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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 13
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Articles

Mean flow properties for equatorially trapped internal water wave–current interactions

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Pages 2333-2345 | Received 07 Jul 2016, Accepted 04 Aug 2016, Published online: 16 Aug 2016

References

  • Hsu H-C. Some nonlinear internal equatorial flows. Nonlinear Anal. Real Wold Appl. 2014;18:69–74.
  • Constantin A. Some three-dimensional nonlinear equatorial flows. J. Phys. Oceanogr. 2013;43:165–175.
  • Cushman-Roisin B, Beckers JM. Introduction to geophysical fluid dynamics: physical and numerical aspects. Vol. 101. Oxford: Academic Press; 2011.
  • Fedorov AV, Brown J-M. Equatorial waves. In: Steel J, editor. Encyclopedia of ocean sciences. San Diego (CA): Academic; 2009. p. 3679–3695.
  • Constantin A. Some nonlinear, equatorially trapped, nonhydrostatic internal geophysical waves. J. Phys. Oceanogr. 2014;44:781–789.
  • Constantin A, Johnson RS. The dynamics of waves interacting with the equatorial undercurrent. Geophys. Astrophys. Fluid Dyn. 2015;109:2802–2810.
  • Constantin A, Johnson RS. An exact, steady, purely azimuthal equatorial flow with a free surface. J. Phys. Oceanogr. 2016;46:1935–1945.
  • Stokes GG. On the theory of oscillatory waves. Trans. Camb. Philos. Soc. 1847;8:441–445.
  • Constantin A. Nonlinear water waves with applications to wave-current interactions and tsunamis. Vol. 81. Philadelphia (PA): SIAM; 2011.
  • Constantin A. The trajectories of particles in Stokes waves. Invent. Math. 2006;166:523–535.
  • Constantin A. The flow beneath a periodic travelling surface water wave. J. Phys. A. 2015;48:143001.
  • Constantin A, Strauss W. Pressure beneath a Stokes wave. Comm. Pure Appl. Math. 2010;63:533–557.
  • Henry D. The trajectories of particles in deep-water Stokes waves. Int. Math. Res. Not. 2006;13. Art. ID 23405.
  • Henry D. On the deep-Stokes flow. Int. Math. Res. Not. 2008;1–7. Art. ID rnn 071.
  • Constantin A. Particle trajectories in extreme Stokes waves. IMA J. Appl. Math. 2012;77:293–307.
  • Gerstner F. Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile [Theory of waves including a derived theory of dike profiles]. Ann. Phys. 1809;2:412–445.
  • Rankine WJM. On the exact form and motion of waves near to the surface of deep water. Philos. Trans. 1863;153:127–138.
  • Constantin A. On the deep water wave motion. J. Phys. A: Math. Gen. 2001;34:1405–1417.
  • Henry D. On Gerstner’s water wave. J. Nonlinear Math. Phys. 2008;15;suppl 2:87–95.
  • Dubreil-Jacotin ML. Sur les ondes de type permanent dans les liquides hétérogenes [Standing on the type of waves in heterogeneous fluids]. Atti Accad. Naz. Lincei, Rend. VI. Ser. 1932;15:814–819.
  • Longuet-Higgins MS. Mass transport in water waves. Philos. Trans. R. Soc. Lond. A. 1953;245:535–581.
  • Longuet-Higgins MS. On the transport of mass by time-varying oncean currents. Deep Sea Res. 1969;16:431–447.
  • Constantin A, Germain P. Instability of some equatorially trapped waves. J. Geophys. Res. Oceans. 2013;118:2802–2810.
  • Genoud F, Henry D. Instability of equatorial water waves with an underlying current. J. Math. Fluid Mech. 2014;16:661–667.
  • Henry D. An exact solution for equatorial geophysical water waves with an underlying current. Eur. J. Mech. B Fluids. 2013;38:190–195.
  • Henry D. Internal equatorial water waves in the f-plane. J. Nonlinear Math. Phys. 2015;22:499–506.
  • Henry D. Exact equatorial water waves in the f-plane. Non. Anal. Real World Appl. 2016;28:284–289.
  • Sastre-Gómez S. Global diffeomorphism of the Lagrangian flow-map defining Equatorially trapped water waves. Nonlinear Anal. Ser. A Theory Methods Appl. 2015;125:725–731.
  • Henry D, Hsu H-C. Instability of internal equatorial water waves. J. Differ. Equ. 2015;258:1015–1024.
  • Henry D, Hsu H-C. Instability of equatorial water waves in the f-plane. Discrete Contin. Dyn. Syst. 2015;35:902–916.
  • Hsu H-C. An exact solution for nonlinear internal equatorial waves in the f-plane approximation. J. Math. Fluid Mech. 2014;16:463–471.
  • Ionescu-Kruse D. An exact solution for geophysical edge waves in the f-plane approximation. Nonlinear Anal. Real World Appl. 2015;24:190–195.
  • Kluczek M. Exact and explicit internal equatorially-trapped water waves with underlying currents. doi:10.1007/s00021-016-0281-6.
  • Matioc AV. An exact solution for geophysical equatorial edge waves over a sloping beach. J. Phys. A. 2012;45:365501.
  • Matioc AV. Exact geophysical waves in stratified fluids. Appl. Anal. 2013;92:2254–2261.
  • Rodríguez-Sanjurjo A. Global diffeomorphism of the Lagrangian flow-map for equatorially trapped internal water waves. Forthcoming.
  • Sastre-Gómez S. Global diffeomorphism of the Lagrangian flow-map defining equatorially trapped water waves. Nonlinear Analysis. 2015;125:725–731.
  • Johnson RS. A modern introduction to the mathematical theory of water waves. Cambridge: Cambridge University Press; 1997.
  • Constantin A. An exact solution for equatorially trapped waves. J. Geophys. Res. Oceans. 2012;117:C05029.
  • Bennett A. Lagrangian fluid dynamics. Cambridge: Cambridge University Press; 2006.

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