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A characterization of the symmetric steady water waves in terms of the underlying flow
A boundary integral formulation for particle trajectories in Stokes waves
1. | Instituto Nacional de Matemática Pura e Aplicada/IMPA, Est. D. Castorina, 110, J. Botânico, Rio de Janeiro, RJ 22460-320, Brazil |
References:
[1] |
D. P. Bertsekas, Nonlinear Programming,, $2^{nd}$ edition, (1999).
doi: 10.1038/sj.jors.2600425. |
[2] |
H.-K. Chang, Y.-Y. Chen and J.-C. Liou, Particle trajectories of nonlinear gravity waves in deep water,, Ocean Engineering, 36 (2009), 324.
doi: 10.1016/j.oceaneng.2008.12.007. |
[3] |
A. Constantin, The trajectories of particles in Stokes waves,, Invent. Math., 166 (2006), 523.
doi: 10.1007/s00222-006-0002-5. |
[4] |
A. Constantin, Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis,, SIAM, (2011).
doi: 10.1137/1.9781611971873. |
[5] |
A. Constantin, Mean velocities in a Stokes wave,, Arch. Ration. Mech. Anal., 207 (2013), 907.
doi: 10.1007/s00205-012-0584-6. |
[6] |
A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity,, Duke Math. J., 140 (2007), 591.
doi: 10.1215/S0012-7094-07-14034-1. |
[7] |
A. Constantin, M. Ehrnström and E. Wahlén, Particle trajectories in linear deep-water waves,, Nonlinear Anal. Real World Appl., 9 (2008), 1.
doi: 10.1016/j.nonrwa.2007.03.003. |
[8] |
A. Constantin and W. A. Strauss, Pressure beneath a Stokes wave,, Comm. Pure Appl. Math., 63 (2010), 533.
doi: 10.1002/cpa.20299. |
[9] |
A. Constantin and G. Villari, Particle trajectories in linear water waves,, J. Math. Fulid Mech., 10 (2008), 1336.
doi: 10.1007/s00021-005-0214-2. |
[10] |
M. W. Dingemans, Water Waves Propagation Over Uneven Bottoms,, World Scientific, (1997).
doi: 10.1142/1241-part1. |
[11] |
J. D. Fenton, A fifth-order Stokes theory for steady waves,, Journal of Waterway, 111 (1985), 216.
doi: 10.1061/(ASCE)0733-950X(1985)111:2(216). |
[12] |
J. D. Fenton, Nonlinear wave theories,, The Sea: Ocean Engineering Science, 9 (1990), 1. Google Scholar |
[13] |
P. Guidotti, A new first-kind boundary integral formulation for the Dirichlet-to-Neumman map in 2D,, J. Comput. Phy., 190 (2008), 325.
doi: 10.1016/S0021-9991(03)00277-8. |
[14] |
D. Henry, On the deep-water Stokes wave flow,, IMRN, 2008 (2008), 1.
doi: 10.1093/imrn/rnn071. |
[15] |
M. Isobe, H. Nishimura and K. Horikawa, Expressions of Pertubation Solutions for Conservative Waves by Using Wave Height,, Proceedings of 33rd annual conference of JSCE 1978, (1978), 760. Google Scholar |
[16] |
F. John, Partial Differential Equations,, $4^{th}$ edition, (1982).
|
[17] |
I. G. Jonsson and L. Arneborg, Energy properties and shoaling of higher-order stokes waves on current,, Ocean Engineering, 22 (1995), 819.
doi: 10.1016/0029-8018(95)00008-9. |
[18] |
H. Lamb, Hydrodynamics,, Cambridge, (1895).
|
[19] |
M. S. Longuet-Higgins, Eulerian and Lagrangian aspects of surface waves,, J. Fluid Mech., 173 (1986), 683.
doi: 10.1017/S0022112086001325. |
[20] |
, Available at:, , (). Google Scholar |
[21] |
H. Okamoto and M. Shōji, The Mathematical Theory of Permanent Progressive Water-Waves,, World Scientific, (2001).
|
[22] |
H. Okamoto and M. Shōji, Trajectories of fluid particles in a periodic water wave,, Phil. Trans. R. Soc. A, 370 (2012), 1661.
doi: 10.1098/rsta.2011.0447. |
[23] |
F. Ruellan and A. Wallet, Trajectoires internes das un clapotis partiel,, La Houille Blanche, 5 (1950), 483. Google Scholar |
[24] |
L. Skjelbreia and J. Hendrinck, Fifth Order Gravity Wave Theory,, JProceedings of 7th conference on coastal engineering, (1960), 184. Google Scholar |
[25] |
J. J. Stoker, Water Waves. The Mathematical Theory with Applications,, Intersciene Publ. Inc., (1957).
|
[26] |
G. G. Stokes, On the theory of oscillatory waves,, Trans. Cambridge Phil. Soc., 8 (1847), 441.
doi: 10.1017/CBO9780511702242.013. |
[27] |
L. N. Trefethen, Spectral Methods in MATLAB,, SIAM, (2001).
doi: 10.1137/1.9780898719598. |
[28] |
M. Umeyama, Eulerian-Lagrangian analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry,, Phil. Trans. R. Soc. A, 370 (2012), 1687.
