论文标题
从福柯摆的几何形状到行星波的拓扑
From the geometry of Foucault pendulum to the topology of planetary waves
论文作者
论文摘要
拓扑绝缘子的物理学使您可以理解和预测沿边缘或界面捕获的单向波的存在。在这篇综述中，我们描述了这些想法如何适应地球物理和天体物理波。我们特别处理行星赤道波的情况，该赤道波强调了行星旋转和球形之间的关键相互作用，以解释波浪的出现，这些波只能向东方传播能量。这些最小成分恰恰是在绒毛摆的几何解释中提出的成分。我们讨论了这个经典的力学示例，以介绍整体和矢量束的概念，然后用来计算赤道浅水波的拓扑特性。
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.
