大气湍流能谱的精细结构及能量级串

REFINED STRUCTURE OF ENERGY SPECTRUM AND ENERGY CASCADE IN ATMOSPHERIC TURBULENCE

利用小波变换和傅里叶分析对近地层大气湍流脉动资料进行了分析 ,发现波数空间能谱著名的“ - 5 3”标度律成立的区间中存在突变点 ;还发现对应于小波变换时间尺度 2 j,j=1,2 ,… ,j0 ,高频分量按照 2 (j- 2 ) - 1(j>1)的方式级串 ,这符合同步级串的物理图象 ;在标度区间内高频分量作用于幂律局部特征的效果是平均的 ,不存在影响标度指数的特征频谱 .利用不同高度大气湍流资料和不同小波基函数作变换 ,结果是一致的 .我们还对H =1 3的分形布朗运动产生的随机序列进行了对比实验 ,发现从能谱角度 ,实际发达大气湍流偏离高斯分布的程度很小 ,二者的差别只在高阶标度律时明显 .

Using wavelet and Fourier transform we make an analysis of velocity fluctuation data of atmospheric turbulence in the near surface layer. We find that there are some abrupt points in the well-known energy sepctrum of “-5/3” scaling law in the wave-number domain. If the timescale of wavelet transform varies with 2 j, j=1,2,...j 0 ,the eddy of high-frequency components will cascade in a manner of 2 (j-2) -1(j>1), which is in accordance with the physical picture of synchro-cascade pattern. There are no characteristic spectrum components, because the effects of the high frequency componets on the properties of spectrum are the same in the region in which the scaling law is hold. We get the same result using different basic functions to data of atmosphere turbulence at different heights. The comparing experiments are also made between a number of random series about the fractal Brown motion with Husrt exponent H=1/3. The results show that the deviation of real full developed atmopheric turbulence from Guassian distibution is very small, and the difference only occurs in the case of the high order scaling law.