Skip to main content
Article thumbnail
Location of Repository

On some properties of traveling water waves with vorticity

By Eugen Varvaruca

Abstract

We prove that for a large class of vorticity functions the crests of any corresponding traveling gravity water wave of finite depth are necessarily points of maximal horizontal velocity. We also show that for waves with nonpositive vorticity the pressure everywhere in the fluid is larger than the atmospheric pressure. A related a priori estimate for waves with nonnegative vorticity is also given

Publisher: Society for Industrial and Applied Mathematics
Year: 2008
OAI identifier: oai:centaur.reading.ac.uk:17523

Suggested articles

Citations

  1. Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth, doi
  2. (1880). Considerations relative to the greatest height of oscillatory irrotational waves which can be propagated without change of form, in Math. and Phys. Papers I, Cambridge
  3. (2007). Deep-water waves with vorticity: Symmetry and rotational behaviour,
  4. (2004). Exact steady periodic water waves with vorticity,
  5. (2006). Global bifurcation theory of deep-water waves with vorticity, doi
  6. Large-amplitude steady rotational water waves, doi
  7. (1981). On periodic water-waves and their convergence to solitary waves in the long-wave limit,
  8. (1981). On solitary water-waves of finite amplitude,
  9. (1978). On the existence of a wave of greatest height and Stokes’s conjecture, doi
  10. On the existence of extreme waves and the Stokes conjecture with vorticity, submitted; also available online at http://arXiv.org/abs/0707.2224.
  11. (1978). On the existence theory for irrotational water waves, doi
  12. (1982). On the Stokes conjecture for the wave of extreme form,
  13. (2007). Particle trajectories in solitary water waves,
  14. (1982). Proof of the Stokes conjecture in the theory of surface waves, doi
  15. (2007). Rotational steady water waves near stagnation,
  16. (2006). Singularities of Bernoulli free boundaries, doi
  17. (2007). Stability properties of steady water waves with vorticity,
  18. (1988). steady surface waves on water of finite depth with constant vorticity, doi
  19. (1996). Stokes waves, doi
  20. (2007). Symmetry of steady periodic gravity water waves with vorticity,
  21. (1997). The Stokes and Krasovskii conjectures for the wave of greatest height, doi
  22. (2006). The trajectories of particles in Stokes waves,
  23. (2006). Variational formulations for steady water waves with vorticity,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.