AI 中文总结
研究随机二维波场中岛屿周围涡旋的形成，建立有或无科里奥利效应的统计理论并实验验证。确定不同拓扑电荷涡旋概率与岛屿大小等关系，发现岛屿边界涡旋出现概率高且亚波长岛屿增强涡旋形成，解释潮汐涡旋形成并建立一般机制。
AI 中文摘要
波涡旋是干涉场的基本拓扑特征，出现在波幅消失的节点处。在二维波场中，一类不同的涡旋可以围绕岛屿或‘空洞’形成，波强度在边界处保持有限甚至达到峰值。本文针对随机二维波场中岛屿周围的涡旋，在有和没有科里奥利效应的情况下，建立了统计理论并进行实验验证。确定了不同拓扑电荷涡旋的概率与岛屿大小和科里奥利参数的关系。发现岛屿边界涡旋出现概率高，亚波长岛屿增强涡旋形成。结果解释了特定大小海洋岛屿周围潮汐涡旋的形成，并建立了在不同波系统中围绕缺陷产生局部高强度涡旋的一般机制。
英文摘要
Wave vortices are fundamental topological features of interference fields, occurring at nodal points where the wave amplitude vanishes. A distinct class of vortices can instead form around it islands or `holes' in two-dimensional wavefields, where the wave intensity remains finite and may even peak at the boundary. In particular, such vortices occur in M2 ocean tides around New Zealand, Madagascar, Iceland, and Svalbard, yet the conditions governing their appearance have remained elusive. Here we develop a statistical theory of vortices around islands in random two-dimensional wavefields, with and without the Coriolis effect, and test it experimentally. We determine the probabilities of vortices with different topological charges as functions of island size and Coriolis parameter. We find that island-bound vortices emerge with unexpectedly high probability, approaching 50% in non-rotating systems and nearly 100% in rotating systems. Moreover, for a broad range of parameters, the presence of a subwavelength island dramatically enhances vortex formation compared with homogeneous random wavefields. Our results explain the formation of tidal vortices around ocean islands of particular sizes (~0.1 of the characteristic wavelength) and establish a general mechanism for generating localized high-intensity vortices around defects in diverse wave systems, from water waves to nanophotonic structures.
Comments8 pages, 4 figures
