Wave-topology interactions underlie phenomena across physics, from condensed matter to cosmology, with the Aharonov-Bohm (AB) effect providing a paradigmatic example. Classical analogues in fluid dynamics have shown that travelling surface waves scattered off vortices develop wavefront dislocations, with topological effects studied close to the vortex core. Here, we demonstrate that standing surface waves scattered by a single vortex give rise to global nodal structures – lines of zero wave amplitude – whose number is quantized, and may oscillate in time. This behaviour reveals a non-local topological response, in contrast with previously reported, spatially confined interactions. Our findings establish hydrodynamics as a versatile platform for exploring wave-topology interplay and quantum interference phenomena, such as AB caging and topological localization, with potential implications for photonic, acoustic, and quantum metamaterials. Wave-topology interactions lie at the heart of numerous physical phenomena, from condensed matter systems to cosmological models, exemplified by the Aharonov-Bohm effect. Drawing on its classical analogues in fluid dynamics, this study demonstrates that standing surface waves scattered by a vortex induce quantized, nonlocal nodal structures, offering potential for hydrodynamic emulation of quantum interference phenomena with implications for photonic, acoustic, and quantum metamaterials.
Singh et al. (Mon,) studied this question.