Free-surface,purely azimuthal equatorial flows in spherical coordinates with stratification |
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Authors: | D Henry CI Martin |
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Institution: | School of Mathematical Sciences, University College Cork, Cork, Ireland |
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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: | 35Q31 35Q35 35Q86 35R35 76E20 Azimuthal flows Variable (linear) density Spherical coordinates Coriolis force Implicit function theorem Short-wavelength perturbation |
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