Discrete variance decay analysis of spurious mixing

IF 3.1 3区 地球科学 Q2 METEOROLOGY & ATMOSPHERIC SCIENCES Ocean Modelling Pub Date : 2024-11-09 DOI:10.1016/j.ocemod.2024.102460
Tridib Banerjee , Sergey Danilov , Knut Klingbeil , Jean-Michel Campin
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Abstract

This work examines the use of discrete variance decay of tracers to estimate locally in space and time the numerical mixing caused by different processes during a tracer transport step. Expressions for local discrete variance decay (DVD) rates are directly derived from discrete tracer equations without any assumptions on discrete fluxes of the second moment. They relate the DVD rates to the fluxes of the first moment through the faces of scalar control cell. Mixing associated with advective and diffusive fluxes is thus estimated. The new framework avoids the need for second-moment flux definition when solved directly on finite-volume cell faces but still invokes certain second-moment fluxes when the face DVD rates are partitioned to cells sharing the face. These implied discrete fluxes depend on the partitioning and are non-unique. For third- or higher-order advection schemes, the DVD rates are contaminated by dispersive errors intrinsic to the approach, introducing uncertainty to the locality of any estimates produced by it. Additional temporal averaging or coarse-graining is thus necessary. Through the application of this technique, numerical mixing is found to be correlated with the distribution of eddy kinetic energy. Numerical mixing induced by vertical advection is found to be relatively small and correlated with the distribution of buoyancy fluxes. The explored high-order schemes are found to demonstrate levels of spurious mixing which may locally exceed physical mixing.
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杂散混合的离散方差衰减分析
这项研究利用示踪剂的离散方差衰减来估算示踪剂传输步骤中不同过程在空间和时间上造成的局部数值混合。局部离散方差衰减(DVD)率的表达式直接来自离散示踪剂方程,无需对第二时刻的离散通量做任何假设。它们将 DVD 率与通过标量控制单元面的第一时刻通量联系起来。这样就可以估算出与平流和扩散通量相关的混合情况。当直接求解有限体积单元面时,新框架避免了第二时刻通量定义的需要,但当面的 DVD 率被分割到共享面的单元时,仍会调用某些第二时刻通量。这些隐含的离散通量取决于分区,并且是非唯一的。对于三阶或更高阶的平流方案,DVD 率会受到该方法固有的分散误差的污染,从而为其产生的任何估计值的定位带来不确定性。因此,有必要进行额外的时间平均或粗粒化。通过应用这种技术,发现数值混合与涡旋动能的分布相关。垂直平流引起的数值混合相对较小,并且与浮力通量的分布相关。研究发现,所探讨的高阶方案显示的虚假混合程度可能会局部超过物理混合程度。
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来源期刊
Ocean Modelling
Ocean Modelling 地学-海洋学
CiteScore
5.50
自引率
9.40%
发文量
86
审稿时长
19.6 weeks
期刊介绍: The main objective of Ocean Modelling is to provide rapid communication between those interested in ocean modelling, whether through direct observation, or through analytical, numerical or laboratory models, and including interactions between physical and biogeochemical or biological phenomena. Because of the intimate links between ocean and atmosphere, involvement of scientists interested in influences of either medium on the other is welcome. The journal has a wide scope and includes ocean-atmosphere interaction in various forms as well as pure ocean results. In addition to primary peer-reviewed papers, the journal provides review papers, preliminary communications, and discussions.
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