What controls the decay of passive scalars in smooth flows? art. no. 097103
What controls the decay of passive scalars in smooth flows? art. no. 097103
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DOI：
10.1063/1.2033908
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发表时间：
2005-09-01
影响因子：
4.6
通讯作者：
Vanneste, J
中科院分区：
文献类型：
--
作者：
Haynes, PH;Vanneste, J
研究了均匀随机二维流动中释放的被动标量方差的指数衰减。考虑了两类流动：短相关时间（Kraichnan）流动和有限时间后完全去相关的更新流动。对于这两类，可以推导出浓度协方差的封闭演化方程，并找到方差衰减率gamma(2)作为线性算子的特征值。通过对小扩散系数kappa极限下的特征值问题的渐近分析，我们建立了gamma(2)要么是(i)局部控制，由流动的拉伸特征控制，要么是（ii）全局控制，由流动的大尺度输运性质和区域几何控制。我们将gamma(2)的特征值问题与编码拉伸率的大偏差统计的Cramer函数联系起来；因此，我们证明了由Antonsen等人提出的拉格朗日拉伸理论。流体8,3094(1996)]和其他资料提供了(i)状态下伽马(2)为kappa ->的正确估计。然而，当区域尺度明显大于流动尺度时，它们在（ii）状态下失效，而（ii）状态总是相关的。在数学上，这两种类型的控制是由由gamma(2)识别的特征值的极限行为kappa -> 0来区分的：在局部情况(i)中，它与连续谱的下限相吻合，而在全局情况（ii）中，它是一个孤立的离散特征值。对γ(2)的扩散校正在两种制度之间是不同的，在制度(i)中像1/log(2) kappa一样缩放，在制度（ii）中像kappa（sigma）一样缩放0 < sigma < 1。我们用数值方法验证了克雷契南流和更新流的理论结果。(c) 2005年美国物理研究所。
The exponential decay of the variance of a passive scalar released in a homogeneous random two-dimensional flow is examined. Two classes of flows are considered: short-correlation-time (Kraichnan) flows, and renewing flows, with complete decorrelation after a finite time. For these two classes, a closed evolution equation can be derived for the concentration covariance, and the variance decay rate gamma(2) is found as the eigenvalue of a linear operator. By analyzing the eigenvalue problem asymptotically in the limit of small diffusivity kappa, we establish that gamma(2) is either controlled (i) locally, by the stretching characteristics of the flow, or (ii) globally, by the large-scale transport properties of the flow and by the domain geometry. We relate the eigenvalue problem for gamma(2) to the Cramer function encoding the large-deviation statistics of the stretching rates; hence we show that the Lagrangian stretching theories developed by Antonsen et al. [Phys. Fluids 8, 3094 (1996)] and others provide a correct estimate for gamma(2) as kappa -> 0 in regime (i). However, they fail in regime (ii), which is always the relevant one if the domain scale is significantly larger than the flow scale. Mathematically, the two types of controls are distinguished by the limiting behavior as kappa -> 0 of the eigenvalue identified with gamma(2): in the local case (i) it coincides with the lower limit of a continuous spectrum, while in the global case (ii) it is an isolated discrete eigenvalue. The diffusive correction to gamma(2) differs between the two regimes, scaling like 1/log(2) kappa in regime (i), and like kappa(sigma) for some 0 < sigma < 1 in regime (ii). We confirm our theoretical results numerically both for Kraichnan and renewing flows. (c) 2005 American Institute of Physics.