应用小波分析研究湍流相干结构(Ⅱ) 相干结构波形的重构及局部奇异性分析

COHERENT STRUCTURE OF TURBULENCE BASED ON WAVELET ANALYSIS (Ⅱ) WAVE SHAPE AND LOCAL SINGULARITY OF COHERENT STRUCTURE

基于对小波变换的分析 ,确定了能较准确地反映信号振幅的相干结构波形重构公式 .采用Morlet小波能有效地重构出不受基波干扰的次谐波波形 .结合Morlet小波分辨率高的优点和正交小波正交性的优点 ,提出了实际含噪声信号中相干结构波形的重构公式 ,既可重构出次谐波的波形 ,又可排除高频噪声的干扰 .提出了基于小波分析的湍流中相干结构局部奇异性分析的研究方法 ,可以计算相干结构的结构指数 .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 .

The wave shape of coherent structure in turbulence can be reconstructed with inverse wavelet transform according to its scale. A new equation, which can more truly reconstruct the amplitude of coherent structure, is presented on the based of the analysis of wavelet transform. Morlet wavelet has a high resolution and can distinguish fundamental wave from subharmonic, however, it can not eliminate the disturbance of high frequency signals. The resolution of orthonormal wavelet is low, but it can eliminate the disturbance of high frequency signals without any other digital filter due to its orthogonality. Therefore, a new equation is presented utilizing the peculiarities of Morlet wavelet and orthonormal wavelet, which is f(x,a)=1H Ψ 1Ψ 2 ∫ +∞ -∞ (W Ψ 1 f)(b,a) Ψ 2a,b (x)1a d b, where a=a m,Ψ 1 is Morlet wavelet,Ψ 2 is a orthonormal wavelet. This equation can not only reconstruct the wave shape of subharmonic, but also overcome the interference of high frequency noise. Based on the character of wavelet analysis, a research method of local singularity of coherent structure is presented. In this method, local intermittency measure of a orthonormal wavelet at coherent structure scale is used to determine the position of a singularity in the coherent structure, and the Mexican hat wavelet modulus at the neighborhood of half the scale of coherent structure is used to calculate every exponent. At last all exponents are averaged by α= ?α(x i)? i . This algorithm can calculate the structure exponent of coherent structure in turbulence. The conclusions are validated with simulative signal and the results show that the reconstruction equation can be used to truly reconstruct the wave shape and amplitude of coherent structure and be used to calculate the structure exponents of coherent structure, though there is strong disturbance of high frequency signals. At last, the conclusions are validated with three-dimensional fluctuation velocities of a round jet flow near the nozzle exit. The results show that the structure exponent of coherent structure is about 1.6.