论文标题
圆柱坐标方法，涉及南极圆极电流的内波
A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current
论文作者
论文摘要
在本文中，我们为地球物理流体动力学方程式设计了一种新的精确和部分明确的解决方案，以实现不连续的密度分布的无粘性和不可压缩的方位流流，并以圆柱坐标为强迫术语。所获得的溶液代表具有相关自由表面的稳定，纯粹的，分层的流动，以及适合描述南极圆极电流的界面。为了进行功能分析，我们证明了在自由表面施加的压力与所得的表面变形之间的关系明确定义，并表明压力沿界面的连续性产生了一个方程，该方程式描述了界面的形状。此外，考虑一个特定的示例可以表明可以明确确定接口。最后，我们得出了关于界面的无限规律性，并获得了表面压力及其失真之间的预期单调性。
In this paper, we devise a new exact and partially explicit solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible azimuth flow with a discontinuous density distribution and subjected to forcing terms in terms of cylindrical coordinates. The obtained solution represents a steady, purely azimuthal, stratified flow with an associated free surface and an interface that is suitable for describing the Antarctic Circumpolar Current. Resorting to a functional analysis, we demonstrate that the relationship between the imposed pressure at the free surface and the resulting surface deformation is well-defined and show that the continuity of the pressure along the interface generates an equation that describes implicitly the shape of the interface. Moreover, a particular example is considered to show that the interface can be determined explicitly. Finally, we derive an infinite regularity about the interface and obtain the expected monotonicity properties between the surface pressure and its distortion.
