An explicit analytical expression for bed-load layer thickness based on maximum entropy principle

Kumbhakar, Manotosh; Kundu, Snehasis; Ghoshal, Koeli

doi:10.1016/j.physleta.2018.05.045

Cited by 18 publications

(9 citation statements)

References 47 publications

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“…By fitting Equation (11) with collected laboratory data, the value for η could be estimated. Figure 2 shows the comparison of the proposed 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. Table 2 lists the calculated R values between the Tsallis entropy based expression and each data set, as well as the values of the Lagrange multipliers λ 0 and λ 1 , and the fitting parameter η .…”

Section: Comparison With Laboratory Data Sets and Discussionmentioning

confidence: 99%

“…Table 2 lists the calculated R values between the Tsallis entropy based expression and each data set, as well as the values of the Lagrange multipliers λ 0 and λ 1 , and the fitting parameter η . Table 3 presents the comparison result (i.e., the calculated R value) among ten existing deterministic models, the Shannon entropy-based expression given by Kumbhakar et al [ 3 ] and each data set, as well as the Tsallis entropy-based expression.…”

Section: Comparison With Laboratory Data Sets and Discussionmentioning

confidence: 99%

“…Previous studies have indicated that the thickness of the bed-load movement is largely related to the dimensionless shear stress

[ 1 , 2 , 29 , 30 ]. Recently, Kumbhakar et al [ 3 ] put forward the following power-type hypothesis regrading CDF to be a good choice:

where

and

are upper and lower values of

, and η is a real parameter.…”

Section: Methodology For Determination Of the Bed-load Thicknessmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Kumbhakar et al [ 3 ] adopted the Shannon entropy concept to estimate the bed-load thickness in open channels, which motivates us to investigate the possibility of another more general form of entropy, Tsallis entropy, for evaluating the thickness of the bed-load layer. Therefore, this study attempts to propose an entropy-based formula for the bed-load layer thickness in open channels by adopting Tsallis entropy.…”

Section: Introductionmentioning

confidence: 99%

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

Zhu

2019

Entropy

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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.

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Section: Comparison With Laboratory Data Sets and Discussionmentioning

confidence: 99%

Section: Comparison With Laboratory Data Sets and Discussionmentioning

confidence: 99%

“…Previous studies have indicated that the thickness of the bed-load movement is largely related to the dimensionless shear stress

[ 1 , 2 , 29 , 30 ]. Recently, Kumbhakar et al [ 3 ] put forward the following power-type hypothesis regrading CDF to be a good choice:

where

and

are upper and lower values of

, and η is a real parameter.…”

Section: Methodology For Determination Of the Bed-load Thicknessmentioning