Exact Pollard-like internal water waves

References

• A. Bennett, Lagranian fluid dynamics. Cambridge University Press (2006).
   Google Scholar
• J.P. Boyd, Dynamics of the equatorial ocean. Springer-Verlag, Berlin (2018).
   Google Scholar
• A. Constantin, On the deep water wave motion. J. Phys. A, 7 (2001), 1405–1417. doi: 10.1088/0305-4470/34/7/313
   Google Scholar
• A. Constantin, The trajectories of particles in Stokes waves. Invent. Math., 166 (2006), 523–535. doi: 10.1007/s00222-006-0002-5
   Web of Science ®Google Scholar
• A. Constantin, Nonlinear water waves with applications to wave-current interactions and tsunamis. CBMS-NSF Regional Conference Series in Applied Mathematics, 81 (2011).
   Google Scholar
• A. Constantin, An exact solution for Equatorially trapped waves. J. Geophys. Res.-Oceans, 117 (2012), 1–8. doi: 10.1029/2012JC007879
   Web of Science ®Google Scholar
• A. Constantin, Some three-dimensional nonlinear Equatorial flows. J. Phys. Oceanogr., 43 (2013), 165–175. doi: 10.1175/JPO-D-12-062.1
   Web of Science ®Google Scholar
• A. Constantin, Some Nonlinear, Equatorially trapped, nonhydrostatic internal geophysical waves. J. Phys. Oceanogr., 44 (2014), 781–789. doi: 10.1175/JPO-D-13-0174.1
   Web of Science ®Google Scholar
• A. Constantin, P. Germain, Instability of some equatorially trapped waves. J. Geophys. Res.-Oceans, 118 (2013), 2802–2810. doi: 10.1002/jgrc.20219
   PubMed Web of Science ®Google Scholar
• A. Constantin, R.S. Johnson, The dynamics of waves interacting with the Equatorial Undercurrent. Geophys. Astrophys. Fluid Dyn., 109 (2015), 311–358. doi: 10.1080/03091929.2015.1066785
   Web of Science ®Google Scholar
• A. Constantin, R.S. Johnson, Current and future prospects for the application of systematic theoretical methods to the study of problems in physical oceanography. Phys. Lett. A, 380 (2016), 3007–3012. doi: 10.1016/j.physleta.2016.07.036
   Web of Science ®Google Scholar
• A. Constantin, S. Monismith, Gerstner waves in the presence of mean currents and rotation. J. Fluid Mech., 820 (2017), 511–528. doi: 10.1017/jfm.2017.223
   Web of Science ®Google Scholar
• B. Cushman-Rosin, J.-M. Beckers, Introduction to geophysical fluid dynamic. Academic Press (2011).
   Google Scholar
• T. Garrison, R. Ellis, Oceanography: An Invitation to Marine Science. Cengage Learning, (Ninth Edition 2016).
   Google Scholar
• F. Gerstner, Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile. Ann. Phys. (Berl.), 32 (1809), 412–445. doi: 10.1002/andp.18090320808
   Google Scholar
• A.E. Gill, Atmosphere-Ocean Dynamics. Academic Press, 1982.
   Google Scholar
• D. Henry, On Gerstner’s water wave. J. Nonlinear Math. Phys., 15 (2008), 87–95. doi: 10.2991/jnmp.2008.15.S2.7
   Web of Science ®Google Scholar
• D. Henry, On the deep-water Stokes wave flow. Int. Math. Res. Notices. IMRN, (2008).
