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A nonlinear, three-dimensional model for ocean flows, motivated by some observations of the Pacific Equatorial Undercurrent and thermocline

Lookup NU author(s): Emeritus Professor Robin Johnson



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


© 2017 Author(s). Using the salient properties of the flow observed in the equatorial Pacific as a guide, an asymptotic procedure is applied to the Euler equation written in a suitable rotating frame. Starting from the single overarching assumption of slow variations in the azimuthal direction in a two-layer, steady flow that is symmetric about the equator, a tractable, fully nonlinear, and three-dimensional system of model equations is derived, with the Coriolis terms consistent with the β-plane approximation retained. It is shown that this asymptotic system of equations can be solved exactly. The ability of this dynamical model to capture simultaneously fundamental oceanic phenomena, which are closely inter-related (such as upwelling/downwelling, zonal depth-dependent currents with flow reversal, and poleward divergence along the equator), is a novel and compelling feature that has hitherto been elusive. While details are presented for the equatorial flow in the Pacific, the analysis demonstrates that other flow configurations can be accommodated within the framework of this approach, depending on the choice of the underlying velocity profile and of the various parameters; the method is therefore applicable to a range of ocean flows with a similar three-dimensional structure.

Publication metadata

Author(s): Constantin A, Johnson RS

Publication type: Article

Publication status: Published

Journal: Physics of Fluids

Year: 2017

Volume: 29

Issue: 5

Print publication date: 01/05/2017

Online publication date: 30/05/2017

Acceptance date: 09/05/2017

Date deposited: 21/06/2017

ISSN (print): 1070-6631

ISSN (electronic): 1089-7666

Publisher: American Institute of Physics Inc.


DOI: 10.1063/1.4984001


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