由垂直涡量和Aharonov-Bohm效应引起的错位波前的散射I：浅水
Scattering of dislocated wavefronts by vertical vorticity and the Aharonov-Bohm effect I: Shallow water
摘要：
当表面波与浅水中的垂直涡旋相互作用时，后者在入射波前中引起位错，这类似于Aharonov-Bohm效应中发生的情况，即电子被受限磁场散射。除了这两个物理系统之间的这种全局相似性之外，还有散射。本文报道了这种散射的详细计算，这是定量的不同，从电子的情况下，表面波穿透内部的漩涡，而电子不穿透螺线管。这种差异，加上支配两个物理系统的方程中的附加差异，导致表面波情况下的完全不同的散射，其主要特征是散射截面中的强不对称性。这些影响发生的假设和近似下，仔细考虑，并指出其适用性的情况下，散射的声波涡。
英文摘要：
When a surface wave interacts with a vertical vortex in shallow water the latter induces a dislocation in the incident wavefronts that is analogous to what happens in the Aharonov-Bohm effect for the scattering of electrons by a confined magnetic field. In addition to this global similarity between these two physical systems there is scattering. This paper reports a detailed calculation of this scattering, which is quantitatively different from the electronic case in that a surface wave penetrates the inside of a vortex while electrons do not penetrate a solenoid. This difference, together with an additional difference in the equations that govern both physical systems lead to a quite different scattering in the case of surface waves, whose main characteristic is a strong asymmetry in the scattering cross section. The assumptions and approximations under which these effects happen are carefully considered, and their applicability to the case of scattering of acoustic waves by vorticity is noted.
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