Skip to main content

Stability of capillary waves on deep water

  • Conference paper
  • First Online:
Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1230))

  • 541 Accesses

Abstract

The stability of periodic capillary waves of permanent form on deep water to three dimensional disturbances is studied using numerical methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Chen and P. G. Saffman, Steady gravity-capillary waves on deep water I. Weakly nonlinear waves, Stud. Appl. Math. 60: 183–210 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  2. B. Chen and P. G. Saffman, Numerical evidence for the existence of new types of gravity waves of permanent form on deep water, Stud, Appl. Math. 62: 1–21 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  3. B. Chen and P. G. Saffman, Steady gravity-capillary waves on deep water II. Numerical results for finite amplitude, Stud. Appl. Math. 62: 95–111 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  4. G. D. Crapper, An exact solution for progressive capillary waves of arbitrary amplitude, J. Fluid Mech. 2: 532–540 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  5. M. S. Longuet-Higgins, The instabilities of gravity waves of finite amplitude in deep water I. Superharmonics, Proc. Roy. Soc. Lond., A 360: 471–488 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. S. Longuet-Higgins, The instabilities of gravity waves of finite amplitude in deep water II. Subharmonics, Proc. Roy. Soc. Lond., A 360: 489–505 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  7. M. S. Longuet-Higgins and M. J. H. Fox, Theory of the almosthighest wave: the inner solutions, J. Fluid Mech. 80: 721–741 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  8. J. W. McLean, Instabilities of finite-amplitude water waves, J. Fluid Mech. 114: 315–330 (1982).

    Article  MATH  Google Scholar 

  9. J. W. McLean, Y. C. Ma, D. U. Martin. P. G. Saffman and H. C. Yuen, Three-dimensional instability of finite amplitude water waves, Phys. Rev. Lett. 46: 817–820 (1981).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jean-Pierre Hennart

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Chen, B., Saffman, P.G. (1986). Stability of capillary waves on deep water. In: Hennart, JP. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 1230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072682

Download citation

  • DOI: https://doi.org/10.1007/BFb0072682

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17200-0

  • Online ISBN: 978-3-540-47379-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics