基于Weierstrass-Mandelbrot函数的分形风速脉动仿真

On the Use of Weierstrass-Mandelbrot Function to Simulate Fractal Wind Fluctuations

实际风速脉动普遍具有自相似分形特征,而传统的谐波合成法和线性滤波法仿真的风速脉动均不具有自相似分形特征。因此,基于随机型Weierstrass-Mandelbrot函数,设计了一种能够仿真自相似风速脉动的方案。其中,表征风速脉动自相似特征的重要参数分形维度可与湍流惯性区能谱的幂指数建立联系。将该方案仿真的风速脉动与实际风速脉动一些重要的统计特征,如功率谱和概率密度函数等,进行了比较,结果表明提出的新方案能有效仿真风速脉动的中高频变化及其概率分布特征。

Classical methods, such as the harmonic wave superimposing method and the linear filtering method, cannot simulate the universal fractal feature of wind fluctuations. The authors proposed a simple method using the stochastic Weierstrass-Mandelbrot function to simulate wind fluctuations with the fractal feature. The fractal dimension, which is an important parameter that describes the fractal feature of wind fluctuations, can be related to the exponents of the inertial-range spectrum. Simulation results show that the method can effectively simulate the probability distributions and variations of wind fluctuations in the medium-high frequency range.