Isopycnal averaging at constant height. Part II: relating to the residual streamfunction in eulerian space
Isopycnal averaging at constant height. Part II: relating to the residual streamfunction in eulerian space
复制标题
恒定高度下的等密度平均。
DOI：
10.1175/jpo2650.1
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发表时间：
2004
影响因子：
3.5
通讯作者：
Mei
中科院分区：
文献类型：
--
作者：
A. Nurser;Mei
在第一部分中，“垂直”输送流函数被定义为等高等压流函数的结果，就像经向流函数是恒纬度平均的结果一样。第二部分讨论了这两个等压流函数与由变换的欧拉平均产生的欧拉剩余流函数之间的关系。经向等压流函数可以用泰勒展开来近似，从而得到包含水平涡通量的欧拉剩余流函数。这种泰勒展开近似在内部工作得很好，消除了与简单的欧拉平均流函数相关的虚假混合。然而，它在地表附近失效，在那里，等辉石出露到地表。用类似的方法可以证明，垂直等压流函数形式上可以用包含垂直涡通量的残差流函数来近似。然而，如果水平等轴线位移很大，即使在海洋内部，这种近似也是不成立的。受两种不同剩余流函数的启发，探索了一种更一般形式的瞬变电磁公式。结果表明，不同的瞬变电磁剩余流函数是由涡通量沿等轴线分解成导致平流的分量和沿垂直或水平方向的剩余扩散分量而产生的。理论上，扩散通量可以朝向任何方向，尽管在实践中，方向应该是平流或扩散通量都不能越过任何边界(表面、侧壁和底部)。然而，如何以物理上有意义的方式合并不断变化的方向尚不清楚。讨论了各种方法。
In Part I , the “vertical” transport streamfunction was defined as resulting from isopycnic averaging at constant height in the same way that the meridional streamfunction results from averaging at constant latitude. Part II here discusses the relationship between these two isopycnic streamfunctions and the Eulerian residual streamfunction that arises from the transformed Eulerian mean (TEM). It is known that the meridional isopycnic streamfunction can be approximated by a Taylor expansion to give an Eulerian residual streamfunction involving the horizontal eddy flux. This Taylor expansion approximation works well in the interior, removing the spurious mixing associated with the simple Eulerian-averaged streamfunction. However, it fails near the surface where isopycnals outcrop to the surface. It can be shown in a similar way that the vertical isopycnic streamfunction can formally be approximated by a residual streamfunction involving the vertical eddy flux. However, if horizontal isopycnal displacements are large, this approximation fails even in the ocean interior. Inspired by the two different residual streamfunctions, a more general form of TEM formulation is explored. It is shown that the different TEM residual streamfunctions arise from decomposing the eddy flux into a component along isopycnals, which leads to advective flow, and a remaining diffusive component, which is oriented either vertically or horizontally. In theory the diffusive flux can be oriented in any direction, although in practice the orientation should be such that neither the advective flow nor the diffusive flux cross any boundary (surface, sidewalls, and bottom). However, it is not clear how to merge the continuously changing orientation in a physically meaningful way. A variety of approaches are discussed.