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Estimating the Bed-Load Layer Thickness in Open Channels by Tsallis Entropy

Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China
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Entropy 2019, 21(2), 123; https://doi.org/10.3390/e21020123
Received: 20 December 2018 / Revised: 23 January 2019 / Accepted: 28 January 2019 / Published: 29 January 2019
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering II)
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Abstract

In the research field of river dynamics, the thickness of bed-load is an important parameter in determining sediment discharge in open channels. Some studies have estimated the bed-load thickness from theoretical and/or experimental perspectives. This study attempts to propose the mathematical formula for the bed-load thickness by using the Tsallis entropy theory. Assuming the bed-load thickness is a random variable and using the method for the maximization of the entropy function, the present study derives an explicit expression for the thickness of the bed-load layer as a function with non-dimensional shear stress, by adopting a hypothesis regarding the cumulative distribution function of the bed-load thickness. This expression is verified against six experimental datasets and are also compared with existing deterministic models and the Shannon entropy-based expression. It has been found that there is good agreement between the derived expression and the experimental data, and the derived expression has a better fitting accuracy than some existing deterministic models. It has been also found that the derived Tsallis entropy-based expression has a comparable prediction ability for experimental data to the Shannon entropy-based expression. Finally, the impacts of the mass density of the particle and particle diameter on the bed-load thickness in open channels are also discussed based on this derived expression. View Full-Text
Keywords: Tsallis entropy; probability distribution; bed-load; thickness; open channels Tsallis entropy; probability distribution; bed-load; thickness; open channels
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Zhu, Z.; Yu, J. Estimating the Bed-Load Layer Thickness in Open Channels by Tsallis Entropy. Entropy 2019, 21, 123.

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