Exact, purely azimuthal stratified equatorial flows in cylindrical coordinates. (English) Zbl 1406.35251

Summary: 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.


35Q31 Euler equations
35Q35 PDEs in connection with fluid mechanics
35Q86 PDEs in connection with geophysics
35R35 Free boundary problems for PDEs
76E20 Stability and instability of geophysical and astrophysical flows
76U05 General theory of rotating fluids
Full Text: DOI