Particle trajectories in linear water waves

Journal of Mathematical Fluid Mechanics

Volumn 10, Issue 1, 2008, Pages 1-18

  Constantin, Adrian ^a,b   Villari, Gabriele ^c  

^a TRINITY COLLEGE DUBLIN   (Ireland)

^b LUND UNIVERSITY   (Sweden)

^c Dipartimento di Matematica U Dini   (Italy)

Author keywords

Linear theory; Particle trajectory; Water waves

Indexed keywords

GRAVITATION; THEOREM PROVING;

LINEAR THEORY; PARTICLE TRAJECTORY;

WATER WAVES;

GRAVITATION; THEOREM PROVING; WATER WAVES;

GRAVITY WAVE; LINEARITY; THEORY; TRAJECTORY; WATER WAVE;

EID: 40249098867     PISSN: 14226928     EISSN: 14226952     Source Type: Journal    
DOI: 10.1007/s00021-005-0214-2     Document Type: Article

References (30)

1. D. J. ACHESON, Elementary Fluid Dynamics, The Clarendon Press, Oxford Univ. Press, New York, 1990.
2. V. I. ARNOLD, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1989.
3. A. E. BRYSON, Waves in Fluids, National Committee for Fluid Mechanics Films, Encyclopaedia Britannica Educational Corporation, 425 North Michigan Avenue, Chicago, IL 60611.
4. A. CONSTANTIN, On the deep water wave motion, J. Phys. A 34 (2001), 1405-1417.
5. A. CONSTANTIN and J. ESCHER, Symmetry of steady periodic surface water waves with vorticity, J. Fluid Mech. 498 (2004), 171-181.
6. A. CONSTANTIN and W. STRAUSS, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math. 57 (2004), 481-527.
7. A. CONSTANTIN, D. SATTINGER and W. STRAUSS, Variational formulations for steady water waves with vorticity, J. Fluid. Mech. 548 (2006), 151-163.
8. G. D. CRAPPER, Introduction to Water Waves, Ellis Horwood Ltd., Chichester, 1984.
9. L. DEBNATH, Nonlinear Water Waves, Academic Press, Inc., Boston, MA, 1994.
10. F. GERSTNER, Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile, Ann. Phys. 2 (1809), 412-445.
11. J. GUCKENHEIMER and P. HOLMES, Nonlinear Oscillations, Dynamical Systems, and Bi-furcations of Vector Fields, Springer-Verlag, New York, 1990.
12. J. K. HALE, Ordinary Differential Equations, Wiley-Interscience, New York-London-Sydney, 1969.
13. R. S. JOHNSON, A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge Univ. Press, Cambridge, 1997.
14. D. W. JORDAN and P. SMITH, Nonlinear Ordinary Differential Equations, Oxford Univ. Press, Oxford, 1999.
15. K. E. KENYON, Shallow water gravity waves: a note on the particle orbits, J. Oceanography 52 (1996), 353-357.
16. H. LAMB, Hydrodynamics, Cambridge, Univ. Press, 1895.
17. T. LEVI-CIVITA, What are waves? Rice Inst. Pamphlet 25 (1938), 168-205.
18. J. LIGHTHILL, Waves in Fluids, Cambridge Univ. Press, Cambridge, 1978.
19. M. S. LONGUET-HLGGINS, The trajectories of particles in steep, symmetric gravity waves, J. Fluid Mech. 94 (1979), 497-517.
20. M. S. LONGUET-HLGGINS, Eulerian and Lagrangian aspects of surface waves, J. Fluid Mech. 173 (1986), 683-707.
21. L. M. MILNE-THOMSON, Theoretical Hydrodynamics, The Macmillan Co., London, 1938.
22. J. MILNOR, Morse Theory, Annals of Mathematics Studies, Princeton University Press, Princeton, N.J., 1963.
23. G. SANSONE and R. CONTI, Non-linear Differential Equations, The Macmillan Co., New York 1964.
24. A. SOMMERFELD, Mechanics of Deformable Bodies, Academic Press, Inc., New York, N. Y., 1950.
25. J. J. STOKER, Water Waves. The Mathematical Theory with Applications, Interscience Publ., Inc., New York, 1957.
26. G. G. STOKES, On the theory of oscillatory waves, Trans. Cambridge Phil. Soc. 8 (1847), 441-455.
27. J. F. TOLAND, Stokes waves, Topol. Methods Nonlinear Anal. 7 (1996), 1-48.
28. F. URSELL, Mass transport in gravity waves, Proc. Cambridge Phil. Soc. 40 (1953), 145-150.
29. C.-S. YIH, The role of drift mass in the kinetic energy and momentum of periodic water waves and sound waves, J. Fluid Mech. 331 (1997), 429-438.
30. A. CONSTANTIN, The trajectories of particles in Stokes waves, Inventiones Mathematicae. DOI: 10.1007/s00222-006-0002-5.