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Recovering surface profiles of solitary waves on a uniform stream from pressure measurements
| 1. | Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom |
References:
| [1] |
C. J. Amick and J. F. Toland, On solitary water waves of finite amplitude, Arch. Rat. Mech. Anal., 76 (1981), 9-95.
doi: 10.1007/BF00250799. |
| [2] |
A. Baquerizo and M. A. Losada, Transfer function between wave height and wave pressure for progressive waves, by Y.-Y. Kuo and J.-F. Chiu: Comments, Coast. Engng., 24 (1995), 351-353.
doi: 10.1016/0378-3839(94)00038-Y. |
| [3] |
C. T. Bishop and M. A. Donelan, Measuring waves with pressure transducers, Coast. Engng., 11 (1987), 309-328.
doi: 10.1016/0378-3839(87)90031-7. |
| [4] |
D. Clamond and A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech., 714 (2013), 463-575.
doi: 10.1017/jfm.2012.490. |
| [5] |
D. Clamond, New exact relations for easy recovery of steady wave profiles from bottom pressure measurements, J. Fluid Mech., 726 (2013), 547-558.
doi: 10.1017/jfm.2013.253. |
| [6] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535.
doi: 10.1007/s00222-006-0002-5. |
| [7] |
A. Constantin and J. Escher, Particle trajectories in solitary water waves, Bull. Amer. Math. Soc. (N.S.), 44 (2007), 423-431.
doi: 10.1090/S0273-0979-07-01159-7. |
| [8] |
A. Constantin, On the particle paths in solitary water waves, Quart. Appl. Math., 68 (2010), 81-90. |
| [9] |
A. Constantin, On the recovery of solitary wave profiles from pressure measurements, J. Fluid Mech., 699 (2012), 376-384.
doi: 10.1017/jfm.2012.114. |
| [10] |
A. Constantin, J. Escher and H.-C. Hsu, Pressure beneath a solitary water wave: Mathematical theory and experiments, Arch. Rat. Mech. Anal., 201 (2011), 251-269.
doi: 10.1007/s00205-011-0396-0. |
| [11] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave, Commun. Pure Appl. Math., 63 (2010), 533-557.
doi: 10.1002/cpa.20299. |
| [12] |
W. Craig and P. Sternberg, Symmetry of solitary waves, Commun. Part. Diff. Equ., 13 (1988), 603-633.
doi: 10.1080/03605308808820554. |
| [13] |
B. Deconinck, D. Henderson, K. L. Oliveras and V. Vasan, Recovering the water-wave surface from pressure measurements, in 10th International Conference on Mathematical and Numerical Aspects of Waves, WAVES 2011, Vancouver, 2011. |
| [14] |
J. Escher and T. Schlurmann, On the recovery of the free surface from the pressure within periodic traveling water waves, J. Nonlinear Math. Phys., 15 (2008), 50-57.
doi: 10.2991/jnmp.2008.15.s2.4. |
| [15] |
F. G. Friedlander, Introduction to the Theory of Distributions, Second edition, Cambridge University Press, Cambridge, 1998. |
| [16] |
D. Henry, On the pressure transfer function for solitary water waves with vorticity, Math. Ann., 357 (2013), 23-30.
doi: 10.1007/s00208-013-0899-0. |
| [17] |
Y.-Y. Kuo and Y.-F. Chiu, Transfer function between the wave height and wave pressure for progressive waves, Coast. Engng., 23 (1994), 81-93.
doi: 10.1016/0378-3839(94)90016-7. |
| [18] |
J. B. Mcleod, The rate of decay of solitary waves of finite amplitude, Appl. Anal., 17 (1983), 37-50.
doi: 10.1080/00036818308839482. |
| [19] |
K. L. Oliveras, V. Vasan, B. Deconinck and D. Henderson, Recovering the water-wave profile from pressure measurements, SIAM J. Appl. Math., 72 (2012), 897-918.
doi: 10.1137/110853285. |
| [20] |
R. S. Strichartz, A Guide to Distribution Theory and Fourier Transforms, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1994. |
| [21] |
C.-H. Tsai, M.-C. Huang, F.-J. Young, Y.-C. Lin and H.-W. Li, On the recovery of surface wave by pressure transfer function, Ocean Engng., 32 (2005), 1247-1259.
