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Rotational superradiant scattering in a vortex flow

Nature Physics volume 13, pages 833–836 (2017)Cite this article

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Abstract

When an incident wave scatters off 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 superradiance1,2,3,4. 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 hole5,6,7,8,9,10, as well as to hydrodynamics, due to the close relation to over-reflection instabilities11,12,13.

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Figure 1: Wave characteristics of the surface perturbation ξ, filtered at a single frequency, for six different frequencies.
Figure 2: Reflection coefficients for various frequencies and various values of m.
Figure 3: Reflection coefficients for different values of m, for the frequency f = 3.70 Hz (stars).
Figure 4: PIV measurements of the velocity field averaged of 10 experiments.

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Acknowledgements

We are indebted to the technical and administrative staff in the School of Physics & Astronomy where our experimental setup is hosted. In particular, we want to thank T. Wright and T. Napier for their support, hard work and sharing their technical knowledge and expertise with us to set up the experiment in Nottingham. Furthermore we would like to thank B. Unruh, S. Liberati, J. Niemela, L. Lehner, V. Cardoso, M. Berry, V. Pagneux, D. Faccio, F. Orucevic, J. Schmiedmayer and T. Fernholz for discussions regarding the experiment, and we wish to thank M. Berry, V. Cardoso, D. Faccio, L. Lehner, S. Liberati and B. Unruh for comments on the paper. Although all experiments have been conducted at The University of Nottingham, the initial stages of the experiment took place at ICTP / SISSA in Trieste (Italy) and would not have been possible without the support by J. Niemela, S. Liberati and G. Martinelli. S.W. would like to thank M. Penrice, A. Prain, M. Danailov, I. Cudin, H. Tanner, Z. Fifer, A. Finke and D. Russon for their contributions at different stages of the experiment. S.W. would also like to thank T. Sotiriou for the many discussions on all aspects of the project. A.C. acknowledges funding received from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska Curie grant agreement no. 655524. M.R. acknowledges financial support from the São Paulo Research Foundation (FAPESP), Grants No. 2005/04219-0, No. 2010/20123-1, No. 2013/09357-9, No. 2013/15748-0 and No. 2015/14077-0. M.R. and T. Ted are also grateful to S.W. and the University of Nottingham for hospitality while this work was being completed. S.W. acknowledges financial support provided under the Royal Society University Research Fellow (UF120112), the Nottingham Advanced Research Fellow (A2RHS2), the Royal Society Project (RG130377) grants and the EPSRC Project Grant (EP/P00637X/1). The initial stages of the experiment were funded by S.W.’s Research Awards for Young Scientists (in 2011 and 2012) and by the Marie Curie Career Integration Grant (MULTI-QG-2011).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

    Theo Torres, Sam Patrick, Antonin Coutant & Silke Weinfurtner

  2. CMCC - Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), 09210-170 Santo André, São Paulo, Brazil

    Maurício Richartz

  3. Department of Civil Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver V6T 1Z4, Canada

    Edmund W. Tedford

  4. School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK

    Silke Weinfurtner

  5. Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, UK

    Silke Weinfurtner

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  1. Theo Torres
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Correspondence to Silke Weinfurtner.

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Torres, T., Patrick, S., Coutant, A. et al. Rotational superradiant scattering in a vortex flow. Nature Phys 13, 833–836 (2017). https://doi.org/10.1038/nphys4151

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