Scattering of dislocated wave fronts by vertical vorticity and the Aharonov-Bohm effect. I. Shallow water

Abstract

When a surface wave interacts with a vertical vortex in shallow water the latter induces a dislocation in the incident wave fronts 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 the scattering of acoustic waves by vorticity is noted.

Rotating black holes in a draining bathtub: Superradiant scattering of gravity waves

“…2 for different values of these background parameters. For each curve, the location of the event horizon, found using (45), is indicated by an asterisk. Note thathðrÞ is always a strictly increasing function ofr, so that the slope of the water surfaceh 0 ðrÞ is always a decreasing function.…”

“…By using a combination of theory and numerical simulations, we have calculated the reflection coefficients for incident waves and have shown that there exists a window of physical parameter space where our approximations are satisfied and superradiant amplification is predicted. It is important to note that this effect is different from the hydrodynamic analogue of the Aharonov-Bohm effect, which is characterized by dislocation and discontinuity in the incident wavefronts [44][45][46][47].…”

Resonant magnetic vortices

“…16,17,18 for the acoustical AB effect, Refs. 19,20,21,22 for the hydrodynamical AB effect and Ref. 23 for the optical AB effect).…”

Torsion effects on a relativistic position-dependent mass system

“…It is worth mentioning other works that have investigated the Aharonov-Bohm effect [55][56][57][58][59][60][61][62][63][64][65]. In this way, the Klein-Gordon equation (18) becomes:…”