Scattering of dislocated wave fronts by vertical vorticity and the Aharonov-Bohm effect. II. Dispersive waves

Experimental study of surface waves scattering by a single vortex and a vortex dipole

Surface waves interacting with filamentary vortex offer an interesting tool to characterize static and dynamics of surface vorticity. An experimental study of the scattered wave by a single vortex as well as by a vortex dipole is reported. On a plane wave front, the vortex circulation introduces a spatial phase shift that gives rise to dislocated waves. Dislocations can be explained by the effect of the differential advection due to the vortex flow, on the propagating wave front. Both the Burgers vector of dislocations and the scattering cross section are measured in the deep water regime. The analogy between the wave-vortex interaction and the Aharonov-Bohm effect in quantum mechanics is explored by contrasting the Burgers vectors of dislocations as well as the form of the scattered wave in both cases. For the case of the hard core vortex, spiral waves are observed in agreement with theoretical works on both the Aharanov-Bohm effect and classical surface wave mechanics.

Normal-mode-vortex interactions

Standing surface waves that interact with a confined, vertical, vorticity field with zero net circulation are studied both analytically and experimentally. The surface waves are generated by vertical vibration, and constant vorticity injection is achieved by a rotating disk flush mounted in the cell. Experimental results are indicative of a local wave-vortex interaction (no dislocation), and a simple theoretical model is able to explain them in quantitative detail.

Irregular scattering of acoustic rays by vortices

The scattering of high-frequency sound wave, under geometrical acoustic approximation, by three stationary vortices in two dimensions is investigated. For a sufficiently high Mach number of the vortex flow, the scattering of sound rays becomes irregular, displaying a new example of chaotic scattering for a time-reversal breaking system. The fractal dimension, as well as the unstable and stable manifolds of the scattering dynamics, is presented.