Free-surface, purely azimuthal equatorial flows in spherical coordinates with stratification

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2019-JDE-Henry-Martin.pdf(348.79 KB)
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Date
2018-11-22
Authors
Henry, David
Martin, Calin I.
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Elsevier
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Abstract
In this paper we derive an exact solution to the governing equations for geophysical fluid dynamics in spherical coordinates which incorporates fluid stratification. This solution represents a steady, purely–azimuthal equatorial flow with an associated free-surface. Following the derivation of the solution we demonstrate that there is a well-defined relationship between the imposed pressure at the free-surface and the resulting distortion of the surface's shape. Finally, the solution for stratified fluid flow is subjected to a short-wavelength stability analysis.
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Keywords
Azimuthal flows , Variable (linear) density , Spherical coordinates , Coriolis force , Implicit function theorem , Short-wavelength perturbation
Citation
Henry, D. and Martin, C. I. (2019) 'Free-surface, purely azimuthal equatorial flows in spherical coordinates with stratification', Journal of Differential Equations, 266, pp. 6788-6808. doi: 10.1016/j.jde.2018.11.017