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.
Highlights
In the context of river dynamics, the investigation of the physical mechanism of non-cohesive sediment transport in open channels is a fundamental subject that has gained great attention from researchers (e.g., [1,2,3])
Assuming the dimensionless bed-load layer thickness, δ, defined by δ/d, where d is the particle diameter, to be a random variable, this study attempts to derive the mathematical formula for the Entropy 2019, 21, 123 thickness of the bed-load layer based on the Tsallis entropy theory
Tsallis entropy-based expression (Equation (12)), and ten existing deterministic models, as well as the Shannon entropy-based expression given by Kumbhakar et al [3], with six laboratory data sets
Summary
In the context of river dynamics, the investigation of the physical mechanism of non-cohesive sediment transport in open channels is a fundamental subject that has gained great attention from researchers (e.g., [1,2,3]). There are two different sediment movement forms: bed load and suspended load. The transport of bed-load is achieved via the main flow of the turbulent flow. Suspended load refers to those small-sized sediment particles that are suspended in the flow and are transported from the upstream of the river to the downstream [4]. The transport of suspended load is achieved by the fluctuating part of the turbulent flow. For bed-load discharge and suspended load discharge, completely different formulae have been developed for estimation [4,5]. It could be vital to determine suspended load and bed-load before estimating the total sediment discharge [4,5].
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