Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence
Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence
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DOI：
10.1063/1.870077
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发表时间：
1999-07
影响因子：
4.6
通讯作者：
Y. Kaneda;T. Ishihara;K. Gotoh
中科院分区：
文献类型：
--
作者：
Y. Kaneda;T. Ishihara;K. Gotoh
本文提出了一种计算湍流中拉格朗日和欧拉两点两时间速度关联式的时间差的泰勒展开的方法。展开式基于给定动力学条件下欧拉和拉格朗日速度场的泰勒级数以及初始条件和边界条件。展开式中最低的几个系数使我们能够构造关联的近似值。将该方法应用于服从Navier-Stokes动力学的湍流，得到了近似结果，特别是Pade近似，与中等雷诺数下均匀各向同性湍流的直接数值模拟符合得很好。利用拉格朗日关联式和欧拉关联式的泰勒级数的二阶系数与零阶系数之比，分别给出了拉格朗日和欧拉微时间尺度的估计值τL和τE。
A method is developed for generating the Taylor expansions in powers of the time difference of the Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. The expansions are based on the Taylor series of the Eulerian and Lagrangian velocity fields subject to given dynamics along with initial and boundary conditions. The lowest few coefficients in the expansions enable us to construct approximations to the correlations. An application of the method to turbulence obeying the Navier-Stokes dynamics yields approximations, particularly Pade approximations that agree well with direct numerical simulations of homogeneous isotropic turbulence at moderate Reynolds numbers. The ratios of the second-order to the zeroth-order coefficients of the Taylor series of the Lagrangian and Eulerian correlations give, respectively, the estimates for the Lagrangian and Eulerian micro time scales τL and τE. An analysis of a high resolution (5123 grid points) direct numerical simulation database at large R...