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Some problems in physical oceanography (including the use of rotating spherical coordinates) treated as exercises in classical fluid mechanics: Methods and examples

Lookup NU author(s): Emeritus Professor Robin Johnson


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© 2018 Elsevier Ltd The ideas and methods typically associated with classical fluid mechanics are briefly introduced and then applied to some problems in physical oceanography. The main thrust is to show that this approach is surprisingly successful, avoiding the need to invoke any modelling (based, for example, on physical principles without an accompanying derivation) or to implement numerical methods. The governing equations in a spherical, rotating coordinate system are presented, together with a suitable non-dimensionalisation, leading to a discussion of the available asymptotic approximations. The tangent plane, and f- and β-plane approximations, are also mentioned. A number of examples (inviscid), taken from the recent literature, are described, with the emphasis on the formulation and methods employed. The first, used as an introduction to the ideas, is based on the β-plane approximation and describes the slow evolution of the flow along the Pacific Equator (the EUC); a fully three-dimensional, nonlinear flow structure is constructed. The next pair of examples (which are quite closely related) are exact solutions of the full set of governing equations; one relates to the velocity profile typical of the EUC, and the other to the jet-like flow structures that contribute to the Antarctic Circumpolar Current. The final example shows how a theory for (nonlinear) large gyres, rotating in the thin ocean layer on the surface of a sphere, can be constructed. A few general comments and observations are made in conclusion.

Publication metadata

Author(s): Johnson RS

Publication type: Article

Publication status: Published

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

Year: 2018

Issue: ePub ahead of Print

Online publication date: 03/09/2018

Acceptance date: 02/04/2018

ISSN (print): 0967-0645

ISSN (electronic): 1879-0100

Publisher: Elsevier Ltd


DOI: 10.1016/j.dsr2.2018.08.010


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