Multi-scale, Geometrical Study of Eddy-structure in Turbulence

研究人员和他的学生们致力于开发一种新的计算数学框架，用于识别和表征湍流中的涡状结构。一般的方法包括一个多尺度分析的湍流体积数据集，然后由感兴趣的结构和它们的几何特征的eduction。通过曲波变换进行多尺度分析，对不同尺度的体数据进行等轮廓线处理，实现结构的提取。的几何特征是基于概率密度函数的形状指数和曲率，在面积覆盖，与每个结构。这允许一组结构的全局表征以及研究和比较包含在该组结构中的相关结构组。研究人员已经开发了基本框架，该框架已经在再现合成"虚拟双折射“的几何特征的基础上进行了验证测试。目前的工作主要集中在研究周期立方体中标量湍流的几何结构，这些结构是通过512^3直接数值模拟得到的。进一步的发展正在进行中，以完善和改进这一框架的提取和分类水平，以更好地适应湍流数据库的属性。该方法也被应用于由K. Horiuti（日本名古屋）。研究中的湍流场包括标量耗散和可从速度梯度导出的量，如涡量、速度梯度张量的不变量、这些量的函数（用于识别局部涡量主导区域）和压力泛函。该方法也将被应用到非均匀湍流场，如那些从湍流通道流。从列奥纳多·达芬奇绘制出详细的涡流图像的时代，到现在计算机图形学和自然现象可视化的时代，人们一直对描述和理解湍流流体流动的自然几何形状着迷。但是，尽管进行了大量的研究，湍流涡流的结构和形态仍然难以捉摸。更好地了解这种结构，既可以阐明自然界的一个深奥的奥秘，同时也可以为改进湍流预测模型的发展提供坚实的基础，这些模型可以应用于许多不同的科学和工程领域，从银河系尺度，到太阳系动力学，星星形成和恒星内部动力学，太阳风，地球气候建模，环境流体动力学和工业及工程应用。本研究的动机是最近可用的高保真数据库表示非常详细和现实的湍流fields.The调查员和他的学生联合收割机从计算机科学领域的新模式识别技术结合新的应用数学方法的基础上"多尺度“分析，研究这些数据。这项工作的意义在于，它将为分析超大型湍流流体流数据场的基本几何结构和内容提供一种新的方法。通过论文和档案期刊的出版物提供文档。这将允许潜在用户将本工作中开发的建模方法应用于大型数据库从数值模拟和实验两方面得到。流体流动以外的应用，任何一组连续的领域，设想。

The investigator and his students work to develop a new computational-mathematical framework for the identification and characterization of eddy-like structures in turbulence. The general methodology consists of a multi-scale analysis of a turbulence volume data set followed by the eduction of structures of interest and their geometrical characterization. The multi-scale analysis is performed through the curvelet transform.The eduction of structures is achieved by isocontouring the volume data sets for different scales. The geometrical characterization is based on the probability density functions of shape index and curvedness, in terms of area coverage,associated with each structure. This allows a global characterization of the set of structures as well as the study and comparison of relevant groups of structures contained within this set. The investigator has already developed the basic framework which has been subjected to validation testing based on reproducing the geometrical character of a synthetic ``virtual turbulence''. The work is presently focused on studying the geometrical structure of scalar turbulence obtained from 512^3 direct-numerical simulation in a periodic cube. Further development is in progress to refine and improve this framework at the extraction and classification levels in order to better adapt it to the properties of turbulence data bases. The methodology is also being applied to the 256^3, 512^3 and 1024^3 data sets of the same turbulence image (at three different resolutions) provided by K. Horiuti (Nagoya Japan). Turbulent fields under study include the scalar dissipation and quantities derivable from velocity gradients such as vorticity, invariants of the velocity-gradient tensor, functions of these quantities that identify local, vorticity-dominant regions, and functionals of the pressure. The methodology will also be applied to non-homogeneous turbulent fields such as those obtained from turbulent channel flow. From the time of Leonardo Da Vinci, who crafted detailed images of eddying fluid flow, the to present era of enhanced computer graphics and the visualization of natural phenomena, there has been an ongoing fascination with both characterizing and understanding the natural geometry of turbulent fluid flow.But despite intense study, the structure and morphology of turbulent eddies remains elusive. A better understanding of this structure should both elucidate one of nature's profound mysteries and at the same time provide a firm basis for the development of improved predictive models for turbulent fluid flow for application to many diverse areas of science and engineering ranging from the galactic scale, through solar-system dynamics, star formation and stellar interior dynamics, the solar wind, climate modeling of planet earth, to environmental fluid dynamics and industrial and engineering applications. The present research is motivated by the recent availability of high-fidelity data bases representing very detailed and realistic turbulent flow fields obtained from intensive computer simulation.The investigator and his students combine novel pattern-recognition techniques from the field of computer science with new applied-mathematical methods based on ``multi-scale'' analysis, to study these data. The significance of this work is that it will provide a new methodology for analysing the underlying geometrical structure and content of extremely large, turbulent fluid-flow data fields.The computer codes developed in this research will be made openly available, with documentation through publications in thesis dissertations and in archival journals.This should allow potential users to apply the modeling methodologies developed in this work to large data bases obtained from both numerical-simulation and experiment. Applications beyond fluid flows, to any set of continuous fields, are envisioned.