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Lookup NU author(s): Emeritus Professor Robin Johnson
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© 2022 American Institute of Mathematical Sciences. All rights reserved. In this survey article, we provide a mathematical description of oceanic and atmospheric flows, based on the incompressible Navier-Stokes equation (for the ocean), and the compressible version with an equation of state and the first law of thermodynamics for the atmosphere. We show that, in both cases, the only fundamental assumption that we need to make is that of a thin shell on a (nearly) spherical Earth, so that the main elements of spherical geometry are included, with all other attributes of the fluid motion retained at leading order. (The small geometrical correction that is needed to represent the Earth's geoid as an oblate spheroid is briefly described.) We argue that this is the only reliable theoretical approach to these types of fluid problem. A generic formulation is presented for the ocean, and for the steady and unsteady atmosphere, these latter two differing slightly in the details. Based on these governing equations, a number of examples are presented (in outline only), some of which provide new insights into familiar flows. The examples include the Ekman flow and large gyres in the ocean; and in the atmosphere: Ekman flow, geostrophic balance, Brunt-Väisälä frequency, Hadley-Ferrel-polar cells, harmonic waves, equatorially trapped waves.
Author(s): Johnson RS
Publication type: Article
Publication status: Published
Journal: Communications on Pure and Applied Analysis
Year: 2022
Volume: 21
Issue: 7
Pages: 2357-2381
Print publication date: 01/07/2022
Acceptance date: 02/04/2018
ISSN (print): 1534-0392
ISSN (electronic): 1553-5258
Publisher: American Institute of Mathematical Sciences
URL: https://doi.org/10.3934/cpaa.2022040
DOI: 10.3934/cpaa.2022040
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