A scaling law for the shear-production range of second-order structure functions
A scaling law for the shear-production range of second-order structure functions
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DOI：
10.1017/jfm.2016.427
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发表时间：
2016-08-01
影响因子：
3.7
通讯作者：
Chamecki, M.
中科院分区：
文献类型：
--
作者：
Pan, Y.;Chamecki, M.
量纲分析表明，耗散长度尺度（l（c）= u（星星）（3）/是的一个元素）是固体边界附近中性分层湍流剪切流中二阶流向结构函数的剪切产生范围的适当尺度，包括光滑和粗糙壁边界层以及冠层（如作物、森林和城市）上方的剪切层。这些流动有两个共同的主要特征：（i）一个单一的速度尺度，即摩擦速度（u（星星））和（ii）大涡的存在，规模与外部长度尺度远大于当地的积分长度尺度。不作任何假设的局部积分尺度，这是成比例的l（是一个元素）的缩放分析是一致的Kolmogorov的结果的惯性子范围。这里的一个元素是湍流动能耗散率（TKE），它代表惯性子区中的能量级联率。的缩放产生的二阶流向结构函数的对数律依赖于（r/l（是的一个元素）），其中r是流向的空间分离。大涡模拟（LES）的结果在模型冠层上方的粗糙子层，其中的本地生产和耗散的TKE之间的不平衡是远远大于在惯性层的壁湍流和本地的整体规模的影响，两个外部长度尺度证实了这种标度律。对数律依赖于（r/l（是的一个元素））的参数估计与壁湍流惯性层的报告是合理的协议。这导致了两个重要的结论。首先，l（是一个元素）缩放的有效性扩展到剪切流与生产和耗散之间的更大的不平衡，表明可能的普遍性的剪切生产范围内的固体边界附近的流动。其次，从建模的角度来看，l（是的一个元素）是表征具有多个外部施加长度尺度的剪切流中的湍流的适当尺度。
Dimensional analysis suggests that the dissipation length scale (l(c) = u(star)(3)/is an element of) is the appropriate scale for the shear-production range of the second-order streamwise structure function in neutrally stratified turbulent shear flows near solid boundaries, including smooth-and rough-wall boundary layers and shear layers above canopies (e.g. crops, forests and cities). These flows have two major characteristics in common: (i) a single velocity scale, i.e. the friction velocity (u(star)) and (ii) the presence of large eddies that scale with an external length scale much larger than the local integral length scale. No assumptions are made about the local integral scale, which is shown to be proportional to l(is an element of) for the scaling analysis to be consistent with Kolmogorov's result for the inertial subrange. Here is an element of is the rate of dissipation of turbulent kinetic energy (TKE) that represents the rate of energy cascade in the inertial subrange. The scaling yields a log-law dependence of the second-order streamwise structure function on (r/l(is an element of)), where r is the streamwise spatial separation. This scaling law is confirmed by large-eddy simulation (LES) results in the roughness sublayer above a model canopy, where the imbalance between local production and dissipation of TKE is much greater than in the inertial layer of wall turbulence and the local integral scale is affected by two external length scales. Parameters estimated for the log-law dependence on (r/l(is an element of)) are in reasonable agreement with those reported for the inertial layer of wall turbulence. This leads to two important conclusions. Firstly, the validity of the l(is an element of)-scaling is extended to shear flows with a much greater imbalance between production and dissipation, indicating possible universality of the shear-production range in flows near solid boundaries. Secondly, from a modelling perspective, l(is an element of) is the appropriate scale to characterize turbulence in shear flows with multiple externally imposed length scales.