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Irrotational, Two-Dimensional Surface Waves in Fluids

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Analogue Gravity Phenomenology

Part of the book series: Lecture Notes in Physics ((LNP,volume 870))

Abstract

The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying bottom topography. Most importantly, the conserved norm for the surface waves is derived, important for quantisation of these waves and their use in analogue models for black holes.

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References

  1. Misner, C.M., Thorne, K.S., Wheeler, J.A.: Gravitation. Freemann, San Francisco (1973)

    Google Scholar 

  2. Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Spacetime. Cambridge University Press, Cambridge (1973)

    Book  Google Scholar 

  3. Schützhold, R., Unruh, W.G.: Phys. Rev. D 66, 044019 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  4. Keller, J.B.: Surface waves on water of non-uniform depth. J. Fluid Mech. 4, 607 (1958)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Birkoff, J.C.W.: Computation of combined refraction-diffraction. In: Khaskhachikh, G.D., Plakida, M.É., Popov, I.Ya. (eds.) Proceedings 13th International Conference on Coastal Engineering, Vancouver, p. 471. Springer, Berlin (1972)

    Google Scholar 

  6. Wald, R.M.: General Relativity. University of Chicago Press, Chicago (1984)

    Book  MATH  Google Scholar 

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Acknowledgements

This work was supported by The Canadian Institute for Advanced Research (CIfAR) and by The Natural Science and Engineering Research Council of Canada (NSERC) and was completed while the author was a visitor at the Perimeter Institute.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada

    William G. Unruh

Authors
  1. William G. Unruh
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Correspondence to William G. Unruh .

Editor information

Editors and Affiliations

  1. School of Engineering and Physical Science, Heriot-Watt University, Edinburgh, United Kingdom

    Daniele Faccio

  2. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Francesco Belgiorno

  3. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Sergio Cacciatori

  4. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Vittorio Gorini

  5. Int. School for Adv. Studies (SISSA), Trieste, Italy

    Stefano Liberati

  6. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Ugo Moschella

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Unruh, W.G. (2013). Irrotational, Two-Dimensional Surface Waves in Fluids. In: Faccio, D., Belgiorno, F., Cacciatori, S., Gorini, V., Liberati, S., Moschella, U. (eds) Analogue Gravity Phenomenology. Lecture Notes in Physics, vol 870. Springer, Cham. https://doi.org/10.1007/978-3-319-00266-8_4

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