Exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates

Jifeng Chu, Calin Iulian Martin*, Kateryna Marynets

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

We present here exact solutions to the equations of geophysical fluid dynamics that depict inviscid flows moving in the azimuthal direction on a circular path, around the globe, and which admit a velocity profile below the surface and along it. These features render this model suitable for the description of the Antarctic circumpolar current (ACC). The governing equations we work with–taken to be the Euler equations written in spherical coordinates–also incorporate forcing terms which are generally regarded as means that ensure the general balance of the ACC. Our approach allows for a variable density (depending on the depth and latitude) of discontinuous type which divides the water domain into two layers. Thus, the discontinuity gives rise to an interface. The velocity in both layers and the pressure in the lower layer are determined explicitly, while the pressure in the upper layer depends on the free surface and the interface. Functional analytical techniques render (uniquely) the surface and interface-defining functions in an implicit way. We conclude our discussion by deriving relations between the monotonicity of the surface pressure and the monotonicity of the surface distortion that concur with the physical expectations. A regularity result concerning the interface is also derived.

Original languageEnglish
Pages (from-to)734-747
Number of pages14
JournalApplicable Analysis
Volume103 (2024)
Issue number4
DOIs
Publication statusPublished - 2023

Keywords

  • Coriolis force
  • discontinuous stratification
  • Exact solutions in spherical coordinates
  • forcing terms
  • the Antarctic Circumpolar Current

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