On the non-local geometry of turbulence
On the non-local geometry of turbulence
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DOI：
10.1017/s002211200800092x
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发表时间：
2008-04
影响因子：
3.7
通讯作者：
I. Bermejo-Moreno;D. Pullin;K. Horiuti
中科院分区：
文献类型：
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作者：
I. Bermejo-Moreno;D. Pullin;K. Horiuti
提出了一种多尺度方法来研究湍流中涡流结构的非局部几何。从给定的三维场开始，这包括三个主要步骤：提取，表征和结构分类。提取步骤分为两个阶段。首先，将基于曲线变换的多尺度分解应用于全三维场，得到一个有限的分量三维场，每个尺度一个。其次，通过在一个或多个等高线水平上对每个分量场进行等高线化，得到一组代表该等高线水平上结构的封闭等高线面。表征阶段是基于联合概率密度函数（p.d.f），就每个单独的等曲面上的面积覆盖而言，两个微分几何属性，形状指数和弯曲度，加上曲面的无量纲全局不变量拉伸参数。综上所述，这定义了等面的几何特征。分类步骤是基于一组有限参数的构造，这些参数是从每个结构的关节p.d.f.的矩的代数函数中获得的，这些函数将其位置指定为多维“特征空间”中的一个点。对于指定的等高线值，在每个尺度上特征空间中的点集表示该尺度上的所有结构。这样就可以应用聚类技术来搜索具有共同几何形状的结构组。本文给出了该技术首次应用于5123强迫各向同性湍流（Reλ = 265）下标量混合的直接数值模拟得到的被动标量场的结果。随着尺度的减小，从大尺度的斑点状结构过渡到惯性尺度范围内具有小或中等拉伸的斑点状和管状结构，再到耗散尺度范围内具有高水平拉伸的管状和片状结构。讨论了这些结果对被动标量搅拌和湍流混合的动力学行为的意义。
A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed.