When an incident wave scatters o of an obstacle, it is partially reflected and partially transmitted. In theory, if the obstacle is rotating, waves can be amplified in the process, extracting energy from the scatterer. Here we describe in detail the first laboratory detection of this phenomenon, known as superradiance [1][2][3][4] . We observed that waves propagating on the surface of water can be amplified after being scattered by a draining vortex. The maximum amplification measured was 14% ± 8%, obtained for 3.70 Hz waves, in a 6.25-cm-deep fluid, consistent with the superradiant scattering caused by rapid rotation. We expect our experimental findings to be relevant to black-hole physics, since shallow water waves scattering on a draining fluid constitute an analogue of a black hole [5][6][7][8][9][10] , as well as to hydrodynamics, due to the close relation to over-reflection instabilities [11][12][13] . In water, perturbations of the free surface manifest themselves by a small change ξ(t, x) of the water height. On a flat bottom, and in the absence of flow, linear perturbations are well described by superpositions of plane waves of definite frequency f (Hz) and wavevector k (rad m −1 ). When surface waves propagate on a changing flow, the surface elevation is generally described by the sum of two contributions ξ = ξ I + ξ S , where ξ I is the incident wave produced by a source, for example, a wave generator, while ξ S is the scattered wave, generated by the interaction between the incident wave and the background flow. In this work, we are interested on the properties of this scattering on a draining vortex flow which is assumed to be axisymmetric and stationary. At the free surface, the velocity field is given in cylindrical coordinates by v = v r e r + v θ e θ + v z e z .Due to the symmetry, it is appropriate to describe ξ I and ξ S using polar coordinates (r, θ). Any wave ξ(t, r, θ ) can be decomposed into partial waves 10,14 ,where m ∈ Z is the azimuthal wavenumber and ϕ f ,m (r) denotes the radial part of the wave. Each component of this decomposition has a fixed angular momentum proportional to m, instead of a fixed wavevector k. (To simplify notation, we drop the indices f ,m in the following.) Since the background is stationary and axisymmetric, waves with different f and m propagate independently. Far from the centre of the vortex, the flow is very slow, and the radial part ϕ(r) becomes a sum of oscillatory solutions,where k = ||k|| 2 is the wavevector norm. This describes the superposition of an inward wave of (complex) amplitude A in propagating towards the vortex, and an outward wave propagating away from it with amplitude A out . These coefficients are not independent. The A in values, one for each f and m component, are fixed by the incident part ξ I . If the incident wave is a plane wave ξ = ξ 0 e −2iπft+ik·x , then the partial amplitudes are given by A in = ξ 0 e imπ+iπ/4 / √ 2πk. In other words, a plane wave is a superposition containing all azimuthal waves, something that we have exploited...

We study the scattering of surface water waves with irrotational draining vortices. At small depth, this system is a mathematical analogue of a rotating black hole and can be used to mimic some of its peculiar phenomenon. Using ray-tracing methods, we exhibit the existence of unstable orbits around vortices at arbitrary depth. These orbits are the analogue of the light rings of a black hole. We show that these orbits come in pairs, one co-rotating and one counter-rotating, at an orbital radius that varies with the frequency. We derived an explicit formula for this radius in the deep water regime. Our method is validated by comparison with recent experimental data from a wavetank experiment. We finally argue that these rings will generate a discrete set of damped resonances that we characterize and that could possibly be observed in future experiments.

Black holes are like bells; once perturbed they will relax through the emission of characteristic waves. The frequency spectrum of these waves is independent of the initial perturbation and, hence, can be thought of as a 'fingerprint' of the black hole. Since the 1970s scientists have considered the possibility of using these characteristic modes of oscillation to identify astrophysical black holes. Inspired by the black hole-fluid analogy, we demonstrate the universality of the black-hole relaxation process through the observation of characteristic modes emitted by a hydrodynamical vortex flow. The characteristic frequency spectrum is measured and agrees with theoretical predictions obtained using techniques developed for astrophysical black holes. Our findings allow for the first identification of a hydrodynamical vortex flow through its characteristic waves. The flow velocities inferred from the observed spectrum agree with a direct flow measurement. Our approach establishes a noninvasive method, applicable to vortex flows in fluids and superfluids alike, to identify the wavecurrent interactions and hence the effective field theories describing such systems.

