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An Expression for Velocity Lag in Sediment-Laden Open-Channel Flows Based on Tsallis Entropy Together with the Principle of Maximum Entropy

1
Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China
2
Department of Civil and Environmental Engineering, Nagaoka University of Technology 1603-1, Kami-Tomioka, Nagaoka 940-2188, Japan
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(5), 522; https://doi.org/10.3390/e21050522
Received: 3 April 2019 / Revised: 16 May 2019 / Accepted: 22 May 2019 / Published: 23 May 2019
In the context of river dynamics, some experimental results have shown that particle velocity is different from fluid velocity along the stream-wise direction for uniform sediment-laden open-channel flows; this velocity difference has been termed velocity lag in the literature. In this study, an analytical expression for estimating the velocity lag in open-channel flows was derived based on the Tsallis entropy theory together with the principle of maximum entropy. The derived expression represents the velocity lag as a function of a non-dimensional entropy parameter depending on the average and maximum values of velocity lag from experimental measurements. The derived expression was tested against twenty-two experimental datasets collected from the literature with three deterministic models and the developed Shannon entropy-based model. The Tsallis entropy-based model agreed better with the experimental datasets than the deterministic models for eighteen out of the twenty-two total real cases, and the prediction accuracy for the eighteen experimental datasets was comparable to that of the developed Shannon entropy-based model (the Tsallis entropy-based expression agreed slightly better than the Shannon entropy-based model for twelve out of eighteen test cases, whereas for the other six test cases, the Shannon entropy-based model had a slightly higher prediction accuracy). Finally, the effects of the friction velocity of the flow, the particle diameter, and the particles’ specific gravity on the velocity lag were analyzed based on the Tsallis entropy-based model. This study shows the potential of the Tsallis entropy theory together with the principle of maximum entropy to predict the stream-wise velocity lag between a particle and the surrounding fluid in sediment-laden open-channel flows. View Full-Text
Keywords: Tsallis entropy; velocity lag; sediment-laden flow; open channels Tsallis entropy; velocity lag; sediment-laden flow; open channels
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Zhu, Z.; Yu, J.; Dou, J.; Peng, D. An Expression for Velocity Lag in Sediment-Laden Open-Channel Flows Based on Tsallis Entropy Together with the Principle of Maximum Entropy. Entropy 2019, 21, 522.

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