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Progressive waves on a blunt interface
Internal Gerstner waves on a sloping bed
1. | Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna |
References:
[1] |
A. Aleman and A. Constantin, Harmonic maps and ideal fluid flows,, Arch. Rat. Mech. Anal., 204 (2012), 479.
doi: 10.1007/s00205-011-0483-2. |
[2] |
A. Bennett, Lagrangian Fluid Dynamics,, Cambridge University Press, (2006).
doi: 10.1017/CBO9780511734939. |
[3] |
B. Bolzano, Leben franz joseph ritters von gerstner,, Abhandlungen der kön. böhmischen Gesellschaft der Wissenschaften, (1837). Google Scholar |
[4] |
A. Constantin, Edge waves along a sloping beach,, J. Phys. A: Mathematical General, 34 (2001), 9723.
doi: 10.1088/0305-4470/34/45/311. |
[5] |
A. Constantin, The trajectories of particles in Stokes waves,, Invent. Math., 166 (2006), 523.
doi: 10.1007/s00222-006-0002-5. |
[6] |
A. Constantin, An exact solution for equatorially trapped waves,, J. Geophys. Res., 117 (2012).
doi: 10.1029/2012JC007879. |
[7] |
A. Constantin, On the modelling of equatorial waves,, Geophys. Res. Lett., 39 (2012), 1.
doi: 10.1029/2012GL051169. |
[8] |
A. Constantin, Some three-dimensional non-linear equatorial flows,, J. Phys. Oceanography, 43 (2013), 165. Google Scholar |
[9] |
A. Constantin, M. Ehrnström and G. Villari, Particle trajectories in linear deep-water waves,, Nonlinear Anal. Real World Appl., 9 (2008), 1336.
doi: 10.1016/j.nonrwa.2007.03.003. |
[10] |
A. Constantin and P. Germain, Instability of some equatorially trapped waves,, J. Geophys. Res.-Oceans, 118 (2013), 2802.
doi: 10.1002/jgrc.20219. |
[11] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave,, Commun. Pure Appl. Math., 63 (2010), 533.
doi: 10.1002/cpa.20299. |
[12] |
A. Constantin and G. Villari, Particle trajectories in linear water waves,, J. Math. Fluid Mech., 10 (2006), 1.
doi: 10.1007/s00021-005-0214-2. |
[13] |
D. Farmer and J. Smith, Nonlinear internal waves in a fjord,, in Elsevier Oceanography Series (editor, 23 (1978), 465.
doi: 10.1016/S0422-9894(08)71294-7. |
[14] |
W. Froude, On the rolling of ships,, Transactions of the Institution of Naval Architects, 11 (1861), 180.
doi: 10.1080/03071847309433595. |
[15] |
C. Garrett and W. Munk, Internal waves in the ocean,, Annual Review of Fluid Mechanics, (1979), 339.
doi: 10.1146/annurev.fl.11.010179.002011. |
[16] |
F. Gerstner, Theorie der Wellen samt einer daraus abgeleiteten theorie der deichprofile,, Abh. der kön. böhmischen Gesellschaft der Wissenschaften, (1804). Google Scholar |
[17] |
F. Gerstner, Theorie der Wellen,, Ann. Phys., 32 (1809), 412.
doi: 10.1002/andp.18090320808. |
[18] |
K. R. Helfrich and W. K. Melville, Long nonlinear internal waves,, Ann. Rev. Fluid Mech., 38 (2006), 395.
doi: 10.1146/annurev.fluid.38.050304.092129. |
[19] |
D. Henry, On the deep-water stokes wave flow,, Int. Math. Res. Not., 2008 (2008).
doi: 10.1093/imrn/rnn071. |
[20] |
D. Henry, An exact solution for equatorial geophysical water waves with an underlying current,, Eur. J. Mech. - B/Fluids, 38 (2013), 18.
doi: 10.1016/j.euromechflu.2012.10.001. |
[21] |
R. S. Johnson, A Modern Introduction to the Mathematical Theory of Water Waves,, Cambridge University Press, (1997).
doi: 10.1017/CBO9780511624056. |
[22] |
R. S. Johnson, Edge waves: Theories past and present,, Philos. Trans. Roy. Soc. London Ser. A, 365 (2007), 2359.
doi: 10.1098/rsta.2007.2013. |
[23] |
H. Kalisch, Periodic traveling water waves with isobaric streamlines,, J. Non-linear Math. Phys., 11 (2004), 461.
doi: 10.2991/jnmp.2004.11.4.3. |
[24] |
P. D. Komar, Beach processes and sedimentation,, Prentice-Hall, (1976). Google Scholar |
[25] |
A.-V. Matioco, An exact solution for geophysical equatorial edge waves over a sloping beach,, J. Phys. A, 45 (2012).
