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首页> 外文期刊>Applied Mathematical Modelling >Velocity fields with power-law spectra for modeling turbulent flows
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Velocity fields with power-law spectra for modeling turbulent flows

机译：具有幂律谱的速度场用于湍流建模

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摘要

We consider a generalization of homogeneous and isotropic Cinlar 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|~(-5/3) scaling 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.
机译：我们考虑对均质和各向同性的Cinlar速度场进行推广，以捕获幂律谱。随机速度场是非高斯的，其表示受拉格朗日和欧拉观测的启发。通过改变模型的随机参数，可以产生各种各样的湍流。速度场是泊松散粒噪声的一种功能形式，其构造是通过其类型和到达时间随机化的漩涡的叠加。我们介绍了作为空间参数的涡流类型与作为时间参数的衰减参数之间的依赖性。结果，实现了先前与Ornstein-Uhlenbeck速度场一起使用的空间远距离相关性和幂律谱。我们表明，对于涡旋直径的概率分布，相应的幂律形式足以满足该结果。参照惯性尺度的Kolmogorov理论进一步指定了概率分布的参数。特别地，获得频谱的| k |〜（-5/3）缩放。在扩散极限中，我们显示了控制衰减和到达速度的参数，以及涡旋直径减小时其旋转速度的增加。也就是说，涡旋到达快，衰减快并且以小半径快速旋转以达到布朗极限。

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