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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 10
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Articles

The modeling of the equatorial undercurrent using the Navier–Stokes equations in rotating spherical coordinates

Pages 2069-2077 | Received 10 Aug 2019, Accepted 21 Sep 2019, Published online: 30 Sep 2019

References

  • Constantin A, Ivanov RI. Equatorial wave-current interactions. Comm Math Phys. 2019;370:1–48. doi: 10.1007/s00220-019-03483-8
  • Cronin MF, Kessler WS. Near-surface shear flow in the tropical Pacific Cold Tongue Front. J Phys Oceanogr. 2009;39:1200–1215. doi: 10.1175/2008JPO4064.1
  • Constantin A, Johnson RS. Large-scale oceanic currents as shallow-water asymptotic solutions of the Navier-Stokes equation in rotating spherical coordinates. Deep Sea Res Part II: Top Stud Oceanogr. 2019;160:32–40. doi: 10.1016/j.dsr2.2018.12.007
  • Boyd JP. Dynamics of the equatorial ocean. Berlin: Springer; 2018.
  • Henry D. Nonlinear features of equatorial ocean flows. Oceanography. 2018;31:22–27. doi: 10.5670/oceanog.2018.305
  • Fedorov AV, Brown JN. Equatorial waves. In: Steele J, editor. Encyclopedia of ocean sciences. Academic Press; 2009, p. 3679–3695.
  • Constantin A. An exact solution for equatorially trapped waves. J Geophys Res: Oceans. 2012;117:C05029. doi: 10.1029/2012JC007879
  • Constantin A. Some nonlinear, equatorially trapped, nonhydrostatic internal geophysical waves. J Phys Oceanogr. 2014;44:781–789. doi: 10.1175/JPO-D-13-0174.1
  • Constantin A, Germain P. Instability of some equatorially trapped waves. J Geophys Res: Oceans. 2013;118:2802–2810. doi: 10.1002/jgrc.20219
  • Henry D. An exact solution for equatorial geophysical water waves with an underlying current. Eur J Mech B/Fluids. 2013;38:18–21. doi: 10.1016/j.euromechflu.2012.10.001
  • Henry D. Equatorially trapped nonlinear water waves in a β-plane approximation with centripetal forces. J Fluid Mech. 2016;804:R1. doi: 10.1017/jfm.2016.544
  • Constantin A, Johnson RS. The dynamics of waves interacting with the Equatorial Undercurrent. Geophys Astrophys Fluid Dyn. 2015;109:311–358. doi: 10.1080/03091929.2015.1066785
  • Henry D, Martin CI. Exact, free-surface equatorial flows with general stratification in spherical coordinates. Arch Ration Mech Anal. 2019;233:497–512. doi: 10.1007/s00205-019-01362-z
  • Basu B. On a three-dimensional nonlinear model of Pacific equatorial ocean dynamics: velocities and flow paths. Oceanography. 2018;31:51–58. doi: 10.5670/oceanog.2018.309
  • Basu B. Some numerical investigations into a nonlinear three-dimensional model of the Pacific equatorial ocean flows. Deep Sea Res Part II: Top Stud Oceanogr. 2019;160:7–15. doi: 10.1016/j.dsr2.2018.11.013
  • Constantin A, Johnson RS. An exact, steady, purely azimuthal equatorial flow with a free surface. J Phys Oceanogr. 2016;46:1935–1945. doi: 10.1175/JPO-D-15-0205.1
  • 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. doi: 10.1063/1.4984001
  • Constantin A, Johnson RS. On the nonlinear, three-dimensional structure of equatorial oceanic flows. J Phys Oceanogr. 2019;49:2029–2042. doi: 10.1175/JPO-D-19-0079.1
  • Constantin A, Johnson RS. Ekman-type solutions for shallow-water flows on a rotating sphere: a new perspective on a classical problem. Phys Fluids. 2019;31:021401. doi: 10.1063/1.5083088
  • Lukas R. Pacific ocean equatorial currents. In: Thorpe SA, Turekian KK, editors. Encyclopedia of ocean sciences. Elsevier; 2001, p. 2069–2076.
  • Marshall J, Plumb RA. Atmosphere, ocean and climate dynamics: an introductory text. London: Academic Press; 2016.
  • Vallis GK. Atmosphere and ocean fluid dynamics. Cambridge: Cambridge University Press; 2006.
  • Constantin A, Johnson RS. Steady large-scale ocean flows in spherical coordinates. Oceanography. 2018;31:42–50. doi: 10.5670/oceanog.2018.308
  • Constantin A, Johnson RS. Large gyres as a shallow-water asymptotic solution of Euler's equation in spherical coordinates. Proc Roy Soc London A. 2017;473, Art. No. 20170063. doi: 10.1098/rspa.2017.0063
  • Haziot S. Study of an elliptic partial differential equation modelling the Antarctic Circumpolar Current. Discr Cont Dyn Syst. 2019;39:4415–4427. doi: 10.3934/dcds.2019179
  • Marynets K. Two-point boundary problem for modeling the jet flow of the Antarctic Circumpolar Current. Electron J Diff Eq. 2018;56:1–12. Paper No. 56.
  • Marynets K. A nonlinear two-point boundary-value problem in geophysics. Monatsh Math. 2019;188:287–295. doi: 10.1007/s00605-017-1127-x
  • Marynets K. On a two-point boundary-value problem in geophysics. Appl Anal. 2019;98:553–560. doi: 10.1080/00036811.2017.1395869
  • Marynets K. On the modeling of the flow of the Antarctic Circumpolar Current. Monatsh Math. 2019;188:561–565. doi: 10.1007/s00605-017-1147-6
  • 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. doi: 10.1175/JPO-D-16-0121.1
  • Walton DWHAntarctica: global science from a frozen continent. Cambridge: Cambridge University Press; 2013.
  • Haziot S, Marynets K. Applying the stereographic projection to modeling of the flow of the Antarctic Circumpolar Current. Oceanography. 2018;31:68–75. doi: 10.5670/oceanog.2018.311
  • Ionescu-Kruse D. A three-dimensional autonomous nonlinear dynamical system modelling equatorial ocean flows. J Diff Eqs. 2018;264:4650–4668. doi: 10.1016/j.jde.2017.12.021
  • Ionescu-Kruse D, Martin CI. Local stability for an exact steady purely azimuthal equatorial flow. J Math Fluid Mech. 2018;20:27–34. doi: 10.1007/s00021-016-0311-4
  • Izumo T. 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. 2005;55:110–123. doi: 10.1007/s10236-005-0115-1
  • Martin CI. On the existence of free-surface azimuthal equatorial flows. Appl Anal. 2017;96:1207–1214. doi: 10.1080/00036811.2016.1180370
  • Marynets K. The Antarctic Circumpolar Current as a shallow-water asymptotic solution of Euler's equation in spherical coordinates. Deep Sea Res Part II: Top Stud Oceanogr. 2019;160:58–62. doi: 10.1016/j.dsr2.2018.11.014