由垂直涡量和Aharonov-Bohm效应引起的错位波前的散射II：色散波
Scattering of dislocated wavefronts by vertical vorticity and the Aharonov-Bohm effect II: Dispersive waves
摘要：
本文将前人关于浅水中垂直涡对表面波散射的结果推广到色散水波的情况。色散效应的处理扰动周围的浅水限制，一阶的深度与波长的比值。类似于Aharonov-Bohm效应的入射波前的位错仍然被观察到。在短波长下，散射在性质上类似于非色散情况。然而，在中等波长下，根据毛细管长度是小于还是大于$\sqrt{3}$乘以深度，存在两种明显不同的散射机制。位错的特征在于一个参数，这取决于相速度和群速度。计算的有效范围与浅水情况相同：波长小于涡半径，低马赫数。这些限制的影响被仔细考虑。
英文摘要：
Previous results on the scattering of surface waves by vertical vorticity on shallow water are generalized to the case of dispersive water waves. Dispersion effects are treated perturbatively around the shallow water limit, to first order in the ratio of depth to wavelength. The dislocation of the incident wavefront, analogous to the Aharonov-Bohm effect, is still observed. At short wavelengths the scattering is qualitatively similar to the nondispersive case. At moderate wavelengths, however, there are two markedly different scattering regimes according to wether the capillary length is smaller or larger than $\sqrt{3}$ times depth. The dislocation is characterized by a parameter that depends both on phase and group velocity. The validity range of the calculation is the same as in the shallow water case: wavelengths small compared to vortex radius, and low Mach number. The implications of these limitations are carefully considered.
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