Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Exact azimuthal internal waves with an underlying current
Pages: 4391 - 4398, Issue 8, August 2017

doi:10.3934/dcds.2017188      Abstract        References        Full text (297.0K)           Related Articles

Hung-Chu Hsu - Department of Marine Environment and Engineering, National Sun Yat-sen University, Kaohsiung 80424, Taiwan (email)

1 A. Constantin, Edge waves along a sloping beach, J. Phys. A, 34 (2001), 9723-9731.       
2 A. Constantin, The trajectories of particles in Stokes waves, Int. Math., 166 (2006), 523-535.       
3 A. Constantin and W. Strauss, Pressure beneath a Stokes wave, Comm. Pure Appl. Math., 63 (2010), 533-557.       
4 A. Constantin, An exact solution for equatorially trapped waves, J. Geophys. Res.-Oceans, 117 (2012), C05029.
5 A. Constantin, Some three-dimensional nonlinear equatorial flows, J. Phys. Oceanogr., 43 (2013), 165-175.
6 A. Constantin and P. Germain, Instability of some equatorially trapped waves, J. Geophys. Res.-Oceans, 118 (2013), 2802-2810.
7 A. Constantin, Some nonlinear, Equatorial trapped, nonhydrostatic internal geophysical waves, J. Phys. Oceanogr., 44 (2014), 781-789.
8 A. Constantin and R. S. Johnson, The dynamics of waves interacting with the Equatorial Undercurrent, Geophys. Astrophys. Fluid Dyn., 109 (2015), 311-358.       
9 A. Constantin and R. S. Johnson, An exact, steady, purely azimuthal equatorial flow with a free surface, J. Phys. Oceanogr., 46 (2016), 1935-1945.
10 A. V. Fedorov and W. K. Melville, Kelvin fronts on the equatorial thermocline, J. Phys. Oceanogr., 30 (2000), 1692-1705.
11 F. Gerstner, Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile (in German), Ann. Phys., 2 (1809), 412-445.
12 R. J. Greatbatch, Kelvin wave fronts, Rossby solitary waves and the nonlinear spin-up of the equatorial oceans, J. Geophys. Res., 90 (1985), 9097-9107.
13 D. Henry, The trajectories of particles in deep-water Stokes waves, Int. Math. Res. Not. Art., 2006 (2006), ID23405, 13pp.       
14 D. Henry, An exact solution for equatorial geophysical water waves with an underlying current, Eur. J. Mech. B Fluids, 38 (2013), 18-21.       
15 D. Henry, Internal equatorial water waves in the $f$-plane, J. Nonlinear Mathematical Physics, 22 (2015), 499-506.       
16 D. Henry and H. C. Hsu, Instability of internal equatorial water waves, J. Differ. Equ., 258 (2015), 1015-1024.       
17 D. Henry, Equatorially trapped nonlinear water waves in the $\beta$-plane approximation with centripetal forces, J. Fluid Mech., 804 (2016), R1, 11pp.       
18 H. C. Hsu, Some nonlinear internal equatorial flow, Nonlinear Anal. Real World Appl., 18 (2014), 69-74.       
19 H. C. Hsu, An exact solution for nonlinear internal Equatorial waves in the $f$-plane approximation, J. Math. Fluid Mech., 16 (2014), 463-471.       
20 H. C. Hsu, Some nonlinear internal equatorial waves with a strong underlying current, Appl. Math. Lett., 34 (2014), 1-6.       
21 H. C. Hsu, An exact solution for equatorial waves, Monatsh Math., 175 (2015), 143-152.       
22 H. C. Hsu and C. I. Martin, Free-surface capillary-gravity azimuthal equatorial flows, Nonlinear Anal., 144 (2016), 1-9.       
23 H. C. Hsu, Exact steady azimuthal equatorial internal waves in rotational stratified fluids, Preprint J. Math. Fluid Mech., (2017).
24 D. Ionescu-Kruse, An exact solution for geophysical edge waves in the $f$-plane approximation, Nonlinear Anal. Real World Appl., 24 (2015), 190-195.       
25 T. Izumo, The Equatorial current, meridional overturning circulation, and their roles in mass and heat exchanges during the El Nino events in the tropical Pacific Ocean, Ocean Dyn., 55 (2005), 110-123.
26 J. N. Moum, J. D. Nash and W. D. Smyth, Narrowband oscillations in the upper equatorial ocean. Part I: Interpretation as shear instability, J. Phys. Oceanogr., 41 (2011), 397-411.

Go to top