A multifractal model for linking Lagrangian and Eulerian velocity structure functions
A multifractal model for linking Lagrangian and Eulerian velocity structure functions
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DOI：
10.1007/s10409-014-0049-2
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发表时间：
2014-05
影响因子：
3.5
通讯作者：
Yu-Feng Dong;G. Jin
中科院分区：
文献类型：
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作者：
Yu-Feng Dong;G. Jin
建立了一个多重分形模型，将拉格朗日多重分形维与欧拉多重分形维联系起来。我们提出拉格朗日量的特征时间尺度应该是拉格朗日时间尺度，而不应该是以往拉格朗日统计研究中广泛使用的欧拉时间尺度。利用该模型，我们可以从已有的欧拉速度结构函数的标度指数数据或模型中得到拉格朗日速度结构函数的标度指数。通过与实验结果、直接数值模拟结果和以往理论模型的比较，验证了该模型的正确性。对比表明，该模型能较好地预测拉格朗日速度结构函数的标度指数，特别是对于大于6阶的标度指数。
A multifractal model is developed to connect the Lagrangian multifractal dimensions with their Eulerian counterparts. We propose that the characteristic time scale of a Lagrangian quantity should be the Lagrangian time scale, and it should not be the Eulerian time scale which was widely used in previous studies on Lagrangian statistics. Using the present model, we can obtain the scaling exponents of Lagrangian velocity structure functions from the existing data or models of scaling exponents of Eulerian velocity structure functions. This model is validated by comparing its prediction with the results of experiments, direct numerical simulations, and the previous theoretical models. The comparison shows that the proposed model can better predict the scaling exponents of Lagrangian velocity structure functions, especially for orders larger than 6.