   Google Scholar
• D. Henry, An exact solution for equatorial geophysical water waves with an underlying current. Eur. J. Mech. B/Fluid, 38 (2013), 18–21. doi: 10.1016/j.euromechflu.2012.10.001
   Web of Science ®Google Scholar
• D. Henry, Internal Equatorial water waves in the f-plane. J. Nonlinear Math. Phys., 22 (2015), 499–506. doi: 10.1080/14029251.2015.1113046
   Web of Science ®Google Scholar
• D. Henry, Exact Equatorial water waves in the f-plane. Nonlinear Anal. Real World Appl., 28 (2016), 284–289. doi: 10.1016/j.nonrwa.2015.10.003
   Web of Science ®Google Scholar
• D. Henry, Equatorially trapped nonlinear water waves in a β-plane approximation with centripetal forces. J. Fluid Mech., 804 (2016), 1–11. doi: 10.1017/jfm.2016.544
   Web of Science ®Google Scholar
• D. Henry, On three dimensional Gerstner-like equatorial water. Philos. Trans. R. Soc. Lond. A, 376 (2017), 1–16, doi:10.1098/rsta.2017.0088.
   Web of Science ®Google Scholar
• H.-C. Hsu, An exact solution for nonlinear internal Equatorial waves in the f -plane approximation. J. Math. Fluid Mech., 16 (2014), 463–471. doi: 10.1007/s00021-014-0168-3
   Web of Science ®Google Scholar
• D. Ionescu-Kruse, On Pollard’s wave solution at the Equator. J. Nonlinear Math. Phys., 22 (2015), 523–530. doi: 10.1080/14029251.2015.1113050
   Web of Science ®Google Scholar
• D. Ionescu-Kruse, Instability of Pollard’s exact solution for geophysical ocean flows. Phys. Fluids, 28 (2016), 1–10. doi: 10.1063/1.4959289
   Web of Science ®Google Scholar
• D. Ionescu-Kruse, On the short-wavelength stabilities of some geophysical flows. Philos. Trans. R. Soc. Lond. A, 376 (2017), 1–21, doi:10.1098/rsta.2017.0090.
   Web of Science ®Google Scholar
• G.C. Johnson, M.J. McPhaden, E. Firing, Equatorial Pacific Ocean Horizontal Velocity, Divergence, and Upwelling. J. Phys. Oceanogr., 31 (2000), 839–849. doi: 10.1175/1520-0485(2001)031<0839:EPOHVD>2.0.CO;2
   Web of Science ®Google Scholar
• R.S. Johnson, Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography. Philos. Trans. R. Soc. Lond. A, 376 (2017), 1–19, doi:10.1098/rsta.2017.0092.
   Web of Science ®Google Scholar
• W.S. Kessler and M.J. McPhaden, Oceanic Equatorial waves and the 1991-93 El Niño. Journal of Climate, 8 (1995), 1757–1774. doi: 10.1175/1520-0442(1995)008<1757:OEWATE>2.0.CO;2
   Google Scholar
• M. Kluczek, Exact and explicit internal Equatorially-trapped water waves with underlying currents. J. Math. Fluid Mech., 19 (2017), 305–314. doi: 10.1007/s00021-016-0281-6
   Web of Science ®Google Scholar
• M. Kluczek, Equatorial water waves with underlying currents in the f -plane approximation. Appl. Anal., 97 (2018), 1867–1880. doi: 10.1080/00036811.2017.1343466
   Web of Science ®Google Scholar
• R.T. Pollard, Surface waves with rotation: An exact solution. J. Geophys. Res., 75 (1970), 5895–5898. doi: 10.1029/JC075i030p05895
   Web of Science ®Google Scholar
• V. Prasolov, Polynomials. Springer-Verlag, Berlin (2012).
   Google Scholar
• A.R. Sanjurjo, Internal equatorial water waves and wave-current interactions in the f-plane. Monatsh. Math., 186 (2018), 685–701. doi: 10.1007/s00605-017-1052-z
   Web of Science ®Google Scholar
• A.R. Sanjurjo, Global diffeomorphism of the Lagrangian flow-map for Pollard-like solutions. Ann. Mat. Pura Appl. (1923-), (2018), 1–11, 10.1007/s10231-018-0749-5.
   Google Scholar
• R. Stuhlmeier, Internal Gerstner waves: applications to dead water. Appl. Anal., 93 (2014), 1451–1457. doi: 10.1080/00036811.2013.833609
   Web of Science ®Google Scholar
• G.K. Vallis, Atmospheric and Oceanic Fluid Dynamics, Cambridge University Press (2006).
   Google Scholar