Parameterizing mesoscale eddies with residual and Eulerian schemes, and a comparison with eddy-permitting models
Parameterizing mesoscale eddies with residual and Eulerian schemes, and a comparison with eddy-permitting models
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DOI：
10.1016/j.ocemod.2008.02.005
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发表时间：
2008
期刊：
影响因子：
3.2
通讯作者：
R. Zhao;G. Vallis
中科院分区：
文献类型：
--
作者：
R. Zhao;G. Vallis
在这篇文章中，我们探索和测试了某些旨在描述中尺度未分辨涡旋对更大尺度流动的影响的参数化方案。特别是，我们研究了一种基于方程的剩余或变换的欧拉平均公式的方案，其中涡旋由动量方程中的大垂直粘性来参数化，在示踪(例如，温度或盐度)演化方程中没有出现偏通量参数化，尽管仍保留了参数化沿等径面扩散的项。将残差格式与使用斜扩散(或相当于按斜速度平流)的常规参数化方法以及允许涡流的计算方法进行了比较。虽然在原则上几乎等同于某些形式的斜通量格式，但在某些情况下，尤其是在上边界附近，传统格式对锥度的选择很敏感，而剩余格式则不那么敏感，因此，余量格式比传统格式具有一定的实用优势。残差方案还使得水平粘度--主要用于保持模型稳定性--得以降低。最后，残差方案在一定程度上更容易实现，示踪剂传输更容易解释。另一方面，余量方案至少在形式上给出了变换的速度，而不是欧拉速度，并且并不是在所有情况下都是合适的。
In this paper we explore and test certain parameterization schemes that aim to represent the effects of unresolved mesoscale eddies on the larger-scale flow. In particular, we examine a scheme based on the residual or transformed Eulerian mean formulation of the equations, in which the eddies are parameterized by a large vertical viscosity in the momentum equations, with no skew flux parameterization appearing in the tracer (e.g., temperature or salinity) evolution equations, although terms that parameterize diffusion along isopycnal surfaces remain. The residual scheme is compared both to a conventional parameterization that uses a skew diffusion (or equivalently advection by a skew velocity), and to eddy-permitting calculations. Although in principle almost equivalent to certain forms of skew flux schemes, the residual formulation is found to have certain practical advantages over the conventional scheme in some circumstances, and in particular near the upper boundary where conventional schemes are sensitive to the choice of tapering but the residual scheme is less so. The residual scheme also enables the horizontal viscosity – which is mainly applied to maintain model stability – to be reduced. Finally, the residual scheme is somewhat easier to implement, and the tracer transport is easier to interpret. On the other hand, the residual scheme gives, at least formally, a transformed velocity, not the Eulerian velocity and will not be appropriate in all circumstances.