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