To disseminate the role of the eddy motions on the anisotropic states of the Reynolds stress tensor (\(\varvec{B}\)), we devise a novel methodology based on the quadrant analysis, where the distributions of the invariants of \(\varvec{B}\) are studied on a \(u^{\prime }\)–\(w^{\prime }\) quadrant plane, with \(u^{\prime }\) and \(w^{\prime }\) being the turbulent fluctuations in the streamwise and vertical velocities. We apply this methodology to a near-neutral atmospheric surface layer (ASL) flow, derived from a field experiment dataset having multi-level turbulence measurements. The results show that in a near-neutral ASL flow, the anisotropic states of \(\varvec{B}\) are determined by the distribution of the streamwise and cross-stream velocity variances (\(\sigma _{u}^2\) and \(\sigma _{v}^2\)) on the \(u^{\prime }\)–\(w^{\prime }\) quadrant plane. By studying the contour maps of the invariants of \(\varvec{B}\) on the \(u^{\prime }\)–\(w^{\prime }\) quadrant plane, we discover three distinct zones with elliptical boundaries in the \(u^{\prime }\)–\(w^{\prime }\) plane, across which the anisotropic states of the eddy motions evolve. We find that the eddy motions which occur

1. 1.Inside the inner elliptical zone display rod-like anisotropy being determined by \(\sigma _{v}^2\),
2. 2.Within the annular zone between the inner and outer ellipses display pancake-like anisotropy being determined by both \(\sigma _{u}^2\) and \(\sigma _{v}^2\),
3. 3.Outside the outer elliptical zone display rod-like anisotropy being determined by \(\sigma _{u}^2\).

We also notice that the distinction between these three zones in the \(u^{\prime }\)–\(w^{\prime }\) plane is prominent at the lowest measurement level, but becomes progressively indistinguishable as the measurement height increases.

中文翻译：

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雷诺应力张量通过象限分析表示为近似中性的大​​气表层流动

为了传播涡动运动对雷诺应力张量各向异性状态（\（\ varvec {B} \））的作用，我们基于象限分析设计了一种新颖的方法，其中\（\ varvec {B} \）在\（u ^ {\ prime} \） – \（w ^ {\ prime} \）象限平面上研究，其中\（u ^ {\ prime} \）和\（w ^ {\ prime} \）是沿流向和垂直速度的湍流波动。我们将此方法应用于近中性大气表层（ASL）流动，该流动是从具有多级湍流测量值的现场实验数据集中得出的。结果表明，在接近中性的ASL流中，\（\ varvec {B} \）的各向异性状态由\（u ^ {\ prime）上的流向和跨流速度方差（\（\ sigma _ {u} ^ 2 \）和\（\ sigma _ {v} ^ 2 \）的分布确定} \） – \（w ^ {\ prime} \）象限平面。通过研究轮廓的不变量的映射\（\ varvec {B} \）的\（U ^ {\黄金} \） - \（W ^ {\黄金} \）象限飞机，我们发现有三个不同的区域\（u ^ {\ prime} \） – \（w ^ {\ prime} \）平面中的椭圆边界，涡旋运动的各向异性状态在该边界上演化。我们发现发生的涡流运动

1. 1.在内部椭圆区内，显示由\（\ sigma _ {v} ^ 2 \）确定的棒状各向异性，
2. 2.在内部和外部椭圆之间的环形区域内，显示出由\（\ sigma _ {u} ^ 2 \）和\（\ sigma _ {v} ^ 2 \）决定的煎饼状各向异性，
3. 3.在外部椭圆形区域之外，显示由\（\ sigma _ {u} ^ 2 \）确定的棒状各向异性。

我们还注意到，在最低测量级别，\（u ^ {\ prime} \） – \（w ^ {\ prime} \）平面中的这三个区域之间的区别很明显，但随着测量高度的逐渐变得无法区分增加。