从傅科摆几何到行星波拓扑
From the geometry of Foucault pendulum to the topology of planetary waves
摘要：
拓扑绝缘体的物理特性使得人们有可能理解和预测沿边缘或界面捕获的单向波的存在。在这篇评论中，我们描述了这些想法可以适应地球物理和天体物理波。我们特别处理的情况下，行星赤道波，突出了关键的相互作用之间的旋转和球度的星球，解释波的出现，传播其能量只向东。这些最小的成分正是在福柯摆的几何解释中提出的。我们讨论这个经典的力学例子，引入完整性和向量丛的概念，然后我们使用它来计算赤道浅水波的拓扑性质。
英文摘要：
The physics of topological insulators makes it possible to understand and predict the existence of unidirectional waves trapped along an edge or an interface. In this review, we describe how these ideas can be adapted to geophysical and astrophysical waves. We deal in particular with the case of planetary equatorial waves, which highlights the key interplay between rotation and sphericity of the planet, to explain the emergence of waves which propagate their energy only towards the East. These minimal ingredients are precisely those put forward in the geometric interpretation of the Foucault pendulum. We discuss this classic example of mechanics to introduce the concepts of holonomy and vector bundle which we then use to calculate the topological properties of equatorial shallow water waves.
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