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Stability of Capillary Waves of Finite Amplitude

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Applied Physics, System Science and Computers (APSAC 2017)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 428))

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Abstract

The direct Lyapunov method is used to prove the stability of the exact Crapper solution for capillary waves. The dynamic equations of the capillary wave are presented in the form of an infinite Euler-Lagrange chain of equations for the Stokes coefficients. The stationary solution found for these equations is the Crapper solution for capillary waves. With the help of energy and momentum conservation laws the Lyapunov function is constructed. It is shown that the Lyapunov function is positive definite with respect to any perturbations of waves surfaces, for waves with the period multiple of wavelength.

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References

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Acknowledgements

The study has been supported by the Russian Science Foundation (project N 14-19-01633) in IPMech RAS.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Institutskiy per. 9, 141700, Dolgoprudny, Russia

    Alexander Petrov, Mariana Lopushanski & Vladimir Vanovskiy

  2. Institute for Problems in Mechanics RAS, Pr. Vernadskogo 101-1, 119526, Moscow, Russia

    Alexander Petrov, Mariana Lopushanski & Vladimir Vanovskiy

Authors
  1. Alexander Petrov
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  2. Mariana Lopushanski
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  3. Vladimir Vanovskiy
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Corresponding author

Correspondence to Mariana Lopushanski .

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Editors and Affiliations

  1. Ag. Spyridon, University of Applied Sciences Ag. Spyridon, Athens, Greece

    Klimis Ntalianis

  2. Faculty of Mathematics, Al.I. Cuza University Faculty of Mathematics, Iasi, Romania

    Anca Croitoru

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Petrov, A., Lopushanski, M., Vanovskiy, V. (2018). Stability of Capillary Waves of Finite Amplitude. In: Ntalianis, K., Croitoru, A. (eds) Applied Physics, System Science and Computers. APSAC 2017. Lecture Notes in Electrical Engineering, vol 428. Springer, Cham. https://doi.org/10.1007/978-3-319-53934-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-53934-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53933-1

  • Online ISBN: 978-3-319-53934-8

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