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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
Authors to whom correspondence should be addressed.
Entropy 2019, 21(2), 123;
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)
PDF [1719 KB, uploaded 29 January 2019]


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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