Comparative Study of Turbulent Coherent Structures Educed by Wavelet Transform, Proper Orthogonal Decomposition and Conditional Averaging

湍流剪切流中的相干结构具有低频调制。本文采用适当的正交分解和小波变换研究了湍流平面混合层的相干结构及其低频调制。本文还研究了紊流卡门涡街区紊流平面尾迹的低频调制。此外，还讨论了这两种方法在导出相干结构方面的有效程度。主要结果可以总结如下混合层中相干结构的基本性质可以用固有正交分解的第一特征函数来表示。第一个特征值占总动能的52%适当的正交分解不能提取混合层中心部分速度波动的相干性，这是由相干结构引起的。另一方面，小波变换确实提取了速度波动的相干性。对于速度波动，其功率谱与相干结构有一个显著的峰值，预计情况总是如此平面混合层中的相干结构经历了波长约为其波长6倍的大规模调制。我们发现复Morlet小波变换的模量可以有效地获得这些信息尾迹中卡门涡街的涡旋经历了波长约为涡街波长25倍的大规模调制。

Coherent structures in turbulent shear flows have low-frequency modulations. In this study the coherent structure in a turbulent plane mixing layr and its low-frequency modulation are studied by the proper orthogonal decomposition and the wavelet transform. The low-frequency modulation of the coherent structure is also studied for a turbulent plane wake in a region where the turbulent Karman vortex street prevails. Moreover, the extent to which the two methods are effective in educing the coherent structures are discussed. Main results may be summarized as follows.[1] The fundamental property of the coherent structure in the mixing layr can be represented by the first eigenfunction of the proper orthogonal decomposition. The first eigenvalue occupies 52% of the total kinetic energy.[2] The proper orthogonal decomposition fails to extract that coherent nature of the velocity fluctuations in the central part of the mixing layr which is due to coherent structure. On the other hand, the wavelet transform does extract the coherent nature of the velocity fluctuations. This is expected to be always the case for velocity fluctuations whose power spectrum has a significant peak associated with the coherent structures.[3] The coherent structure in the plane mixing layr experiences a large-scale modulation whose wavelength is approximately six times its wavelength. The modulus of the complex Morlet wavelet transform is found to be effective in obtaining this information.[4] The vortices in the Karman vortex street in the wake experiences a large-scale modulation whose wavelenth is approximately twenty-five times the wavelength of the vortex street.