Extraction of coherent structures in a rotating turbulent flow experiment.
Extraction of coherent structures in a rotating turbulent flow experiment.
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DOI：
10.1103/physreve.72.016311
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发表时间：
2004-10
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影响因子：
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通讯作者：
J. Ruppert-Felsot;O. Praud;E. Sharon;H. Swinney
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文献类型：
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作者：
J. Ruppert-Felsot;O. Praud;E. Sharon;H. Swinney
利用离散小波变换（DWT）和离散小波包变换（DWPT）提取和研究了湍流旋转流体中相干结构的动力学特性。三维湍流是通过旋转罐底部的管（48.4 cm高，39.4 cm直径）的强泵送产生的。该流动随着罐中高度的增加而朝向二维（2D）湍流发展。准二维流动的粒子图像测速仪测量揭示了许多长寿命的相干涡的尺寸范围很广。涡量场表现为涡的产生、合并、散射和破坏。通过对涡量场的DWT和DWPT系数进行阈值处理，将流分离为低熵的“相干”和高熵的“非相干”分量。类似的阈值使用傅立叶变换和JPEG压缩连同Okubo-Weiss标准也进行了测试进行比较。我们发现，小波变换和DWPT产生类似的结果，更有效地代表总流量比基于傅立叶的方法。只有约3%的DWT和DWPT的大振幅系数是必要的，以代表相干分量，并保持涡度概率分布函数（PDF），传输特性，以及空间和时间的相关性。其余的小振幅系数表示非相干分量，其具有接近高斯涡度PDF，不包含相干结构，在时间上迅速失去相关性，并且对流的输运性质没有显著贡献。这表明可以使用相对少量的小波或小波包模式来描述和模拟这种湍流。
The discrete wavelet transform (DWT) and discrete wavelet packet transform (DWPT) are used to extract and study the dynamics of coherent structures in a turbulent rotating fluid. Three-dimensional turbulence is generated by strong pumping through tubes at the bottom of a rotating tank (48.4 cm high, 39.4 cm diameter). This flow evolves toward two-dimensional (2D) turbulence with increasing height in the tank. Particle image velocimetry measurements on the quasi-2D flow reveal many long-lived coherent vortices with a wide range of sizes. The vorticity field exhibits vortex creation, merger, scattering, and destruction. We separate the flow into a low-entropy "coherent" and a high-entropy "incoherent" component by thresholding the coefficients of the DWT and DWPT of the vorticity field. Similar thresholdings using the Fourier transform and JPEG compression together with the Okubo-Weiss criterion are also tested for comparison. We find that the DWT and DWPT yield similar results and are much more efficient at representing the total flow than a Fourier-based method. Only about 3% of the large-amplitude coefficients of the DWT and DWPT are necessary to represent the coherent component and preserve the vorticity probability distribution function (PDF), transport properties, and spatial and temporal correlations. The remaining small-amplitude coefficients represent the incoherent component, which has near Gaussian vorticity PDF, contains no coherent structures, rapidly loses correlation in time, and does not contribute significantly to the transport properties of the flow. This suggests that one can describe and simulate such turbulent flow using a relatively small number of wavelet or wavelet packet modes.