从旋转球上欧拉方程看平流层行星流
Stratospheric planetary flows from the perspective of the Euler equation on a rotating sphere
摘要：
本文致力于欧拉方程在旋转球体上的定常解，以及它们与太阳系外行星大气层和地球极地平流层流动动力学的相关性。对于欧拉方程，在适当的条件下，刚度的结果建立，确保解决方案是带或旋转带的解决方案。阿诺德的稳定性准则的自然模拟证明。在这两种情况下，最低模式Rossby-Haurwitz平稳解（更准确地说，那些流函数属于Laplace-Beltrami算子的前两个本征空间之和的解）都表现为极限情况。我们研究了这些临界定态解的稳定性。还得到了经典Rossby-Haurwitz波的非带定常解的局部和整体分支的结果。最后，我们表明，在旋转球上的欧拉方程的固定解是积木的行波解的3D系统，描述了领先的动态平流层行星流，捕获的特征密度的降低和温度的增加与高度在这个区域的大气。
英文摘要：
This article is devoted to stationary solutions of Euler's equation on a rotating sphere, and to their relevance to the dynamics of stratospheric flows in the atmosphere of the outer planets of our solar system and in polar regions of the Earth. For the Euler equation, under appropriate conditions, rigidity results are established, ensuring that the solutions are either zonal or rotated zonal solutions. A natural analogue of Arnold's stability criterion is proved. In both cases, the lowest mode Rossby-Haurwitz stationary solutions (more precisely, those whose stream functions belong to the sum of the first two eigenspaces of the Laplace-Beltrami operator) appear as limiting cases. We study the stability properties of these critical stationary solutions. Results on the local and global bifurcation of non-zonal stationary solutions from classical Rossby-Haurwitz waves are also obtained. Finally, we show that stationary solutions of the Euler equation on a rotating sphere are building blocks for travelling-wave solutions of the 3D system that describes the leading order dynamics of stratospheric planetary flows, capturing the characteristic decrease of density and increase of temperature with height in this region of the atmosphere.
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