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

Linear confinement of generalized KG-oscillator with a uniform magnetic field in Kaluza-Klein theory and Aharonov-Bohm effect

In this paper, we solve generalized KG-oscillator interacts with a uniform magnetic field in five-dimensional space-time background produced by topological defects under a linear confining potential using the Kaluza–Klein theory. We solve this equation and analyze an analogue of the Aharonov–Bohm effect for bound states. We observe that the energy level for each radial mode depend on the global parameters characterizing the space-time, the confining potential, and the magnetic field which shows a quantum effect.

Black Hole Quasibound States from a Draining Bathtub Vortex Flow

Quasinormal modes are a set of damped resonances that describe how an excited open system is driven back to equilibrium. In gravitational physics these modes characterize the ringdown of a perturbed black hole, e.g., following a binary black hole merger. A careful analysis of the ringdown spectrum reveals the properties of the black hole, such as its angular momentum and mass. In more complex gravitational systems, the spectrum might depend on more parameters and hence allows us to search for new physics. We present a hydrodynamic analog of a rotating black hole that illustrates how the presence of extra structure affects the quasinormal mode spectrum. The analogy is obtained by considering wave scattering on a draining bathtub vortex flow. We show that due to vorticity of the background flow, the resulting field theory corresponds to a scalar field on an effective curved spacetime which acquires a local mass in the vortex core. The obtained quasinormal mode spectrum exhibits long-lived trapped modes, commonly known as quasibound states. Our findings can be tested in future experiments building upon recent successful implementations of analog rotating black holes.

Acoustic nonreciprocity in Coriolis mean flow systems

One way to break acoustic reciprocity is to have a moving wave propagation medium. If the acoustic wave vector and the moving fluid velocity are collinear, the wave vector shift caused by the fluid flow can be used to break. In this paper, an alternative approach is investigated in which the fluid velocity enters the differential equation of the system as a cross product term with the wave vector. A circular field where the fluid velocity increases radially has a Coriolis acceleration term. In such a system, the acoustic wave enters from the central wall and exits from the perimeter wall. In this paper, the differential equation is solved numerically and the effect of fluid velocity on the nonreciprocity factor is examined.

Level splitting at macroscopic scale

A walker is a classical self-propelled wave particle association moving on a fluid interface. Two walkers can interact via their waves and form orbiting bound states with quantized diameters. Here we probe the behavior of these bound states when setting the underlying bath in rotation. We show that the bound states are driven by the wave interaction between the walkers and we observe a level splitting at macroscopic scale induced by the rotation. Using the analogy between Coriolis and Lorentz forces, we show that this effect is the classical equivalent to Zeeman splitting of atomic energy levels.

Path-memory induced quantization of classical orbits

A droplet bouncing on a liquid bath can self-propel due to its interaction with the waves it generates. The resulting “walker” is a dynamical association where, at a macroscopic scale, a particle (the droplet) is driven by a pilot-wave field. A specificity of this system is that the wave field itself results from the superposition of the waves generated at the points of space recently visited by the particle. It thus contains a memory of the past trajectory of the particle. Here, we investigate the response of this object to forces orthogonal to its motion. We find that the resulting closed orbits present a spontaneous quantization. This is observed only when the memory of the system is long enough for the particle to interact with the wave sources distributed along the whole orbit. An additional force then limits the possible orbits to a discrete set. The wave-sustained path memory is thus demonstrated to generate a quantization of angular momentum. Because a quantum-like uncertainty was also observed recently in these systems, the nonlocality generated by path memory opens new perspectives.

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.

Using a partial-wave method for sound-mean-flow scattering problems

We present a semianalytical method, based on a partial-wave expansion and valid in the short wavelength limit for small Mach number flows, to analyze sound-vortical-flow interactions. It is more powerful than ray-tracing methods because it gives both amplitude and phase of the sound wave, and because it is less restrictive on the smallness of the wavelength. In contrast with the Born approximation approach, this method allows the computation of the sound field in the whole interaction domain (including the near field), and preserves energy conservation. Vortical flows with finite circulation are amenable to our analysis, which gives a satisfactory description of wave front dislocation by vorticity, in good agreement with direct numerical simulations. We extend previous versions of this method to the case of smooth vorticity profiles which are observed in aeroacoustics experiments.

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.

Scattering of sound by a vorticity filament: an experimental and numerical investigation

A vorticity filament is investigated experimentally using the transmission of an ultrasonic wave through the flow. The analysis of the wave-front distortion provides noninvasive measurements of the vortex circulation and size. The latter is estimated by analytical calculations of the scattering of a plane wave by a vorticity filament. The case of a cylindrical wave incident on a vortex leads to similar experimental results which are successfully compared to a parabolic equation simulation. Finally, a finite-difference code based on linear acoustics is presented, in order to investigate the structure of the scattered wave numerically.

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.

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

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 wave front, 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 whether the depth is smaller or larger than sqrt[3] times capillary length. In the latter case, dispersion and advection may compensate leading to a spiral interference pattern. 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.