南极绕极流的internal waves柱坐标方法
A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current
摘要：
在本文中，我们设计了一个新的精确的和部分显式的解决方案，地球物理流体动力学的控制方程的无粘和不可压缩的方位流与不连续的密度分布和强迫项在柱坐标。得到的解决方案表示一个稳定的，纯方位角，分层流与相关的自由表面和接口，是适合于描述南极绕极流。借助于一个功能分析，我们证明了在自由表面的施加压力和由此产生的表面变形之间的关系是定义良好的，并表明沿界面的压力的连续性产生一个方程，该方程隐含地描述了界面的形状。此外，一个特定的例子被认为是显示的接口可以明确地确定。最后，我们得到了界面的无穷正则性，并得到了表面压力与变形之间的单调性。
英文摘要：
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.
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