The Antarctic Circumpolar Current as a shallow-water asymptotic solution of Euler's equation in spherical coordinates

We develop a consistent shallow-water approximation of the incompressible Euler equation in a rotating frame in spherical coordinates, coupled with the appropriate boundary conditions, as a model for the flow of the Antarctic Circumpolar Current. By means of the stereographic projection we come to the boundary value problem for a semilinear elliptic partial differential equation, coupled with the Dirichet or Neumann conditions on the boundary of the considered domain. For recent progress in direction of study of the above mentioned problems we refer to Marynets (2018a, 2018b, 2018c).