doi: 10.1142/S1402925112400098. |
[26] |
A.-V. Matioc and B.-V. Matioc, On periodic water waves with Coriolis effects and isobaric streamlines,, J. Nonlinear Math. Phys., 19 (2012).
doi: 10.1142/S1402925112400098. |
[27] |
E. G. Morozov and A. V. Marchenko, Short-period internal waves in an arctic Fjord (Spitsbergen),, Izv. Atmos. Ocean. Phy., 48 (2012), 401.
doi: 10.1134/S0001433812040123. |
[28] |
L. Mysak, Topographically trapped waves,, Ann. Rev. Fluid Mech., 12 (1980), 45.
|
[29] |
F. Nansen, The Norwegian North Polar Expedition 1893-1896, Scientific Results, Volume 5,, The Fridtjof Nansen Fund for the Advancement of Science, (1906). Google Scholar |
[30] |
J. Pedlosky, Geophysical Fluid Dynamics,, Springer, (1982).
doi: 10.1115/1.3157711. |
[31] |
W. J. M. Rankine, On the exact form of waves near the surface of deep water,, Philos. Trans. Roy. Soc. London Ser. A, 153 (1863), 127.
doi: 10.1098/rstl.1863.0006. |
[32] |
F. Reech, Sur la theorie des ondes liquides periodiques,, Comptes Rendus Acad. Sci. Paris, 68 (1869), 1099. Google Scholar |
[33] |
G. G. Stokes, Report on recent researches in hydrodynamics,, in Brit. Assoc. Rep., (1846).
doi: 10.1017/CBO9780511702242.011. |
[34] |
G. G. Stokes, On the theory of oscillatory waves,, Trans. Camb. Phil. Soc., 8 (1847), 441.
doi: 10.1017/CBO9780511702242.013. |
[35] |
R. Stuhlmeier, Internal Gerstner waves: applications to dead water,, Appl. Anal., ().
doi: 10.1080/00036811.2013.833609. |
[36] |
C. Truesdell, The Kinematics of Vorticity,, Indiana University Press, (1954).
|
[37] |
M. Umeyama, Eulerian-Lagrangian analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry,, Philos. Trans. Roy. Soc. London Ser. A, 370 (2012), 1687.
doi: 10.1098/rsta.2011.0450. |
[38] |
C. Yih, Note on edge waves in a stratified fluid,, J. Fluid Mech., 24 (1966), 765.
doi: 10.1017/S0022112066000983. |
show all references
References:
[1] |
A. Aleman and A. Constantin, Harmonic maps and ideal fluid flows,, Arch. Rat. Mech. Anal., 204 (2012), 479.
doi: 10.1007/s00205-011-0483-2. |
[2] |
A. Bennett, Lagrangian Fluid Dynamics,, Cambridge University Press, (2006).
doi: 10.1017/CBO9780511734939. |
[3] |
B. Bolzano, Leben franz joseph ritters von gerstner,, Abhandlungen der kön. böhmischen Gesellschaft der Wissenschaften, (1837). Google Scholar |
[4] |
A. Constantin, Edge waves along a sloping beach,, J. Phys. A: Mathematical General, 34 (2001), 9723.
doi: 10.1088/0305-4470/34/45/311. |
[5] |
A. Constantin, The trajectories of particles in Stokes waves,, Invent. Math., 166 (2006), 523.
doi: 10.1007/s00222-006-0002-5. |
[6] |
A. Constantin, An exact solution for equatorially trapped waves,, J. Geophys. Res., 117 (2012).
doi: 10.1029/2012JC007879. |
[7] |
A. Constantin, On the modelling of equatorial waves,, Geophys. Res. Lett., 39 (2012), 1.
doi: 10.1029/2012GL051169. |
[8] |
A. Constantin, Some three-dimensional non-linear equatorial flows,, J. Phys. Oceanography, 43 (2013), 165. Google Scholar |
[9] |
A. Constantin, M. Ehrnström and G. Villari, Particle trajectories in linear deep-water waves,, Nonlinear Anal. Real World Appl., 9 (2008), 1336.
doi: 10.1016/j.nonrwa.2007.03.003. |
[10] |
A. Constantin and P. Germain, Instability of some equatorially trapped waves,, J. Geophys. Res.-Oceans, 118 (2013), 2802.
