应用小波分析研究湍流相干结构(Ⅰ) 小波分析辨识相干结构的能量最大准则  

DETERMINING COHERENT STRUCTURE WITH ENERGY MAXIMA CRITERION

作　　者：刘海峰 吴韬[1] 王辅臣[1] 龚欣[1] 于遵宏[1] 

机构地区：[1]华东理工大学资源与环境工程学院,上海200237

出　　处：《化工学报》2000年第6期761-765,共5页CIESC Journal

基　　金：国家重点基础研究发展规划项目!(G19990 2 2 10 3);高等学校骨干教师资助计划

摘　　要：根据对小波能谱的分析 ,提出了基于小波分析的辨识相干结构的能量最大准则 ,能分辨湍流信号中多个相近尺度的相干结构 ;根据对不同小波的计算 ,发现常用小波中以Morlet小波的分辨率最高 ,能有效地分辨基波与次谐波 ;并用模拟信号和圆形湍流射流边界层内的实验数据对上述结论进行了验证 .Wavelet analysis is a rapidly developing domain of applied mathematics. It has been used in turbulence, and several methods are presented to study the coherent structure in turbulence. In this paper, two conclusions are made from the relation between wavelet energy spectrum and Fourier energy spectrum. The first conclusion is that the peak height of wavelet energy spectra of sine and cosine waves is proportional to their scale, and the second is that the peak width of wavelet energy spectra of sine and cosine waves is proportional to their scale. Based on wavelet analysis and these two conclusions, a new energy maxima criterion of coherent structure, P(a m)/ a m=max a >0 P(a )/ a , where P is wavelet energy spectrum, which can extract several coherent structures of close scale in turbulence and determine their scales, is presented. At the same time, Morlet wavelet is found to have a higher resolution ratio than Mexican hat wavelet and some orthonormal wavelets, such as Daubechies, Symlets, Meyer and Coiflets, which can distinctly distinguish fundamental wave from subharmonic. So Morlet wavelet is much suited to detect coherent structure in turbulence. The new criterion is validated with simulative signals which are constructed by adding three kinds of noises with different energy spectra exponents (r=0, 1.00, 1.67) to y=sin(16π x )+sin(32π x ) and keeping the intensity of coherent structure about 0.1. The results show that the new criterion can distinguish fundamental wave from subharmonic based on simulative signals with a small coherent structure intensity. At last, the new criterion is validated with three-dimensional fluctuation velocities of a round jet flow near the nozzle exit. The results show that the scale of coherent structure determined by the new criterion is equivalent to the integral scale, and the coherent structure is a large vortex.

关 键 词：小波分析 湍流 相干结构 能谱 FOURIER分析 

分 类 号：O357.5[理学—流体力学] O174.2[理学—力学]