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One-dimensional weakly nonlinear model equations for Rossby waves
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| 1. | Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna |
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Under a Creative Commons license
References:
| [1] |
B. Buffoni and J. F. Toland, Analytic Theory of Global Bifurcation: An Introduction, Princeton University Press, Princeton, NJ, 2003. |
| [2] |
D. Clamond, New exact relations for easy recovery of steady wave profiles from bottom pressure measurements, J. Fluid Mech., 726 (2013), 547-558. |
| [3] |
D. Clamond and A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech., 714 (2013), 463-475. |
| [4] |
A. Constantin, Edge waves along a sloping beach, J. Phys. A, 34 (2001), 9723-9731. |
| [5] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535. |
| [6] |
A. Constantin, Particle trajectories in extreme Stokes waves, IMA J. Appl. Math., 77 (2012), 293-307. |
| [7] |
A. Constantin, On the recovery of solitary wave profiles from pressure measurements, J. Fluid Mech., 699 (2012), 376-384. |
| [8] |
A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity, Duke Math. J., 140 (2007), 591-603. |
| [9] |
A. Constantin and W. A. Strauss, Pressure beneath a Stokes wave, Comm. Pure Appl. Math., 63 (2010), 533-557. |
| [10] |
E. Dancer, Bifurcation theory for analytic operators, Proc. London Math. Soc., 26 (1973), 359-384. |
| [11] |
F. Gerstner, Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile, Ann. Phys., 2 (1809), 412-445. |
| [12] |
D. Henry and R. Ivanov, One-dimensional weakly nonlinear model equations for Rossby waves, Discr. Cont. Dyn. Syst. A, 34 (2014), 3025-3034.
doi: 10.3934/dcds.2014.34.3025. |
| [13] |
H.-C. Hsu, Recovering surface profiles of solitary waves on a uniform stream from pressure measurements, Discr. Cont. Dyn. Syst. A, 34 (2014), 3035-3043.
doi: 10.3934/dcds.2014.34.3035. |
| [14] |
D. Ionescu-Kruse and A.-V. Matioc, Small-amplitude equatorial water waves with constant vorticity: Dispersion relations and particle trajectories, Discr. Cont. Dyn. Syst. A, 34 (2014), 3045-3060.
doi: 10.3934/dcds.2014.34.3045. |
| [15] |
M. Kovalyov, On the nature of large and rogue waves, Discr. Cont. Dyn. Syst. A, 34 (2014), 3061-3093.
doi: 10.3934/dcds.2014.34.3061. |
| [16] |
T. Lyons, Particle trajectories in extreme Stokes waves over infinite depth, Discr. Cont. Dyn. Syst. A, 34 (2014), 3095-3107.
doi: 10.3934/dcds.2014.34.3095. |
| [17] |
C. I. Martin, Dispersion relations for periodic water waves with surface tension and discontinuous vorticity, Discr. Cont. Dyn. Syst. A, 34 (2014), 3109-3123.
doi: 10.3934/dcds.2014.34.3109. |
| [18] |
B.-V. Matioc, A characterization of the symmetric steady water waves in terms of the underlying flow, Discr. Cont. Dyn. Syst. A, 34 (2014), 3125-3133.
doi: 10.3934/dcds.2014.34.3125. |
| [19] |
A. Nachbin and R. Ribeiro-Junior, A boundary integral formulation for particle trajectories in Stokes waves, Discr. Cont. Dyn. Syst. A, 34 (2014), 3135-3153.
doi: 10.3934/dcds.2014.34.3135. |
| [20] |
H. Okamoto, T. Sakajo and M. Wunsch, Steady-states and traveling-wave solutions of the generalized Constantin-Lax-Majda equation, Discr. Cont. Dyn. Syst. A, 34 (2014), 3155-3170.
doi: 10.3934/dcds.2014.34.3155. |
| [21] |
K. Oliveras, V. Vasan, B. Deconinck and D. Henderson, Recovering the water-wave profile from pressure measurements, SIAM J. Appl. Math., 72 (2012), 897-918. |
| [22] |
P. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal., 7 (1971), 487-513. |
| [23] |
M. Stiassnie and R. Stuhlmeier, Progressive waves on a blunt interface, Discr. Cont. Dyn. Syst. A, 34 (2014), 3171-3182.
doi: 10.3934/dcds.2014.34.3171. |
| [24] |
R. Stuhlmeier, Internal Gerstner waves on a sloping bed, Discr. Cont. Dyn. Syst. A, 34 (2014), 3183-3192.
doi: 10.3934/dcds.2014.34.3183. |
| [25] |
J. F. Toland, Energy-minimising parallel flows with prescribed vorticity distribution, Discr. Cont. Dyn. Syst. A, 34 (2014), 3193-3210.
doi: 10.3934/dcds.2014.34.3193. |
| [26] |
J. F. Toland, Non-existence of global energy minimisers in Stokes waves problems, Discr. Cont. Dyn. Syst. A, 34 (2014), 3211-3217.
doi: 10.3934/dcds.2014.34.3211. |
| [27] |
V. Vasan and K. Oliveras, Pressure beneath a traveling wave with constant vorticity, Discr. Cont. Dyn. Syst. A, 34 (2014), 3219-3239.
doi: 10.3934/dcds.2014.34.3219. |
| [28] |
S. Walsh, Steady stratified periodic gravity waves with surface tension: Local bifurcation, Discr. Cont. Dyn. Syst. A, 34 (2014), 3241-3285.
doi: 10.3934/dcds.2014.34.3241. |
| [29] |
S. Walsh, Steady stratified periodic gravity waves with surface tension: Global bifurcation, Discr. Cont. Dyn. Syst. A, 34 (2014), 3287-3315.
