论文标题
波浪拓扑带到海岸
Wave topology brought to the coast
论文作者
论文摘要
由于开尔文在拉普拉斯潮汐方程中的开创性工作，因此在沿海动力学的背景下发现了捕获波的动物学。其中，最初由开尔文计算出来的那个起着特定的作用，因为它是一种单向模式，填补了不同波段之间的频率间隙。这种开尔文波的存在对于边界形状的变化和海岸基础模型的变化是可靠的。这表明拓扑解释迄今仍是难以捉摸的。在这里，我们通过利用重新制定浅水动力学来纠正这种情况，该动态强调了与浓缩物理学中著名的霍尔丹模型的类比。对于底层地形的任何轮廓，通过计算第一个Chern数字来预测分散关系中从一个波带到另一波段的模式的数量，该数字在双重，更简单的波浪问题中描述了复杂特征模的拓扑。
Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is an unidirectional mode filling a frequency gap between different wave bands. The existence of such Kelvin waves is robust to changes in the boundary shape and in changes of the underlying model for the coast. This suggests a topological interpretation that has yet up to now remained elusive. Here we rectify the situation, by taking advantage of a reformulation of the shallow water dynamics that highlights an analogy with the celebrated Haldane model in condensed matter physics. For any profile of bottom topography, the number of modes that transit from one wave band to another in the dispersion relation is predicted by computing a first Chern number describing the topology of complex eigenmodes in a dual, simpler wave problem.
