On a two-point boundary-value problem in geophysics

References

• Vallis GK . Geophysical fluid dynamics: whence, whither and why? Proc R Soc London A. 2016;472:20160140.
   PubMed Web of Science ®Google Scholar
• Gabler RE , Petersen JF , Trapasso LM . Essentials of physical geography. Belmont (CA): Thomson Brooks/Cole; 2007.
   Google Scholar
• Garrison T . Essentials of oceanography. Stamford (CT): National Geographic Society/Cengage Learning; 2014.
   Google Scholar
• Viudez A , Dritschel DG . Vertical velocity in mesoscale geophysical flows. J Fluid Mech. 2015;483:199–223.
   Web of Science ®Google Scholar
• Constantin A , Johnson RS . Large gyres as a shallow-water asymptotic solution of Euler’s equation in spherical coordinates. Proc R Soc London A. 2017;473:20170063.
   PubMed Web of Science ®Google Scholar
• Constantin A . Nonlinear water waves with applications to wave-current interactions and tsunamis, CBMS-NSF regional conference series in applied mathematics. Vol. 81. Philadelphia (PA): SIAM; 2011.
   Google Scholar
• Apel JR . Principles of ocean physics. London: Academic Press; 1987.
   Google Scholar
• Constantin A , Johnson RS . The dynamics of waves interacting with the equatorial undercurrent. Geophys Astrophys Fluid Dynam. 2015;109:311–358.
   Web of Science ®Google Scholar
• Jonsson IG . Wave-current interactions. In: Le Méhauté B , Hanes DM , editors. The Sea, Ocean engineering science. Wiley Interscience; 1990. p. 65–120.
   Google Scholar
• Constantin A , Strauss W , Varvaruca E . Global bifurcation of steady gravity water waves with critical layers. Acta Math. 2016;217:195–262.
   Web of Science ®Google Scholar
• Ewing JA . Wind, wave and current data for the design of ships and offshore structures. Marine Struct. 1990;3:421–459.
   Google Scholar
• Chu J . On a nonlinear model for arctic gyres. Monatsh Math. 2017; 9 pages. DOI:10.1007/s10231-017-0696-6
   Google Scholar
• Constantin A , Johnson RS . An exact, steady, purely azimuthal equatorial flow with a free surface. J Phys Oceanogr. 2016;46:1935–1945.
   Web of Science ®Google Scholar
• Martin CI . Dynamics of the thermocline in the equatorial region of the Pacific ocean. J Nonlinear Math Phys. 2015;22:516–522.
   Web of Science ®Google Scholar
• Constantin A , Johnson RS . An exact, steady, purely azimuthal flow as a model for the antarctic circumpolar current. J Phys Oceanogr. 2016;46:3585–3594.
   Web of Science ®Google Scholar
• Martin CI . On the existence of free-surface azimuthal equatorial flows. Appl Anal. 2017;96:1207–1214.
   Web of Science ®Google Scholar
• Quirchmayr R . A steady, purely azimuthal flow model for the antarctic circumpolar current. Monatsh Math. 2017; 8 pages. DOI:10.1007/s00605-017-1097-z
   Web of Science ®Google Scholar
• Constantin A , Monismith SG . Gerstner waves in the presence of mean currents and rotation. J Fluid Mech. 2017;820:511–528.
   Web of Science ®Google Scholar
• Walton DWH . Antarctica: global science from a frozen continent. Cambridge: Cambridge University Press; 2013.
   Google Scholar
• Constantin A , Escher J . Analyticity of periodic traveling free surface water waves with vorticity. Ann Math. 2011;173:559–568.
   Web of Science ®Google Scholar
• Henry D . Steady periodic waves bifurcating for fixed-depth rotational flows. Quart Appl Math. 2013;71:455–487.
   Web of Science ®Google Scholar
• Henry D . Large amplitude steady periodic waves for fixed-depth rotational flows. Commun Partial Differ Equ. 2013;38:1015–1037.
   Web of Science ®Google Scholar
• da Silva AFT , Peregrine DH . Steep, steady surface waves on water of finite depth with constant vorticity. J Fluid Mech. 1988;195:281–302.
   Web of Science ®Google Scholar
• Moreira RM , Chacaltana JTA . Vorticity effects on nonlinear wave-current interactions in deep water. J Fluid Mech. 2015;778:314–334.
   Web of Science ®Google Scholar
• Thomas GP . Wave-current interactions: an experimental and numerical study. J Fluid Mech. 1990;216:505–536.
   Web of Science ®Google Scholar
• Constantin A . An exact solution for equatorially trapped waves. J Geophys Res Oceans. 2012;117:C05029.
   Web of Science ®Google Scholar
• Constantin A , Germain P . Instability of some equatorially trapped waves. J Geophys Res Oceans. 2013;118:2802–2810.
   PubMed Web of Science ®Google Scholar
• Constantin A . Some nonlinear, equatorially trapped, nonhydrostatic internal geophysical waves. J Phys Oceanogr. 2014;44:781–789.
   Web of Science ®Google Scholar
• Constantin A , Johnson RS . A nonlinear, three-dimensional model for ocean flows, motivated by some observations of the Pacific equatorial undercurrent and thermocline. Phys Fluids. 2017;29:056604.
   Web of Science ®Google Scholar
• Henry D . An exact solution for equatorial geophysical water waves with an underlying current. Eur J Mech B Fluids. 2013;38:18–21.
   Web of Science ®Google Scholar
• Henry D . Equatorially trapped nonlinear water waves in a beta-plane approximation with centripetal forces. J Fluid Mech. 2016;804:R1.
   Web of Science ®Google Scholar