doi: 10.3934/dcds.2014.34.3287. |
show all references
References:
| [1] |
B. Buffoni and J. F. Toland, Analytic Theory of Global Bifurcation: An Introduction, Princeton University Press, Princeton, NJ, 2003. |
| [2] |
D. Clamond, New exact relations for easy recovery of steady wave profiles from bottom pressure measurements, J. Fluid Mech., 726 (2013), 547-558. |
| [3] |
D. Clamond and A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech., 714 (2013), 463-475. |
| [4] |
A. Constantin, Edge waves along a sloping beach, J. Phys. A, 34 (2001), 9723-9731. |
| [5] |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523-535. |
| [6] |
A. Constantin, Particle trajectories in extreme Stokes waves, IMA J. Appl. Math., 77 (2012), 293-307. |
| [7] |
A. Constantin, On the recovery of solitary wave profiles from pressure measurements, J. Fluid Mech., 699 (2012), 376-384. |
| [8] |
A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity, Duke Math. J., 140 (2007), 591-603. |
| [9] |
A. Constantin and W. A. Strauss, Pressure beneath a Stokes wave, Comm. Pure Appl. Math., 63 (2010), 533-557. |
| [10] |
E. Dancer, Bifurcation theory for analytic operators, Proc. London Math. Soc., 26 (1973), 359-384. |
| [11] |
F. Gerstner, Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile, Ann. Phys., 2 (1809), 412-445. |
| [12] |
D. Henry and R. Ivanov, One-dimensional weakly nonlinear model equations for Rossby waves, Discr. Cont. Dyn. Syst. A, 34 (2014), 3025-3034.
doi: 10.3934/dcds.2014.34.3025. |
| [13] |
H.-C. Hsu, Recovering surface profiles of solitary waves on a uniform stream from pressure measurements, Discr. Cont. Dyn. Syst. A, 34 (2014), 3035-3043.
doi: 10.3934/dcds.2014.34.3035. |
| [14] |
D. Ionescu-Kruse and A.-V. Matioc, Small-amplitude equatorial water waves with constant vorticity: Dispersion relations and particle trajectories, Discr. Cont. Dyn. Syst. A, 34 (2014), 3045-3060.
doi: 10.3934/dcds.2014.34.3045. |
| [15] |
M. Kovalyov, On the nature of large and rogue waves, Discr. Cont. Dyn. Syst. A, 34 (2014), 3061-3093.
doi: 10.3934/dcds.2014.34.3061. |
| [16] |
T. Lyons, Particle trajectories in extreme Stokes waves over infinite depth, Discr. Cont. Dyn. Syst. A, 34 (2014), 3095-3107.
doi: 10.3934/dcds.2014.34.3095. |
| [17] |
C. I. Martin, Dispersion relations for periodic water waves with surface tension and discontinuous vorticity, Discr. Cont. Dyn. Syst. A, 34 (2014), 3109-3123.
doi: 10.3934/dcds.2014.34.3109. |
| [18] |
B.-V. Matioc, A characterization of the symmetric steady water waves in terms of the underlying flow, Discr. Cont. Dyn. Syst. A, 34 (2014), 3125-3133.
doi: 10.3934/dcds.2014.34.3125. |
| [19] |
A. Nachbin and R. Ribeiro-Junior, A boundary integral formulation for particle trajectories in Stokes waves, Discr. Cont. Dyn. Syst. A, 34 (2014), 3135-3153.
doi: 10.3934/dcds.2014.34.3135. |
| [20] |
H. Okamoto, T. Sakajo and M. Wunsch, Steady-states and traveling-wave solutions of the generalized Constantin-Lax-Majda equation, Discr. Cont. Dyn. Syst. A, 34 (2014), 3155-3170.
doi: 10.3934/dcds.2014.34.3155. |
| [21] |
K. Oliveras, V. Vasan, B. Deconinck and D. Henderson, Recovering the water-wave profile from pressure measurements, SIAM J. Appl. Math., 72 (2012), 897-918. |
| [22] |
P. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal., 7 (1971), 487-513. |
| [23] |
M. Stiassnie and R. Stuhlmeier, Progressive waves on a blunt interface, Discr. Cont. Dyn. Syst. A, 34 (2014), 3171-3182.
doi: 10.3934/dcds.2014.34.3171. |
| [24] |
R. Stuhlmeier, Internal Gerstner waves on a sloping bed, Discr. Cont. Dyn. Syst. A, 34 (2014), 3183-3192.
doi: 10.3934/dcds.2014.34.3183. |
| [25] |
J. F. Toland, Energy-minimising parallel flows with prescribed vorticity distribution, Discr. Cont. Dyn. Syst. A, 34 (2014), 3193-3210.
doi: 10.3934/dcds.2014.34.3193. |
| [26] |
J. F. Toland, Non-existence of global energy minimisers in Stokes waves problems, Discr. Cont. Dyn. Syst. A, 34 (2014), 3211-3217.
doi: 10.3934/dcds.2014.34.3211. |
| [27] |
V. Vasan and K. Oliveras, Pressure beneath a traveling wave with constant vorticity, Discr. Cont. Dyn. Syst. A, 34 (2014), 3219-3239.
doi: 10.3934/dcds.2014.34.3219. |
| [28] |
S. Walsh, Steady stratified periodic gravity waves with surface tension: Local bifurcation, Discr. Cont. Dyn. Syst. A, 34 (2014), 3241-3285.
doi: 10.3934/dcds.2014.34.3241. |
| [29] |
S. Walsh, Steady stratified periodic gravity waves with surface tension: Global bifurcation, Discr. Cont. Dyn. Syst. A, 34 (2014), 3287-3315.
doi: 10.3934/dcds.2014.34.3287. |
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