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Statistics of stretching of fluid lines and surfaces, and turbulent mixing

流体线和表面的拉伸以及湍流混合的统计

基本信息

批准号：
14540385
负责人：
KIDA Shigeo
金额：
$ 2.62万
依托单位：
Kyoto University (2003-2004)National Institute for Fusion Science (2002)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540385/
关键词：
Turbulent mixing Fluid line Fluid surface Stretching rate Tubular vortex Anti-parallel vortices 流対面伸張率

项目摘要

For the purpose of understanding of dynamics and qualitative description of statistics of turbulent mixing the stretching characteristics of fluid lines and surfaces are investigated numerically. The results obtained are summarized as follows. First, we examined, by use of direct numerical simulation and visualization analysis, how they are deformed and at which ratio they are being stretched in homogeneous stationary turbulence. It is shown theoretically that both the length of fluid line and the area of fluid surface increase exponentially in time, and that the accurate values of the stretching rate can never be obtained by the traditional method, i.e. with passive line or surface elements, but only by solving accurately the motion of the fluid lines and surfaces as the present study. Second, it was identified with simultaneous visualization of passive lines and fluid flows the type of fluid motion which causes strong stretching of fluid lines. There exist a number of tubular vortice … More s with concentrated vorticity in turbulence. They have a tendency to approach each other in parallel with opposite direction of vorticity. Fluid lines are stretched strongly around stagnation points of hyperbolic type associated with a pair of anti-parallel vortices. Third, a careful examination of the Reynolds number dependence of stretching rate of fluid line exhibits that it does not obey the Kolmogorov similarity law (as believed before) but increases more rapidly with the Reynolds number. This may be due to the Markovian multiplicative characteristics of the stretching process, i.e. the non-uniformity of the spatial distributions of stretched fluid line, especially the degree of fold, increases with the Reynolds number. The precise value of the exponential stretching rates of passive objects in turbulence and its Reynolds dependence would be useful in determination of parameters in turbulence modeling as well as important in understanding of dynamical characteristics of turbulence itself. Less

为了更好地理解湍流混合的动力学特性和定性描述湍流混合的统计特性，本文用数值方法研究了流体线和表面的拉伸特性。所得结果总结如下：首先，通过直接数值模拟和可视化分析，我们检查了它们是如何变形的，以及它们在均匀静止湍流中以何种比例被拉伸。从理论上证明，流体线的长度和流体表面的面积都随时间呈指数增长，而拉伸速率的精确值不能用传统的方法，即被动的线或面元，而只能像本研究那样精确地求解流体线和面的运动。其次，在被动线和流体流动同时可视化的情况下，确定了导致流体线强烈拉伸的流体运动类型。湍流中存在大量的管状涡，涡量集中。它们倾向于以相反的涡度方向平行地相互接近。流体线在与一对反平行涡旋相关的双曲型滞止点周围被强烈拉伸。第三，对流体线拉伸速率的雷诺数依赖关系的仔细研究表明，它不服从柯尔莫哥罗夫相似定律（如以前所认为的），而是随着雷诺数的增加而迅速增加。这可能是由于拉伸过程的马尔可夫乘法特性，即拉伸流体线的空间分布的不均匀性，特别是褶皱程度，随着雷诺数的增加而增加。被动物体在湍流中的指数拉伸率的精确值及其与雷诺数的依赖关系将有助于湍流建模参数的确定，对理解湍流本身的动力学特性也很重要。少