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Relaxation oscillations in a nearly inviscid Faraday system

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Abstract

In the nearly inviscid regime parametrically driven surface gravity-capillary waves couple to a streaming flow driven in oscillatory viscous boundary layers. In an elliptical container of small eccentricity this coupling can lead to relaxation oscillations.

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References

  1. Arnol’d, V.I., Afrajmovich, V.S., Il’yashenko, Yu.S., Shil’nikov, L.P.: Bifurcation Theory and Catastrophe Theory. In Encyclopaedia of Mathematical Sciences, Vol. 5, V.I. Arnol’d (ed.), Springer-Verlag, NY (1994)

  2. Douady, S., Fauve, S., Thual, O.: Oscillatory phase modulation of parametrically forced surface waves. Europhys. Lett. 10, 309–315 (1989)

  3. Eckhaus, W.: Relaxation oscillations, including a standard chase on french ducks. Lecture Notes in Mathematics, 985, pp. 449–494, Springer-Verlag, NY (1983)

  4. Guckenheimer, J., Hoffman, K., Weckesser, W.: Numerical computation of canards. Int. J. Bif. Chaos 10, 2669–2687 (2000)

  5. Higuera, M., Porter, J., Knobloch, E.: Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation. Physica D 162, 155–187 (2002)

  6. Higuera, M., Knobloch, E., Vega, J.M.: Dynamics of nearly inviscid Faraday waves in almost circular containers. Physica D, submitted

  7. Higuera, M., Vega, J.M., Knobloch, E.: Coupled amplitude-streaming flow equations for nearly inviscid Faraday waves in small aspect ratio containers. J. Nonlin. Sci. 12, 505–551 (2002)

  8. Martel, C., Nicolás, J.A., Vega, J.M.: Surface-wave damping in a brimful circular cylinder. J. Fluid Mech. 360, 213–228 (1998). See also Corrigendum 373, 379 (1998)

  9. Martín, E., Martel, C., Vega, J.M.: Drift instability of standing Faraday waves. J. Fluid Mech. 467, 57–79 (2002)

  10. Miles, J.W.: Internally resonant surface waves in a circular cylinder. J. Fluid Mech. 149, 1–14 (1984)

  11. Moehlis, J., Knobloch, E.: Forced symmetry breaking as a mechanism for bursting. Phys. Rev. Lett. 80, 5329–5332 (1998)

  12. Vega, J.M., Knobloch, E., Martel, C.: Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio. Physica D 154, 313–336 (2001)

  13. Wang, X.J., Rinzel, J.: Oscillatory and bursting properties of neurons. In Brain Theory and Neural Networks. M.A. Arbib (ed.), MIT Press: Cambridge, MA (1995)

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Correspondence to Edgar Knobloch.

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H.J.S. Fernando

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Higuera, M., Knobloch, E. & Vega, J. Relaxation oscillations in a nearly inviscid Faraday system. Theor. Comput. Fluid Dyn. 18, 323–333 (2004). https://doi.org/10.1007/s00162-004-0144-2

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  • DOI: https://doi.org/10.1007/s00162-004-0144-2

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