Using Probability Density Functions to Derive Consistent Closure Relationships among Higher-Order Moments
Using Probability Density Functions to Derive Consistent Closure Relationships among Higher-Order Moments
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DOI：
10.1175/mwr2902.1
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发表时间：
2005-04
影响因子：
3.2
通讯作者：
V. Larson;J. Golaz
中科院分区：
文献类型：
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作者：
V. Larson;J. Golaz
湍流的参数化常预测几个低阶矩，并对高阶矩作闭合假设。原则上，低阶矩和高阶矩具有相同的概率密度函数(PDF)。因此，一个封闭的假设是这个PDF家族的形状。当高阶矩同时涉及速度和热力学标量时，通常假定PDF形状为双或三重增量函数。这相当于假设一个没有亚羽流变化的质量通量模型。然而，可以假定不同于增量函数的PDF族。这是因为假定的PDF方法是相当通用的。本文提出了几个三阶矩和四阶矩的闭包。为了得到闭包，假设矩与特定的PDF族一致，即两个三变量高斯的混合。(此PDF也被某些作者称为双高斯型或双正交型PDF。)与PDF假设不同，本文还提出了标量偏斜度和速度偏斜度之间的简化关系。这个PDF族和偏度关系非常简单，可以产生与矩相关的简单的解析闭包公式。如果某些条件成立，这组力矩是特别可以实现的。这意味着这组矩对应于一个真正的高斯混合PDF，一个在任何地方都是标准化和非负的PDF。本文将新的闭合公式与大涡模拟(LESS)和基于双三角和三重三角PDF的闭合公式进行了比较。本文不在单列模型中实现闭包，并对其进行交互测试。相反，比较是诊断性的；也就是说，从LES中提取低阶矩，并将其视为输入到闭包中的赋值。这将闭包中的错误与单列模型中的错误隔离开来。试验个例为三个大气边界层：信风积层、层积层和晴空对流层。新的关闭有缺点，但在测试的大多数情况下都优于双重或三重三角洲关闭。
Parameterizations of turbulence often predict several lower-order moments and make closure assumptions for higher-order moments. In principle, the low- and high-order moments share the same probability density function (PDF). One closure assumption, then, is the shape of this family of PDFs. When the higher-order moments involve both velocity and thermodynamic scalars, often the PDF shape has been assumed to be a double or triple delta function. This is equivalent to assuming a mass-flux model with no subplume variability. However, PDF families other than delta functions can be assumed. This is because the assumed PDF methodology is fairly general. This paper proposes closures for several third- and fourth-order moments. To derive the closures, the moments are assumed to be consistent with a particular PDF family, namely, a mixture of two trivariate Gaussians. (This PDF is also called a double Gaussian or binormal PDF by some authors.) Separately from the PDF assumption, the paper also proposes a simplified relationship between scalar and velocity skewnesses. This PDF family and skewness relationship are simple enough to yield simple, analytic closure formulas relating the moments. If certain conditions hold, this set of moments is specifically realizable. By this it is meant that the set of moments corresponds to a real Gaussian-mixture PDF, one that is normalized and nonnegative everywhere. This paper compares the new closure formulas with both large eddy simulations (LESs) and closures based on double and triple delta PDFs. This paper does not implement the closures in a single-column model and test them interactively. Rather, the comparisons are diagnostic; that is, low-order moments are extracted from the LES and treated as givens that are input into the closures. This isolates errors in the closures from errors in a single-column model. The test cases are three atmospheric boundary layers: a trade wind cumulus layer, a stratocumulus layer, and a clear convective case. The new closures have shortcomings, but nevertheless are superior to the double or triple delta closures in most of the cases tested.