Free-surface, purely azimuthal equatorial flows in spherical coordinates with stratification
Martin, Calin I.
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.
Azimuthal flows , Variable (linear) density , Spherical coordinates , Coriolis force , Implicit function theorem , Short-wavelength perturbation
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