基于经验小波变换的图像流分解
Image-based flow decomposition using empirical wavelet transform
摘要：
我们提出了一种基于图像的流分解，它是从二维（2D）张量经验小波变换（EWT）（Gilles 2013）发展而来的。我们的想法是分解的瞬时流量数据，或其可视化，自适应地根据平均傅立叶支持空间局部化结构的识别。由此产生的EWT模式代表分解的流，并且每个模式占频谱的一部分，说明了在原始流中叠加有不同尺度的流体物理。与所提出的方法，分解的瞬时三维流变得可行，而不诉诸其时间序列。例子首先集中在喷流和二维尾流之间的相互作用，只有实验可视化。所提出的方法能够分离射流/尾流及其不稳定性。然后将分解应用于早期边界层转捩，直接数值模拟提供了完整的数据集。试验输入为三维流场数据及其使用流向速度和λ2涡识别准则的可视化。对于这两种输入，EWT模式都能很好地提取出流向细长条纹、多重二次不稳定性和螺旋涡丝。从双全局稳定性分析的结果证明EWT模式，代表条纹不稳定性。相对于根据能量或频率提取空间模式的本征正交分解或动态模态分解，EWT提供了一种新的策略，从其空间尺度分解瞬时流。
英文摘要：
We propose an image-based flow decomposition developed from the two-dimensional (2D) tensor empirical wavelet transform (EWT) (Gilles 2013). The idea is to decompose the instantaneous flow data, or its visualisation, adaptively according to the averaged Fourier supports for the identification of spatially localised structures. The resulting EWT modes stand for the decomposed flows, and each accounts for part of the spectrum, illustrating fluid physics with different scales superimposed in the original flow. With the proposed method, decomposition of an instantaneous 3D flow becomes feasible without resorting to its time series. Examples first focus on the interaction between a jet plume and 2D wake, where only experimental visualisations are available. The proposed method is capable of separating the jet/wake flows and their instabilities. Then the decomposition is applied to an early stage boundary layer transition, where direct numerical simulations provided a full data-set. The tested inputs are the 3D flow data and its visualisation using streamwise velocity & λ2 vortex identification criterion. With both types of inputs, EWT modes robustly extract the streamwise-elongated streaks, multiple secondary instabilities and helical vortex filaments. Results from bi-global stability analysis justify the EWT modes that represent the streak instabilities. In contrast to Proper Orthogonal Decomposition or Dynamic Modal Decomposition that extract spatial modes according to energy or frequency, EWT provides a new strategy as to decompose an instantaneous flow from its spatial scales.
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