Bos Wouter J T, Fang Le
LMFA, CNRS, Ecole Centrale de Lyon, Université de Lyon, 69134 Ecully, France.
Ecole Centrale de Pékin, Beihang University, 100191 Beijing, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):043020. doi: 10.1103/PhysRevE.91.043020. Epub 2015 Apr 28.
In turbulent scalar mixing, starting from random initial conditions, the root-mean-square advection term rapidly drops as the flow and the scalar field organize. We show first analytically, for the simplified case of a blob in shear flow with a finite correlation time, how the advection term is reduced compared to a randomly aligned scalar structure. This picture is then generalized to turbulent mixing. These examples show that the rapid depletion of advection depends on the lifetime of turbulent structures, compared to the local straining time scale. A turbulence closure is used to show that the Lagrangian correlation time indeed determines the deviation from Gaussian behavior. In particular it is shown that in the inertial range the depletion mechanism is self-similar, since a constant ratio is observed between the advection spectrum and its Gaussian equivalent. Finally, direct numerical simulation shows that in the limit of an infinite correlation time of the turbulent eddies, corresponding to a frozen velocity field, the mean-square advection tends to a zero fraction of its Gaussian estimate.
在湍流标量混合中，从随机初始条件开始，随着流动和标量场的组织化，均方对流项迅速下降。我们首先通过分析表明，对于具有有限相关时间的剪切流中一个流体块的简化情况，与随机排列的标量结构相比，对流项是如何减少的。然后将此情况推广到湍流混合。这些例子表明，与局部应变时间尺度相比，对流的快速衰减取决于湍流结构的寿命。使用一种湍流闭合模型来表明拉格朗日相关时间确实决定了与高斯行为的偏差。特别地，表明在惯性范围内，衰减机制是自相似的，因为在对流谱与其高斯等效谱之间观察到一个恒定的比率。最后，直接数值模拟表明，在湍流涡旋的无限相关时间的极限情况下，对应于一个冻结的速度场，均方对流趋于其高斯估计值的零分数。
