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We use spherical coordinates to devise a new exact solution to the governingequations of geophysical fluid dynamics for an inviscid and incompressiblefluid with a general density distribution and subjected to forcing terms. Thelatter are of paramount importance for the modeling of realistic flows-that is,flows that are observed in some averaged sense in the ocean. Owing to theemployment of spherical coordinates we do not need to resort to approximations(e.g. of $f$- and $\beta$-plane type) that simplify the geometry in thegoverning equations. Our explicit solution represents a steady purely-azimuthalstratified flow with a free surface, that---thanks to the inclusion of forcingterms and the consideration of the Earth's geometry via sphericalcoordinates---makes it suitable for describing the Antarctic CircumpolarCurrent and enables an in-depth analysis of the structure of this flow. In linewith the latter aspect, we employ functional analytical techniques to provethat the free surface distortion is defined in a unique and implicit way bymeans of the pressure applied at the free surface. We conclude our discussionby setting out relations between the monotonicity of the surface pressure andthe monotonicity of the surface distortion that concur with the physicalexpectations.

Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates