The relationship between a deformation-based eddy parameterization and the LANS-a turbulence model
The relationship between a deformation-based eddy parameterization and the LANS-a turbulence model
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基于变形的涡流参数化与LANS-湍流模型之间的关系
DOI：
10.1016/j.ocemod.2018.04.007
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发表时间：
2018
期刊：
影响因子：
3.2
通讯作者：
Bachman S
中科院分区：
文献类型：
--
作者：
Bachman S
Porta Mana和Zanna（2014年）以及Anstey和Zanna（2017年）提出的最近一类海洋涡旋参数化将大尺度流动建模为非牛顿流体，其亚网格尺度涡旋应力是变形的非线性函数。这个想法，虽然很大程度上是新的海洋建模，有一个历史的湍流建模至少可以追溯到里夫林（1957年）。这类新的参数化导致类似于拉格朗日平均Navier-Stokes-α模型（局域网-α，例如，霍尔姆等人，1998年a）。在本说明中，我们采用基本的张量数学突出这些湍流模型之间的相似性，使用组件的免费符号。我们将Anstey和Zanna（2017）的参数化（最初是在2D中提出的）扩展到3D，并推导出当使用完整的非牛顿应力张量时出现的这种闭合的变体。尽管非牛顿模型和局域网-α模型之间在数学上有相似之处，这可能有助于深入了解数值实现，但这两种湍流模型之间的动能输入和耗散是不同的。
A recent class of ocean eddy parameterizations proposed by Porta Mana and Zanna (2014) and Anstey and Zanna (2017) modeled the large-scale flow as a non-Newtonian fluid whose subgridscale eddy stress is a nonlinear function of the deformation. This idea, while largely new to ocean modeling, has a history in turbulence modeling dating at least back to Rivlin (1957). The new class of parameterizations results in equations that resemble the Lagrangian-averaged Navier–Stokes-αmodel (LANS-α, e.g., Holm et al., 1998a). In this note we employ basic tensor mathematics to highlight the similarities between these turbulence models using component-free notation. We extend the Anstey and Zanna (2017) parameterization, which was originally presented in 2D, to 3D, and derive variants of this closure that arise when the full non-Newtonian stress tensor is used. Despite the mathematical similarities between the non-Newtonian and LANS-αmodels which might provide insight into numerical implementation, the input and dissipation of kinetic energy between these two turbulent models differ.