Skip Navigation

International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn071, 7 pages, doi:10.1093/imrn/rnn071 published on July 12, 2008
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Henry, D.
Social Bookmarking
 Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

On the Deep-Water Stokes Wave Flow

David Henry

School of Mathematics, Trinity College, Dublin 2, Ireland

Correspondence: Correspondence to be sent to: hendavid{at}maths.tcd.ie

We prove a new result detailing the monotonicity of the horizontal velocity component of deep-water Stokes waves along streamlines.



References

  1. Bryson A.E. Waves in Fluids (1964) [videorecording presented by the National Committee for Fluid Mechanics Films; produced by Educational Services]. Chicago, IL: Encyclopaedia Britannica Educational Corporation.
  2. Constantin A. On the deep water wave motion. Journal of Physics A (2001) 34:1405–17.[CrossRef]
  3. Constantin A. Edge waves along a sloping beach. Journal of Physics A (2001) 34:9723–31.[CrossRef]
  4. Constantin A. The trajectories of particles in Stokes waves. Inventiones Mathematicae (2006) 166:523–35.[CrossRef][ISI]
  5. Constantin A., Ehrnström M., Villari G. Particle trajectories in linear deep-water waves. Nonlinear Analysis: Real World Applications (2008) 9:1336–44.[CrossRef][ISI]
  6. Constantin A., Escher J. Symmetry of steady periodic surface water waves with vorticity. Journal of Fluid Mechanics (2004) 498:171–81.[CrossRef][ISI]
  7. Constantin A., Escher J. Symmetry of deep-water waves with vorticity. European Journal of Applied Mathematics (2004) 15:755–68.[CrossRef][ISI]
  8. Constantin A., Strauss W. Pressure and trajectories beneath a Stokes wave. Preprint.
  9. Constantin A., Strauss W. Stability properties of steady water waves with vorticity. Communications on Pure and Applied Mathematics (2007) 60:911–50.[CrossRef][ISI]
  10. Constantin A., Strauss W. Exact steady periodic water waves with vorticity. Communications on Pure and Applied Mathematics (2004) 57:481–527.[CrossRef][ISI]
  11. Constantin A., Sattinger D., Strauss W. Variational formulations for steady water waves with vorticity. Journal of Fluid Mechanics (2006) 548:151–63.[CrossRef][ISI]
  12. Constantin A., Villari G. Particle trajectories in linear water waves. Journal of Mathe-matical Fluid Mechanics (2008) 10:1–18.[CrossRef][ISI]
  13. Debnath L. Nonlinear Water Waves (1994) Boston, MA: Academic Press.
  14. Ehrnström M. Uniqueness for steady periodic water waves with vorticity. International Mathematics Research Notices (2005) 2005:3721–6.[Abstract/Free Full Text]
  15. Ehrnström M., Villari G. Linear water waves with vorticity: rotational features and particle paths. Journal of Differential Equations (2008) 244:1888–909.[CrossRef][ISI]
  16. Fraenkel L. E. An Introduction to Maximum Principles and Symmetry in Elliptic Problems (2000) Cambridge: Cambridge University Press.
  17. von. Gerstner F. Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile. Annals of Physics (1809) 2:412–45.
  18. Henry D. Particle trajectories in linear periodic capillary and capillary-gravity water waves. Philosophical Transactions of the Royal Society, Series A (2007) 365:2241–51.[CrossRef][Medline]
  19. Henry D. Particle trajectories in linear periodic capillary and capillary-gravity deep-water waves. Journal of Nonlinear Mathematical Physics (2007) 14:1–7.[CrossRef][ISI]
  20. Henry D. The trajectories of particles in deep-water Stokes waves. International Mathematics Research Notices (2006) 2006:1–13.
  21. Johnson R. S. A Modern Introduction to the Mathematical Theory of Water Waves (1997) Cambridge: Cambridge University Press.
  22. Lighthill J. Waves in Fluids (1978) Cambridge: Cambridge University Press.
  23. Rankine W. J. M. On the exact form of waves near the surface of deep water. Philosophical Transactions of the Royal Society, Series A (1863) 153:127–38.[CrossRef]
  24. Stoker J. J. Water Waves. The Mathematical Theory with Applications (1957) New York: Interscience Publications.
  25. Stokes G. G. On the theory of oscillatory waves. Transactions of the Cambridge Philosophical Society (1849) 8:441–55.
  26. Toland J. F. Stokes waves. Topological Methods in Nonlinear Analysis (1996) 7:1–48.
  27. Wahlén E. A note on steady gravity waves with vorticity. International Mathematics Research Notices (2005) 2005:389–96.[Abstract/Free Full Text]

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Henry, D.
Social Bookmarking
 Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?