Spectroscopy is a fundamental tool in science which consists in studying the response of a system as a function of frequency. Among its many applications in Physics, Biology, Chemistry and other fields, the possibility of identifying objects and structures through their emission spectra is remarkable and incredibly useful. In this paper we apply the spectroscopy idea to a numerically simulated hydrodynamical flow, with the goal of developing a new, non-invasive flow measurement technique. Our focus lies on an irrotational draining vortex, which can be seen, under specific conditions, as the analogue of a rotating black hole (historically named a dumb hole). This paper is a development of a recent experiment that suggests that irrotational vortices and rotating black holes share a common relaxation process, known as the ringdown phase. We apply techniques borrowed from black hole physics to identify vortex flows from their characteristic spectrum emitted during this ringdown phase. We believe that this technique is a new facet of the fluid-gravity analogy and constitutes a promising way to investigate experimentally vortex flows in fluids and superfluids alike. arXiv:1905.00356v1 [gr-qc] 1 May 2019Analogue Black Hole Spectroscopy; or, how to listen to dumb holes ‡ Note that we use the term sound as a generic term to describe the frequency of generic radiation such as scalar, electromagnetic or gravitational waves.

In the standard cosmological picture the Universe underwent a brief period of near-exponential expansion, known as Inflation. This provides an explanation for structure formation through the amplification of perturbations by the rapid expansion of the fabric of space. Although this mechanism is theoretically well understood, it cannot be directly observed in nature. We propose a novel experiment combining fluid dynamics and strong magnetic field physics to simulate cosmological inflation. Our proposed system consists of two immiscible, weakly magnetised fluids moving through a strong magnetic field in the bore of a superconducting magnet. By precisely controlling the propagation speed of the interface waves, we can capture the essential dynamics of inflationary fluctuations: interface perturbations experience a shrinking effective horizon and are shown to transition from oscillatory to squeezed and frozen regimes at horizon crossing.

In 2016, the Nottingham group detected the rotational superradiance effect. While this experiment demonstrated the robustness of the superradiance process, it still lacks a complete theoretical description due to the many effects at stage in the experiment. In this paper, we shine new light on this experiment by deriving an estimate of the reflection coefficient in the dispersive regime by means of a Wentzel–Kramers–Brillouin analysis. This estimate is used to evaluate the reflection coefficient spectrum of counter-rotating modes in the Nottingham experiment. Our finding suggests that the vortex flow in the superradiance experiment was not purely absorbing, contrary to the event horizon of a rotating black hole. While this result increases the gap between this experimental vortex flow and a rotating black hole, it is argued that it is in fact this gap that is the source of novel ideas. This article is part of a discussion meeting issue ‘The next generation of analogue gravity experiments’.

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Wave scattering phenomena are ubiquitous in almost all Sciences, from Biology to Physics. Interestingly, it has been shown many times that different physical systems are the stage to the same processes. The discoveries of such analogies have resulted in a better understanding of Physics and are indications of the universality of Nature. One stunning example is the observation that waves propagating on a flowing fluid effectively experience the presence of a curved space-time.In this thesis we will use this analogy to investigate, both theoretically and experimentally, fundamental effects occurring around vortex flows and rotating black holes. In particular, we will focus on light-bending, superradiance scattering, and quasi-normal modes emission. The experimental nature of this work will lead us to study these processes in the presence of dispersive effects.First of all, I would like to thank my PhD supervisor, Silke Weinfurtner, for her support, guidance and trust during the years I spent working on this thesis.Her curiosity and broad interest for general physical processes associated to her enthusiasm, optimism, and determination created a very stimulating and exciting environment to be working in. I am also extremely grateful for her genuine care. Her presence was very helpful and reassuring.I would also like to thank her for generating very fruitful collaborations and allowing me to work with incredible people. Maurício Richartz, Sam Dolan, Tasos Avgoustidis, and Richard Hill, it was a real pleasure to work with you and I can only hope to continue doing so in the future. Maurício, thank you for struggling with us on the various experiments.I am also indebted to the administrative and technical staff of the University of Nottingham. In particular, I want to thank Tommy Napier, Andrew Stuart, Ian Taylor, and Terry Wright for their creativity, technical skills and patience to deal with our crazy ideas. Without them, this work could not have been done.Working in the Black Hole Laboratory has been a real pleasure, not only because of the physics I was studying but also because of the people I was sharing