Analysis of shallow turbulent flows using the Hilbert-Huang transform: a tool for exploring the characteristics of turbulence and coherent flow structures
Abstract
The Hilbert-Huang transform (HHT) is a method of spectral analysis that is suitable for application to nonstationary and non-linear signals that holds enormous potential for the analysis of turbulent flows in fluvial, aeolian, and coastal systems. HHT begins with decomposition of the signal into Intrinsic Mode Functions (IMFs) using the Empirical Mode Decomposition method. A Hilbert transform is then applied to each IMF, enabling the calculation of the local spectral characteristics of the signal. Four applications of the HHT are used to demonstrate the utility of this method for spectral analysis of turbulent flows. The method is applied to: (1) velocity measurements of unidirectional flow with high suspended sediment concentration (laboratory), (2) velocity measurements from a combined uni-i-direction and wave flow over a mobile, evolving bed (laboratory), and (3) temperature measurements from the mixing interface of a large river confluence (field). Comparisons among HHT, Fourier, and wavelet analysis are provided, and we identify a number of major benefits of HHT based on these four applications. The results presented show that the spectral method of HHT provides a very useful tool for analysis of turbulence in natural flows and can greatly enhance signal analysis in addition to traditional methods such as Fourier and wavelet analysis.
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