Non‐Gaussian invariant measures for the Majda model of decaying turbulent transport
Non‐Gaussian invariant measures for the Majda model of decaying turbulent transport
复制标题
衰减湍流输运 Majda 模型的非高斯不变测度
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Eric Vanden Eijnden
中科院分区：
文献类型：
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作者：
Eric Vanden Eijnden
研究了随机速度场对标量场的湍流输运问题。标量场振幅表现出罕见但非常大的波动，其典型特征比标量概率分布的高斯尾更肥。这种大波动的存在与流内拉格朗日路径的聚类现象有关。这提出了一种将标量场的大偏差问题转化为测量拉格朗日路径随时间扩展的适当定义过程的小偏差或小球问题的方法。在这里，这种方法被应用于由Majda提出的一个模型，该模型由白时线性剪切流和它的一些推广组成，其中速度场具有有限甚至无限的相关时间。推导了（约简）标量场的非高斯不变测度，特别地，证明了标量的一点分布具有拉伸的指数尾，其拉伸指数取决于模型中的参数。确定了标量行为的不同普适性类，在所有其他参数保持不变的情况下，它们与测量速度场中时间持续效应的指数显示一对一的对应关系。©2001 John Wiley & Sons, Inc
The problem of turbulent transport of a scalar field by a random velocity field is considered. The scalar field amplitude exhibits rare but very large fluctuations whose typical signature are fatter than Gaussian tails for the probability distribution of the scalar. The existence of such large fluctuations is related to clustering phenomena of the Lagrangian paths within the flow. This suggests an approach to turn the large deviation problem for the scalar field into a small deviation, or small ball, problem for some appropriately defined process measuring the spreading with time of the Lagrangian paths. Here, such a methodology is applied to a model proposed by Majda consisting of a white‐in‐time linear shear flow and some generalizations of it where the velocity field has finite, or even infinite, correlation time. The non‐Gaussian invariant measure for the (reduced) scalar field is derived and, in particular, it is shown that the one‐point distribution of the scalar has stretched exponential tails, with a stretching exponent depending of the parameters in the model. Different universality classes for the scalar behavior are identified which, all other parameters being kept fixed, display a one‐to‐one correspondence with a exponent measuring time persistence effects in the velocity field. © 2001 John Wiley & Sons, Inc.