doi: 10.1016/j.oceaneng.2004.10.020. |
show all references
References:
| [1] |
C. J. Amick and J. F. Toland, On solitary water waves of finite amplitude, Arch. Rat. Mech. Anal., 76 (1981), 9-95.
doi: 10.1007/BF00250799. |
| [2] |
A. Baquerizo and M. A. Losada, Transfer function between wave height and wave pressure for progressive waves, by Y.-Y. Kuo and J.-F. Chiu: Comments, Coast. Engng., 24 (1995), 351-353.
doi: 10.1016/0378-3839(94)00038-Y. |
| [3] |
C. T. Bishop and M. A. Donelan, Measuring waves with pressure transducers, Coast. Engng., 11 (1987), 309-328.
doi: 10.1016/0378-3839(87)90031-7. |
| [4] |
D. Clamond and A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech., 714 (2013), 463-575.
doi: 10.1017/jfm.2012.490. |
| [5] |
D. Clamond, New exact relations for easy recovery of steady wave profiles from bottom pressure measurements, J. Fluid Mech., 726 (2013), 547-558.
doi: 10.1017/jfm.2013.253. |
| [6] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535.
doi: 10.1007/s00222-006-0002-5. |
| [7] |
A. Constantin and J. Escher, Particle trajectories in solitary water waves, Bull. Amer. Math. Soc. (N.S.), 44 (2007), 423-431.
doi: 10.1090/S0273-0979-07-01159-7. |
| [8] |
A. Constantin, On the particle paths in solitary water waves, Quart. Appl. Math., 68 (2010), 81-90. |
| [9] |
A. Constantin, On the recovery of solitary wave profiles from pressure measurements, J. Fluid Mech., 699 (2012), 376-384.
doi: 10.1017/jfm.2012.114. |
| [10] |
A. Constantin, J. Escher and H.-C. Hsu, Pressure beneath a solitary water wave: Mathematical theory and experiments, Arch. Rat. Mech. Anal., 201 (2011), 251-269.
doi: 10.1007/s00205-011-0396-0. |
| [11] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave, Commun. Pure Appl. Math., 63 (2010), 533-557.
doi: 10.1002/cpa.20299. |
| [12] |
W. Craig and P. Sternberg, Symmetry of solitary waves, Commun. Part. Diff. Equ., 13 (1988), 603-633.
doi: 10.1080/03605308808820554. |
| [13] |
B. Deconinck, D. Henderson, K. L. Oliveras and V. Vasan, Recovering the water-wave surface from pressure measurements, in 10th International Conference on Mathematical and Numerical Aspects of Waves, WAVES 2011, Vancouver, 2011. |
| [14] |
J. Escher and T. Schlurmann, On the recovery of the free surface from the pressure within periodic traveling water waves, J. Nonlinear Math. Phys., 15 (2008), 50-57.
doi: 10.2991/jnmp.2008.15.s2.4. |
| [15] |
F. G. Friedlander, Introduction to the Theory of Distributions, Second edition, Cambridge University Press, Cambridge, 1998. |
| [16] |
D. Henry, On the pressure transfer function for solitary water waves with vorticity, Math. Ann., 357 (2013), 23-30.
doi: 10.1007/s00208-013-0899-0. |
| [17] |
Y.-Y. Kuo and Y.-F. Chiu, Transfer function between the wave height and wave pressure for progressive waves, Coast. Engng., 23 (1994), 81-93.
doi: 10.1016/0378-3839(94)90016-7. |
| [18] |
J. B. Mcleod, The rate of decay of solitary waves of finite amplitude, Appl. Anal., 17 (1983), 37-50.
doi: 10.1080/00036818308839482. |
| [19] |
K. L. Oliveras, V. Vasan, B. Deconinck and D. Henderson, Recovering the water-wave profile from pressure measurements, SIAM J. Appl. Math., 72 (2012), 897-918.
doi: 10.1137/110853285. |
| [20] |
R. S. Strichartz, A Guide to Distribution Theory and Fourier Transforms, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1994. |
| [21] |
C.-H. Tsai, M.-C. Huang, F.-J. Young, Y.-C. Lin and H.-W. Li, On the recovery of surface wave by pressure transfer function, Ocean Engng., 32 (2005), 1247-1259.
doi: 10.1016/j.oceaneng.2004.10.020. |
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