论文标题
明确和精确的解决方案，涉及南极绕极电流，球形坐标密度可变
Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates
论文作者
论文摘要
我们使用球形坐标来为地球物理流体动力学的管理方程式设计新的精确解决方案，用于具有一般密度分布的无粘性和不可压缩的流体，并受到强迫项。后者对于现实流的建模至关重要，即在海洋中某种平均意义上观察到的流。由于使用球形坐标，我们不需要求助于简化管理方程中几何形状的近似值（例如$ f $ - 和$β$ - 平面类型）。我们的显式解决方案代表具有自由表面的稳定纯粹的纯粹分层流，这是由于包括强迫术语的包含以及通过球形坐标对地球几何形状的考虑 - 适用于描述南极圆极电流，并可以对此流动的结构进行深入分析。与后者一致，我们采用功能分析技术来证明自由表面失真是通过在自由表面上施加的压力以独特而隐式的方式定义的。我们通过在表面压力的单调性与表面扭曲的单调性之间的关系结束了与物理期望的单调性之间的关系来结束讨论。
We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter 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 the employment of spherical coordinates we do not need to resort to approximations (e.g. of $f$- and $β$-plane type) that simplify the geometry in the governing equations. Our explicit solution represents a steady purely-azimuthal stratified flow with a free surface, that---thanks to the inclusion of forcing terms and the consideration of the Earth's geometry via spherical coordinates---makes it suitable for describing the Antarctic Circumpolar Current and enables an in-depth analysis of the structure of this flow. In line with the latter aspect, we employ functional analytical techniques to prove that the free surface distortion is defined in a unique and implicit way by means of the pressure applied at the free surface. We conclude our discussion by setting out relations between the monotonicity of the surface pressure and the monotonicity of the surface distortion that concur with the physical expectations.
