，通过均匀涡旋的纬向带近似分段连续的涡旋分布。我们研究了流动稳定性对涡旋帽的位置，扰动模式和转速的依赖性。线性稳定性分析表明，当旋转体的角速度和北极的涡旋常数相同时，极涡旋盖始终保持稳定；而当旋转体的角速度和北极的涡旋常数相同时，极涡旋盖则始终不稳定。上限边界。我们还计算了不稳定情况下旋转球体上涡旋盖的非线性演化，并将其与线性稳定性分析进行了比较。离开涡旋帽边界的流动是最不稳定的，这与对应于不稳定特征值的特征向量一致。已经发现，固体旋转对极性涡旋盖的演化具有稳定作用。