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

为了理解湍流混合的动力学和定性描述湍流混合的统计特性，本文对流体线和表面的拉伸特性进行了数值研究。所得结果总结如下。首先，我们研究，通过使用直接的数值模拟和可视化分析，它们是如何变形的，以及它们在均匀的静止湍流中被拉伸的比例。从理论上证明了流体线的长度和流体表面的面积都随时间呈指数增长，而拉伸率的精确值不能用传统的方法，即用被动的线或面单元来获得，而只能像本研究那样精确地求解流体线和面的运动。其次，它被确定与被动线和流体流动的同时可视化的流体运动的类型，导致强烈的拉伸的流体线。存在大量的管状涡 关于我们 湍流中涡量集中的情况。它们具有以相反的涡度方向平行地彼此接近的趋势。在与一对反平行涡相关的双曲线型驻点周围，流体线被强烈拉伸。第三，仔细检查的雷诺数的流体线的拉伸率的依赖性表明，它不遵守柯尔莫哥洛夫相似定律（如前所述），但更迅速地增加与雷诺数。这可能是由于拉伸过程的马尔可夫乘法特性，即拉伸后的流体线的空间分布的不均匀性，特别是折叠程度，随雷诺数的增加而增加。湍流中被动物体指数拉伸率的精确值及其与雷诺数的关系对于确定湍流模拟中的参数以及理解湍流本身的动力学特性具有重要意义。少

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