On velocity gradient dynamics and turbulent structure
On velocity gradient dynamics and turbulent structure
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DOI：
10.1017/jfm.2015.452
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发表时间：
2015-10-01
影响因子：
3.7
通讯作者：
Dawson, J. R.
中科院分区：
文献类型：
--
作者：
Lawson, J. W.;Dawson, J. R.
速度梯度张量A = del u的统计量受湍流“结构”的影响，反映了湍流的精细尺度。虽然速度梯度统计和动力学已经得到了很好的表征，但结构和动力学之间的联系主要集中在旋转主导的流动上，并且仅依赖于数值模拟的数据。利用均匀湍流的数值和空间分辨实验数据集，研究了结构对所有以A为特征的局部（不可压缩）流动拓扑结构的作用。通过它们在Q = -Tr(A(2))/2场的条件平均中留下的足迹来研究结构，这与非局部应变产生有关，使用两种互补的条件平均技术获得。第一种是随机估计，它近似于以A为条件的Q场，并在两个数据集中得出定量相似的结构，与随机高斯速度场不同。此外，它与Wilczek & Meneveau （J. Fluid Mech）最近提出的速度梯度动力学模型非常相似。， vol. 756, 2014, pp. 191-225)，但它是在一个限制较少的前提下推导出来的，具有明确确定的关闭系数。第二种技术检查Q字段的真实条件平均值，用于验证随机估计并为模型的改进提供见解。综上所述，这些方法证实了涡旋管是旋转控制区域的主要特征，并且表明剪切层结构在应变控制区域是活跃的。在这两种情况下，这些结构的运动学特征解释了压力Hessian特征向量的排列统计，以及为什么局部和非局部应变产生相互对立。
The statistics of the velocity gradient tensor A = del u, which embody the fine scales of turbulence, are influenced by turbulent 'structure'. Whilst velocity gradient statistics and dynamics have been well characterised, the connection between structure and dynamics has largely focused on rotation-dominated flow and relied upon data from numerical simulation alone. Using numerical and spatially resolved experimental datasets of homogeneous turbulence, the role of structure is examined for all local (incompressible) flow topologies characterisable by A. Structures are studied through the footprints they leave in conditional averages of the Q = -Tr(A(2))/2 field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the Q field conditioned upon A and educes quantitatively similar structure in both datasets, dissimilar to that of random Gaussian velocity fields. Moreover, it strongly resembles a promising model for velocity gradient dynamics recently proposed by Wilczek & Meneveau (J. Fluid Mech., vol. 756, 2014, pp. 191-225), but is derived under a less restrictive premise, with explicitly determined closure coefficients. The second technique examines true conditional averages of the Q field, which is used to validate the stochastic estimation and provide insights towards the model's refinement. Jointly, these approaches confirm that vortex tubes are the predominant feature of rotation-dominated regions and additionally show that shear layer structures are active in strain-dominated regions. In both cases, kinematic features of these structures explain alignment statistics of the pressure Hessian eigenvectors and why local and non-local strain production act in opposition to each other.