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首先利用子波(Wavelet)WTMM理论对Rayleigh-Bénard(R-B)对流温度信号的多分形特性进行了分析,然后采用本文给出的子波反演公式,不加入任何门限地提取了该信号的相干结构。在此基础上,通过对本文定义的一个非相干结构信号的分形特性研究,来反映出相干结构对多分形特性的影响。研究结果表明:代表大尺度运动的相干结构对小尺度上体现出来的多分形谱D(h)几乎没有影响,在这个意义上讲,分形谱D(h)具有不变性。
Firstly, the multi-fractal characteristics of Rayleigh-Bénard (RB) convection temperature signal are analyzed by Wavelet WTMM theory. Then the wavelet inversion formula given in this paper is used to extract the coherence of the signal without adding any threshold structure. On the basis of this, we study the fractal characteristics of a non-coherent structure signal defined in this paper to reflect the influence of coherent structure on the multifractal characteristics. The results show that the fractal spectrum D (h) has invariance in the sense that the coherent structure that represents large-scale motion has little effect on the multi-fractal spectrum D (h) at small scale.