doi: 10.1098/rsta.2011.0450. |
[29] |
F. Ursell, Mass transport in gravity waves,, Proc. Cambridge Phil. Soc., 40 (1953), 145.
doi: 10.1017/S0305004100028140. |
[30] |
G. B. Whitham, Linear and Nonlinear Waves,, John Wiley, (1974).
|
show all references
References:
[1] |
D. P. Bertsekas, Nonlinear Programming,, $2^{nd}$ edition, (1999).
doi: 10.1038/sj.jors.2600425. |
[2] |
H.-K. Chang, Y.-Y. Chen and J.-C. Liou, Particle trajectories of nonlinear gravity waves in deep water,, Ocean Engineering, 36 (2009), 324.
doi: 10.1016/j.oceaneng.2008.12.007. |
[3] |
A. Constantin, The trajectories of particles in Stokes waves,, Invent. Math., 166 (2006), 523.
doi: 10.1007/s00222-006-0002-5. |
[4] |
A. Constantin, Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis,, SIAM, (2011).
doi: 10.1137/1.9781611971873. |
[5] |
A. Constantin, Mean velocities in a Stokes wave,, Arch. Ration. Mech. Anal., 207 (2013), 907.
doi: 10.1007/s00205-012-0584-6. |
[6] |
A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity,, Duke Math. J., 140 (2007), 591.
doi: 10.1215/S0012-7094-07-14034-1. |
[7] |
A. Constantin, M. Ehrnström and E. Wahlén, Particle trajectories in linear deep-water waves,, Nonlinear Anal. Real World Appl., 9 (2008), 1.
doi: 10.1016/j.nonrwa.2007.03.003. |
[8] |
A. Constantin and W. A. Strauss, Pressure beneath a Stokes wave,, Comm. Pure Appl. Math., 63 (2010), 533.
doi: 10.1002/cpa.20299. |
[9] |
A. Constantin and G. Villari, Particle trajectories in linear water waves,, J. Math. Fulid Mech., 10 (2008), 1336.
doi: 10.1007/s00021-005-0214-2. |
[10] |
M. W. Dingemans, Water Waves Propagation Over Uneven Bottoms,, World Scientific, (1997).
doi: 10.1142/1241-part1. |
[11] |
J. D. Fenton, A fifth-order Stokes theory for steady waves,, Journal of Waterway, 111 (1985), 216.
doi: 10.1061/(ASCE)0733-950X(1985)111:2(216). |
[12] |
J. D. Fenton, Nonlinear wave theories,, The Sea: Ocean Engineering Science, 9 (1990), 1. Google Scholar |
[13] |
P. Guidotti, A new first-kind boundary integral formulation for the Dirichlet-to-Neumman map in 2D,, J. Comput. Phy., 190 (2008), 325.
doi: 10.1016/S0021-9991(03)00277-8. |
[14] |
D. Henry, On the deep-water Stokes wave flow,, IMRN, 2008 (2008), 1.
doi: 10.1093/imrn/rnn071. |
[15] |
M. Isobe, H. Nishimura and K. Horikawa, Expressions of Pertubation Solutions for Conservative Waves by Using Wave Height,, Proceedings of 33rd annual conference of JSCE 1978, (1978), 760. Google Scholar |
[16] |
F. John, Partial Differential Equations,, $4^{th}$ edition, (1982).
|
[17] |
I. G. Jonsson and L. Arneborg, Energy properties and shoaling of higher-order stokes waves on current,, Ocean Engineering, 22 (1995), 819.
doi: 10.1016/0029-8018(95)00008-9. |
[18] |
H. Lamb, Hydrodynamics,, Cambridge, (1895).
|
[19] |
M. S. Longuet-Higgins, Eulerian and Lagrangian aspects of surface waves,, J. Fluid Mech., 173 (1986), 683.
doi: 10.1017/S0022112086001325. |
[20] |
, Available at:, , (). Google Scholar |
[21] |
H. Okamoto and M. Shōji, The Mathematical Theory of Permanent Progressive Water-Waves,, World Scientific, (2001).
|
[22] |
H. Okamoto and M. Shōji, Trajectories of fluid particles in a periodic water wave,, Phil. Trans. R. Soc. A, 370 (2012), 1661.
doi: 10.1098/rsta.2011.0447. |
[23] |
F. Ruellan and A. Wallet, Trajectoires internes das un clapotis partiel,, La Houille Blanche, 5 (1950), 483. Google Scholar |
[24] |
L. Skjelbreia and J. Hendrinck, Fifth Order Gravity Wave Theory,, JProceedings of 7th conference on coastal engineering, (1960), 184. Google Scholar |
[25] |
J. J. Stoker, Water Waves. The Mathematical Theory with Applications,, Intersciene Publ. Inc., (1957).
|
[26] |
G. G. Stokes, On the theory of oscillatory waves,, Trans. Cambridge Phil. Soc., 8 (1847), 441.
doi: 10.1017/CBO9780511702242.013. |
[27] |
L. N. Trefethen, Spectral Methods in MATLAB,, SIAM, (2001).
doi: 10.1137/1.9780898719598. |
[28] |
M. Umeyama, Eulerian-Lagrangian analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry,, Phil. Trans. R. Soc. A, 370 (2012), 1687.
doi: 10.1098/rsta.2011.0450. |
[29] |
F. Ursell, Mass transport in gravity waves,, Proc. Cambridge Phil. Soc., 40 (1953), 145.
doi: 10.1017/S0305004100028140. |
[30] |
G. B. Whitham, Linear and Nonlinear Waves,, John Wiley, (1974).
|
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