Lookup NU author(s): Emeritus Professor Robin Johnson
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© 2017 The Author(s) Published by the Royal Society. All rights reserved. This review makes a case for describing many of the flows observed in our oceans, simply based on the Euler equation, with (piecewise) constant density and with suitable boundary conditions. The analyses start from the Euler and mass conservation equations, expressed in a rotating, spherical coordinate system (but the f-plane and ß-plane approximations are also mentioned); five examples are discussed. For three of them, a suitable non-dimensionalization is introduced, and a single small parameter is identified in each case. These three examples lead straightforwardly and directly to new results for: waves on the Pacific Equatorial Undercurrent (EUC) with a thermocline (in the f-plane); a nonlinear, three-dimensional model for EUC-type flows (in the ß-plane); and a detailed model for large gyres. The other two examples are exact solutions of the complete system: a flow which corresponds to the underlying structure of the Pacific EUC; and a flow based on the necessary requirement to use a non-conservative body force, which produces the type of flow observed in the Antarctic Circumpolar Current. (All these examples have been discussed in detail in the references cited.) This review concludes with a few comments on how these solutions can be extended and expanded. This article is part of the theme issue ‘Nonlinear water waves’.
Author(s): Johnson RS
Publication type: Review
Publication status: Published
Journal: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print publication date: 28/01/2018
Online publication date: 11/12/2017
Acceptance date: 02/06/2017
ISSN (print): 1364-503X
ISSN (electronic): 1471-2962
Publisher: Royal Society Publishing