We study the two-dimensional rotating shallow-water model describing Earth’s oceanic layers. It is formally analogue to a Schrödinger equation where the tools from topological insulators are relevant. Once regularized at small scale by an odd-viscous term, such a model has a well-defined bulk topological index. However, in presence of a sharp boundary, the number of edge modes depends on the boundary condition, showing an explicit violation of the bulk-edge correspondence. We study a continuous family of boundary conditions with a rich phase diagram, and explain the origin of this mismatch. Our approach relies on scattering theory and Levinson’s theorem. The latter does not apply at infinite momentum because of the analytic structure of the scattering amplitude there, ultimately responsible for the violation.

我们研究了描述地球海洋层的二维旋转浅水模型。它在形式上类似于薛定ding方程，其中拓扑绝缘体的工具是相关的。一旦通过奇粘性项在小规模进行正则化，这种模型就具有定义明确的整体拓扑指数。但是，在存在尖锐边界的情况下，边缘模式的数量取决于边界条件，这表明明显违反了块状边缘对应关系。我们用丰富的相图研究了一系列连续的边界条件，并解释了这种不匹配的根源。我们的方法依赖于散射理论和莱文森定理。后者不适用于无限动量，因为那里的散射振幅具有解析结构，最终造成了这种违背。