Non-uniform Sediment Transport and Time Scale Analysis in Unsteady and Non-equilibrium Conditions
Kuai, Zheng (Ken)
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While sediment transport in steady uniform flows has been studied extensively, significant amount of sediment movement occurs in unsteady flows. A nonhomogeneous discrete-time Markov chain model is proposed in this study to quantify the bedload discharges under unsteady flow conditions. The proposed two-state Markovian bedload model can be further extended to a three-state sediment transport model by adding a suspended load layer as the third state. As opposed to the homogenous two-state Markovian bedload models in literature, the proposed nonhomogeneous Markov chain model ensures the transition probabilities are really time dependent as they are function of local flow conditions. Furthermore, a full model of both the bedload and the suspended load that does not require an equilibrium sediment transport assumption can be achieved by adding a third layer (the suspended load layer) to the existing two-state model. The proposed stochastic sediment transport model can be used to calculate sediment discharges for an arbitrary size fraction of nonuniform sediment. Sediment transport processes vary at a variety of time scales – from seconds, hours, days to months and years. Recognizing the importance of different varying time scales in the fluvial processes of sediment transport, the Hilbert-Huang Transform method (HHT) is introduced to the field of sediment transport for the time scale analysis. The HHT uses the Empirical Mode Decomposition (EMD) method to decompose a time series into a collection of the Intrinsic Mode Functions (IMFs), and uses the Hilbert Spectral Analysis (HSA) to obtain instantaneous frequency data. The EMD extracts the variability of data with different time scales, and improves the analysis of data series. The HSA can display the succession of time varying time scales, which cannot be captured by the often-used Fast Fourier Transform (FFT) method. This study is one of the earlier attempts to introduce the state-of-the-art data analysis technique for the multiple time sales analysis of sediment transport processes. Three practical applications of the HHT method for data analysis of both suspended sediment and bedload transport time series are presented.