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Study of an elliptic partial differential equation modelling the Antarctic Circumpolar Current

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  • We consider the ocean flow of the Antarctic Circumpolar Current. Using a recently-derived model for gyres in rotating spherical coordinates, and mapping the problem on the sphere onto the plane using the Mercator projection, we obtain a boundary-value problem for a semi-linear elliptic partial differential equation. For constant and linear oceanic vorticities, we investigate existence, regularity and uniqueness of solutions to this elliptic problem. We also provide some explicit solutions. Moreover, we examine the physical relevance of these results.

    Mathematics Subject Classification: Primary: 35Q35, 76U05.

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  • Figure 1.  The Mercator Projection for the ACC: We project the polar angle onto the $ x $-axis and the azimuthal angle onto the $ y $-axis. The South Pole is situated at $ x = -\infty $

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