Dynamics of Partial Differential Equations

Volume 15 (2018)

Number 4

Exact, purely azimuthal stratified equatorial flows in cylindrical coordinates

Pages: 337 – 349

DOI: https://dx.doi.org/10.4310/DPDE.2018.v15.n4.a4


D. Henry (School of Mathematical Sciences, University College Cork, Ireland)

C. I. Martin (School of Mathematical Sciences, University College Cork, Ireland)


This paper is concerned with the derivation of an exact solution to the governing equations for geophysical fluid dynamics expressed in terms of cylindrical coordinates. It is demonstrated, by way of a functional analytic approach, that there is a well-defined relationship between the imposed pressure at the free-surface and the resulting distortion of the surface, and it is established that this relationship exhibits the expected monotonicity properties. This exact solution for stratified fluid flow is then subjected to a shortwavelength perturbation stability analysis.


Azimuthal flows, variable (linear) density, cylindrical coordinates, Coriolis force, implicit function theorem

2010 Mathematics Subject Classification

Primary 35Q31, 35Q35, 35Q86, 35R35. Secondary 76E20.

The authors gratefully acknowledge the support of the Science Foundation Ireland (SFI) under the research grant 13/CDA/2117.

Received 14 March 2018

Published 5 December 2018