Skip to main content
SpringerLink
Log in

On the form of crests in limiting gravity waves

  • Published:
Izvestiya, Atmospheric and Oceanic Physics Aims and scope Submit manuscript

Abstract

Properties of surface singularities and the form of wave crests of limiting gravity waves in steady-state flows of an ideal liquid are considered by analyzing the kinematic boundary condition. It is shown that, for rotational waves, the angle at the crest can have any value from 0° to 180°, while it has the only value 90° in the case of irrotational waves. Two inferences are made from Bernoulli’s integral and the properties of singularities: (i) the Stokes wave is a rotational wave and (ii) no angular points can appear on the profiles of capillary-gravity and capillary waves.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Lamb, Hydrodynamics, 6th ed. (Gostekhizdat, Moscow, 1947; Cambridge University Press, Cambridge, 1932).

    Google Scholar 

  2. M. S. Longuet-Higgins and M. J. H. Fox, “Theory of the Almost-Highest Wave. Part 2. Matching and Analytic Extension,” J. Fluid Mech. 85, 769–786 (1978).

    Article  Google Scholar 

  3. M. S. Longuet-Higgins and E. D. Cokelet, “The Deformation of Steep Surface Waves on Water. Part 1. A Numerical Method of Computation,” Proc. R. Soc. London A350(1660), 1–26 (1976).

    Google Scholar 

  4. M. S. Longuet-Higgins and E. D. Cokelet, “The Deformation of Steep Surface Waves on Water. Part 2. Growth of Normal Mode Instabilities,” Proc. R. Soc. London A364(1716), 1–28 (1978).

    Google Scholar 

  5. G. I. Taylor, “An Experimental Study of Standing Waves,” Proc. R. Soc. London A218, 44–59 (1953).

    Google Scholar 

  6. A. N. Dubovik, “One-Mode Approximation for Periodic Waves on Deep Water,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 40, 271–276 (2004) [Izv., Atmos. Ocean. Phys. 40, 238–243 (2004)].

    Google Scholar 

  7. A. N. Dubovik, “One-Mode Solitary Solutions for Capillary-Gravity Waves on Deep Water,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 40, 410–417 (2004) [Izv., Atmos. Ocean. Phys. 40, 362–369 (2004)].

    Google Scholar 

  8. G. D. Crapper, “An Exact Solution for Progressive Capillary Waves of Arbitrary Amplitude,” J. Fluid Mech. 2, 532–540 (1957).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shirshov Institute of Oceanology, Russian Academy of Sciences, Nakhimovskii pr. 36, Moscow, 117997, Russia

    A. N. Dubovik

Authors
  1. A. N. Dubovik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.N. Dubovik, 2006, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2006, Vol. 42, No. 3, pp. 403–406.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dubovik, A.N. On the form of crests in limiting gravity waves. Izv. Atmos. Ocean. Phys. 42, 371–374 (2006). https://doi.org/10.1134/S0001433806030108

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001433806030108

Keywords

Search

Navigation