Abstract
This study presents an explicit exact solution for nonlinear geophysical equatorial waves in the \(f\)-plane approximation near the Equator. The solution describes in the Lagrangian framework equatorial waves propagating westward in a homogenous inviscid fluid.
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Cushman-Roisin, B., Beckers, J.M.: Introduction to Geophysical Fluid Dynamics, p. 320. Academic Press, New York (2011)
Bennett, A.: Lagrangian Fluid Dynamics, p. 308. Cambridge University Press, Cambridge (2006)
Aleman, A., Constantin, A.: Harmonic maps and ideal fluid flows. Arch. Ration. Mech. Anal. 204(2), 479–513 (2012)
Hsu, H.C., Chen, Y.Y., Hsu, J.R.C.: Nonlinear water waves on uniform current in Lagrangian coordinates. J. Nonlinear Math. Phys. 16(1), 47–61 (2009)
Hsu, H.C., Ng, C.O., Hwung, H.H.: A New Lagrangian asymptotic solution for gravity-capillary waves in water of finite depth. J. Math. Fluid Mech. 14(1), 79–94 (2012)
Hsu, H.C.: Particle trajectories for wave on a linear shear current. Nonlinear Anal. Real World Appl. 14(5), 2013–2021 (2013)
Gerstner, F.: Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile (in German). Ann. Phys. 2, 412445 (1809)
Froude, W.: On the rolling of ships. Trans. Inst. Naval Arch. 3, 45–62 (1862)
Rankine, W.J.M.: On the exact form of waves near the surface of deep water. Philos. Trans. Roy. Soc. London A 153, 127–138 (1863)
Reech, F.: Sur la theory des ondes liquids periodiques. C. R. Acad. Sci. Paris 68, 1099–1101 (1869)
Constantin, A.: Edge waves along a sloping beach. J. Phys. 34A, 97239731 (2001)
Henry, D.: On Gerstner’s water wave. J. Nonlinear Math. Phys. 15, 8795 (2008)
Yih, C.-S.: Note on edge waves in a stratified fluid. J. Fluid Mech. 24, 765767 (1966)
Constantin, A.: On the deep water wave motion. J. Phys. 34A, 14051417 (2001)
Stuhlmeier, R.: On edge waves in stratified water along a sloping beach. J. Nonlinear Math. Phys. 18, 127137 (2011)
Matioc, A.V.: An exact solution for geophysical equatorial edge waves over a sloping beach. J. Phys. A 45, 365501 (2012)
Constantin, A.: An exact solution for equatorially trapped waves. J. Geophys. Res. 117, C05029 (2012). doi:10.1029/2012JC007879
Constantin, A., Germain, P.: Instability of some equatorially trapped waves. J. Geophys. Res. 118, 2802 (2013). doi:10.1002/jgrc.20219
Constantin, A.: Some three-dimensional nonlinear equatorial flows. J. Phys. Oceanogr. 43, 165–175 (2013)
Constantin, A.: Some nonlinear equatorially trapped, non-hydrostatic, internal geophysical waves. J. Phys. Oceanogr. (2014). doi:10.1175/JPO-D-13-0174.1
Constantin, A.: On the modelling of equatorial waves. Geophys. Res. Lett. 39, L05602 (2012)
Constantin, A.: Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 81, p. 321. SIAM, Philadelphia (2011)
Constantin, A.: The trajectories of particles in Stokes waves. Invent. Math. 166, 523535 (2006)
Henry, D.: On the deep-water Stokes flow. Int. Math. Res. Not. 22, (2008). doi:10.1093/imrn/rnn071
Constantin, A., Strauss, W.: Pressure beneath a Stokes wave. Comm. Pure Appl. Math. 53, 533557 (2010)
Longuet-Higgins, M.S.: On the transport of mass by time-varying ocean currents. Deep-Sea Res. 16, 431447 (1969)
Acknowledgments
The author would like to acknowledge the insightful critiquing of the two referees. The author acknowledges the support of the International Wave Dynamics Research Center in Taiwan (NSC 103-2911-I-006-302).
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Communicated by A. Constantin.
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Hsu, HC. An exact solution for equatorial waves. Monatsh Math 176, 143–152 (2015). https://doi.org/10.1007/s00605-014-0618-2
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DOI: https://doi.org/10.1007/s00605-014-0618-2