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Large-scale oceanic currents as shallow-water asymptotic solutions of the Navier-Stokes equation in rotating spherical coordinates

Lookup NU author(s): Dr Adrian Constantin, Emeritus Professor Robin Johnson



This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).


© 2018 The Authors We show that a consistent shallow-water approximation of the incompressible Navier-Stokes equation written in a spherical, rotating coordinate system produces, at leading order in a suitable limiting process, a general linear theory for wind-induced ocean currents which goes beyond the limitations of the classical Ekman spiral. In particular, we obtain Ekman-type solutions which extend over large regions in both latitude and longitude; we present examples for constant and for variable eddy viscosities. We also show how an additional restriction on our solution recovers the classical Ekman solution (which is valid only locally).

Publication metadata

Author(s): Constantin A, Johnson RS

Publication type: Article

Publication status: Published

Journal: Deep-Sea Research Part II: Topical Studies in Oceanography

Year: 2019

Pages: Epub ahead of print

Online publication date: 29/12/2018

Acceptance date: 02/04/2018

Date deposited: 11/02/2019

ISSN (print): 0967-0645

ISSN (electronic): 1879-0100

Publisher: Pergamon Press


DOI: 10.1016/j.dsr2.2018.12.007


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