doi: 10.1002/jgrc.20219. |
[11] |
A. Constantin and W. Strauss, Pressure beneath a Stokes wave,, Commun. Pure Appl. Math., 63 (2010), 533.
doi: 10.1002/cpa.20299. |
[12] |
A. Constantin and G. Villari, Particle trajectories in linear water waves,, J. Math. Fluid Mech., 10 (2006), 1.
doi: 10.1007/s00021-005-0214-2. |
[13] |
D. Farmer and J. Smith, Nonlinear internal waves in a fjord,, in Elsevier Oceanography Series (editor, 23 (1978), 465.
doi: 10.1016/S0422-9894(08)71294-7. |
[14] |
W. Froude, On the rolling of ships,, Transactions of the Institution of Naval Architects, 11 (1861), 180.
doi: 10.1080/03071847309433595. |
[15] |
C. Garrett and W. Munk, Internal waves in the ocean,, Annual Review of Fluid Mechanics, (1979), 339.
doi: 10.1146/annurev.fl.11.010179.002011. |
[16] |
F. Gerstner, Theorie der Wellen samt einer daraus abgeleiteten theorie der deichprofile,, Abh. der kön. böhmischen Gesellschaft der Wissenschaften, (1804). Google Scholar |
[17] |
F. Gerstner, Theorie der Wellen,, Ann. Phys., 32 (1809), 412.
doi: 10.1002/andp.18090320808. |
[18] |
K. R. Helfrich and W. K. Melville, Long nonlinear internal waves,, Ann. Rev. Fluid Mech., 38 (2006), 395.
doi: 10.1146/annurev.fluid.38.050304.092129. |
[19] |
D. Henry, On the deep-water stokes wave flow,, Int. Math. Res. Not., 2008 (2008).
doi: 10.1093/imrn/rnn071. |
[20] |
D. Henry, An exact solution for equatorial geophysical water waves with an underlying current,, Eur. J. Mech. - B/Fluids, 38 (2013), 18.
doi: 10.1016/j.euromechflu.2012.10.001. |
[21] |
R. S. Johnson, A Modern Introduction to the Mathematical Theory of Water Waves,, Cambridge University Press, (1997).
doi: 10.1017/CBO9780511624056. |
[22] |
R. S. Johnson, Edge waves: Theories past and present,, Philos. Trans. Roy. Soc. London Ser. A, 365 (2007), 2359.
doi: 10.1098/rsta.2007.2013. |
[23] |
H. Kalisch, Periodic traveling water waves with isobaric streamlines,, J. Non-linear Math. Phys., 11 (2004), 461.
doi: 10.2991/jnmp.2004.11.4.3. |
[24] |
P. D. Komar, Beach processes and sedimentation,, Prentice-Hall, (1976). Google Scholar |
[25] |
A.-V. Matioco, An exact solution for geophysical equatorial edge waves over a sloping beach,, J. Phys. A, 45 (2012).
doi: 10.1142/S1402925112400098. |
[26] |
A.-V. Matioc and B.-V. Matioc, On periodic water waves with Coriolis effects and isobaric streamlines,, J. Nonlinear Math. Phys., 19 (2012).
doi: 10.1142/S1402925112400098. |
[27] |
E. G. Morozov and A. V. Marchenko, Short-period internal waves in an arctic Fjord (Spitsbergen),, Izv. Atmos. Ocean. Phy., 48 (2012), 401.
doi: 10.1134/S0001433812040123. |
[28] |
L. Mysak, Topographically trapped waves,, Ann. Rev. Fluid Mech., 12 (1980), 45.
|
[29] |
F. Nansen, The Norwegian North Polar Expedition 1893-1896, Scientific Results, Volume 5,, The Fridtjof Nansen Fund for the Advancement of Science, (1906). Google Scholar |
[30] |
J. Pedlosky, Geophysical Fluid Dynamics,, Springer, (1982).
doi: 10.1115/1.3157711. |
[31] |
W. J. M. Rankine, On the exact form of waves near the surface of deep water,, Philos. Trans. Roy. Soc. London Ser. A, 153 (1863), 127.
doi: 10.1098/rstl.1863.0006. |
[32] |
F. Reech, Sur la theorie des ondes liquides periodiques,, Comptes Rendus Acad. Sci. Paris, 68 (1869), 1099. Google Scholar |
[33] |
G. G. Stokes, Report on recent researches in hydrodynamics,, in Brit. Assoc. Rep., (1846).
doi: 10.1017/CBO9780511702242.011. |
[34] |
G. G. Stokes, On the theory of oscillatory waves,, Trans. Camb. Phil. Soc., 8 (1847), 441.
doi: 10.1017/CBO9780511702242.013. |
[35] |
R. Stuhlmeier, Internal Gerstner waves: applications to dead water,, Appl. Anal., ().
doi: 10.1080/00036811.2013.833609. |
[36] |
C. Truesdell, The Kinematics of Vorticity,, Indiana University Press, (1954).
|
[37] |
M. Umeyama, Eulerian-Lagrangian analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry,, Philos. Trans. Roy. Soc. London Ser. A, 370 (2012), 1687.
doi: 10.1098/rsta.2011.0450. |
[38] |
C. Yih, Note on edge waves in a stratified fluid,, J. Fluid Mech., 24 (1966), 765.
doi: 10.1017/S0022112066000983. |
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