We examine stability of the polar vortex that initiates planetary-scale westerly (west to east) atmospheric flow that encircles the pole in middle or high latitude of a planet. In our studies, the polar vortex is modeled as an annular flow (zonal flow) extending radially from a rigid inner boundary to a free outer boundary on a $E_k-$ plane, which is parallel to the equatorial plane but generally displaced in latitude. The vortex is associated with a particular class of exact solution of a nonlinear two-dimensional free boundary problem on the nonstationary motion of a perfect fluid propagating around a solid circle with a sufficiently large radius with included Coriolis effect. The intensity of the polar vortex is parametrized by means of the “average” (in vertical) zonal flow that can be associated with atmospheric flow patterns that are parallel or nearly parallel to the lines of latitude. Perturbations are allowed in the zonal and nominally vertical (inward–outward) direction. A linear stability analysis purportedly suggests that increasing latitude decreases the maximum strength of the vortex that is permitted for stability. Three essential parameters that control stability of the vortex are identified.

我们研究了极涡的稳定性，该极涡产生了围绕行星中高纬度极点的行星尺度西风（西向东）大气流动。在我们的研究中，极涡被建模为环形流动（区域流），该流动从刚性内边界径向延伸到自由外边界${Ë}_{ķ}-$该平面平行于赤道平面，但通常在纬度上位移。该涡旋与非线性二维自由边界问题的一类特定精确解相关，该问题涉及在具有足够大的半径并包含科里奥利效应的实心圆周围传播的理想流体的非平稳运动。极涡的强度通过“平均”（垂直）纬向流参数化，纬向流可以与平行或接近于纬线的大气流模式相关。允许在纬向和名义上垂直（向内-向外）方向上摄动。据称，线性稳定性分析表明，纬度的增加会降低涡旋的最大强度，而这种最大强度有助于稳定。