Velocity fields with power-law spectra for modeling turbulent flows
Velocity fields with power-law spectra for modeling turbulent flows
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用于模拟湍流的具有幂律谱的速度场
DOI：
10.1016/j.apm.2006.08.001
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发表时间：
2007
影响因子：
5
通讯作者：
M. Çağlar
中科院分区：
文献类型：
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作者：
M. Çağlar
我们考虑了均匀和各向同性Çinlar速度场的推广，以捕获幂律谱。随机速度场是非高斯的，其表示由拉格朗日和欧拉观测激发。通过改变模型的随机参数，可以产生大范围的湍流。速度场是泊松弹噪声的泛函形式，它被构造为通过其类型和到达时间随机化的涡流的叠加。我们引入了涡旋类型（空间参数）和衰减参数（时间参数）之间的依赖关系。结果，实现了空间上的远程相关和以前用于Ornstein-Uhlenbeck速度场的幂律谱。我们证明了涡流直径概率分布的幂律形式足以证明这一结果。根据柯尔莫哥洛夫惯性尺度理论，进一步确定了概率分布的参数。特别地，得到了谱的∣k∣−5/3标度。在扩散极限下，我们发现控制涡流衰减、到达率和旋转速度的参数随着直径的减小而增大。也就是说，涡流到达得快，衰减得快，旋转得快，半径小，达到布朗极限。
We consider a generalization of homogeneous and isotropic Çinlar velocity fields to capture power-law spectra. The random velocity field is non-Gaussian with a representation motivated by Lagrangian and Eulerian observations. A wide range of turbulent flows can be generated by varying the stochastic parameters of the model. The velocity field being a functional version of Poisson shot-noise is constructed as the superposition of eddies randomized through their types and arrival times. We introduce a dependence between the eddy types which are spatial parameters and the decay parameter which is temporal. As a result, long-range correlation in space and a power-law spectrum previously used with Ornstein–Uhlenbeck velocity fields are achieved. We show that a corresponding power-law form for the probability distribution of the eddy diameter is sufficient for this result. The parameters of the probability distribution are further specified in view of Kolmogorov theory of the inertial scales. In particular, ∣k∣−5/3scaling of the spectrum is obtained. In the diffusive limit, we show that the parameters governing the decay and the arrival rate, and the speed of rotation of an eddy increase while its diameter decreases. That is, the eddies arrive fast, decay fast, and rotate fast with a small radius for a Brownian limit.