Vortex-dipole surface wave interactions in deep water

  • Francisco Vivanco
  • Francisco Melo
Conference paper
Part of the Nonlinear Phenomena and Complex Systems book series (NOPH, volume 8)


We describe a simple experiment to study the interaction between surface waves and vertical vorticity in the deep water regime. The vortex circulation introduces dislocations on the wavefront which can be explained by the advection of the propagating wavefront, due to the fluid motion. The analogy between wave vortex interactions and the Aharonov-Bohm effect is explored further by considering the case of surface waves interacting with a vorticity dipole.


Surface Wave Burger Vector Vortex Core Single Vortex Magnetic Vector Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Aharonov Y. & Bohm D., „Significance of Electromagnetic Potentials in the Quantum Theory“, Phys. Rev. Lett. 115, 485–489 (1959).MathSciNetADSMATHGoogle Scholar
  2. [2]
    For a review, see for instance M. Peshkin and A. Tonomura, ”The Aharonov-Bohm effect“, Lecture Notes in Physics 340, Springer (1989).CrossRefGoogle Scholar
  3. [3]
    M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill and J. C. Walmsley, „Wavefront Dislocations in the Aharonov-Bohm Effect and its Water Wave Analogue“, Eur. J. Phys. Vol. 1, 154 (1980).MathSciNetCrossRefGoogle Scholar
  4. [4]
    J-H. Shyu and O. M. Phillips, „The Blockage of Gravity and Capillary Waves by Longer Waves and Currents“, J. Fluid. Mech. 217, 115 (1990).ADSMATHCrossRefGoogle Scholar
  5. [5]
    M. S. Longuet-Higgins, „Surface Manifestations of Turbulent Flow“, J. Fluid. Mech. 308, 15 (1996).MathSciNetADSMATHCrossRefGoogle Scholar
  6. [6]
    U. Frisch, Turbulence, Cambridge University Press (1995), Ch. 8.MATHGoogle Scholar
  7. [7]
    C. Baudet, S. Ciliberto and J. F. Pinton, „Spectral analysis of the von Kármán flow using ultrasound scattering“, Phys. Rev. Lett. 67, 193–195 (1991)ADSCrossRefGoogle Scholar
  8. [8]
    P. Roux, J. de Rosny, M. Tanter and M. Fink, „The Aharonov-Bohm Effect Revisited by an Acoustic Time-Reversal Mirror“, Phys. Rev. Lett., D 70, 3170(1997). M. Fink, Physics Today, March (1997).ADSCrossRefGoogle Scholar
  9. [9]
    F. Vivanco, F. Melo, C. Coste and F. Lund, „Surface Wave Scattering by a Vertical Vortex and the Symmetry of the Aharonov-Bohm effect“, Phys. Rev. Lett. 83, 1966 (1999).ADSCrossRefGoogle Scholar
  10. [10]
    C. Coste, M. Umeki and F. Lund, ”Scattering of dislocated wavefronts by vertical vorticity and the Aharonov Bohm effect I: Shallow water waves”, (preprint); C. Coste and F. Lund, ”Scattering of dislocated wavefronts by vertical vorticity and the Aharonov Bohm effect II: Dispersive case”, (preprint).Google Scholar
  11. [11]
    See for instance: C. Nore et al, „Scattering of First Sound by Superfluid Vortices“, Phys. Rev. Lett. 72, 2593, (1994) andADSCrossRefGoogle Scholar
  12. [11a]
    P. Ao and D. Thouless, „Berry’s Phase and the Magnus Force for a Vortex Line in a Superconductor“, Phys. Rev. Lett. 70, 2158–2161 (1993).ADSCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Francisco Vivanco
    • 1
    • 2
  • Francisco Melo
    • 1
    • 2
  1. 1.Departamento de FísicaUniversidad de SantiagoChile
  2. 2.Center for Advances Interdisciplinary Research in MaterialsSantiagoChile

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