In this paper, we are devoted to devising an exact solution to the governing equations for geophysical fluid dynamics with a general density distribution and subjected to forcing terms in terms of cylindrical coordinates. The obtained explicit solution represents a steady purely azimuthal stratified flow with a free surface that is suitable for describing the Antarctic Circumpolar Current. Resorting to a functional analysis, we demonstrate the relationship between the imposed pressure at the free-surface and the resulting distortion of the surface is well-defined and show that this relationship exhibits the expected monotonicity properties.

中文翻译：

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关于南极绕极流的圆柱坐标方法

在本文中，我们致力于为具有总体密度分布并受圆柱坐标强迫项影响的地球物理流体动力学控制方程式给出精确解。所获得的显式解表示具有自由表面的稳定的纯方位角分层流，该自由表面适用于描述南极绕极电流。借助功能分析，我们证明了自由表面上施加的压力与表面产生的变形之间的关系是明确定义的，并表明这种关系表现出预期的单调性。