Entropy Theory for Two-Dimensional Velocity Distribution

Luo, Hao; Singh, Vijay P.

doi:10.1061/(asce)he.1943-5584.0000319

Cited by 81 publications

(44 citation statements)

References 30 publications

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“…Chiu and his associates (Chiu 1987;Chiu 1989;Chiu and Tung 2002) have derived the probability density function for velocity and using the POME, they derived the models for mean velocity distribution, turbulent shear stress distribution and particle suspension concentration distribution. Later on, Singh (1997), Singh (1998), Singh (2010), Singh (2011), Luo and Singh (2011) and Singh and Luo (2011) performed a lot of studies on velocity of an open channel flow on the basis of Shannon entropy and Tsallis entropy theory developed by Tsallis (1988) and Gell-Mann and Tsallis (2004). Recently Kumbhakar and Ghoshal (2016a) and Kumbhakar and Ghoshal (2016b) studied one and two dimensional velocity distributions in open channels using Renyi entropy theory respectively.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Velocity-Dip-Position at the Central Section of Open Channels using Entropy Theory

Kundu

2017

JAFM

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An analytical model to predict the velocity-dip-position at the central section of open channels is presented in this study. Unlike the previous studies where empirical or semi-empirical models were suggested, in this study the model is derived by using entropy theory. Using the principle of maximum entropy, the model for dip-position is derived by maximizing the Shannon entropy function after assuming dimensionless dipposition at the central section as a random variable. No estimation of empirical parameter is required for calculating dip-position from the proposed model. The model is able to predict the location of maximum velocity at the central section of an open channel with any aspect ratio. The developed model of velocity-dipposition is tested with experimental data from twenty-two researchers reported in literature for a wide range of aspect ratio. The model is also compared with other existing empirical models. The present model shows good agreement with the observed data and provides least prediction error compared to other models.

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Section: Introductionmentioning

confidence: 99%

Prediction of Velocity-Dip-Position at the Central Section of Open Channels using Entropy Theory

Kundu

2017

JAFM

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“…In the area of water resources (SINGH, 1997;HUSAIN, 1989), in the application in hydrology (WANG;ZHU, 2001;SINGH, 1998), in historical series of precipitation and flow, mainly. In the prediction of hydrological variables (CONTE, 2005;WEIJS et al, 2010), in the evaluation of the prediction and stability of river flows (MUKHOPADHYAY; KHAN, 2015), in the estimation of the sediment concentration (SINGH; CUI, 2015;CUI;SINGH, 2014;GAN et al, 2014;LIEN;TSAI, 2003;CHIU et al, 2000;LUO;SINGH, 2011;GOMEZ;PHILLIPS, 1999;SING et al, 1988;CHIU, 1988;CHAO-LIN CHIU, 1987;KRSTANOVIC, 1987), in the estimation of the precipitation ratio X flow (SINGH, 2012;CONTE, 2005;SONUGA, 1976), in river processes (XU; ZHAO, 2013;DESHPANDE;KUMAR, 2013), among other applications.…”

Section: Application Of Entropy In Hydrology and Hydraulicsmentioning

confidence: 99%

Principle of maximum entropy in the estimation of suspended sediment concentration

Martins

Poleto

2017

RBRH

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The concern with water quality has been promoting development of better monitoring and control techniques every day. As sediments transport most of water contaminants, their study is fundamental. Given the large number of variables for estimating sediment concentration and high costs of monitoring campaigns, it becomes necessary to develop more accessible methods which bring satisfactory practical results. Therefore, this work deals with application of the principle of maximum entropy, a probabilistic method to determine concentration of sediments in river channels with various concentrations and particle sizes. For this purpose, it was proposed a relationship between the theory of entropy parameters in order to reduce the computational effort. The results were satisfactory at concentrations above 10 g/L with R 2 greater than 0.88. The calculated squared errors in this study were lower than those found when using the theory of entropy by Tsallis and the equation of Rouse, classic models for determining the sediment concentration profile. The applicability of the proposed model and the ease of using the probabilistic method, since it reduces the amount of data needed to perform the estimate, makes it feasible on a global scale.Keywords: Sedimentology; Water resources; Modeling. RESUMOA preocupação com a qualidade das águas vem promovendo o desenvolvimento de técnicas cada dia melhores de monitoramento e controle. Como os sedimentos transportam a maior parte dos contaminantes da água, seu estudo é fundamental. Diante do elevado número de variáveis existentes para a estimativa da concentração de sedimentos e elevados custos de campanhas de monitoramento, torna-se necessário o desenvolvimento de métodos mais acessíveis e que tragam resultados práticos satisfatórios. Para tanto, este trabalho trata da aplicação do princípio da entropia máxima, um método probabilístico, para determinar a concentração de sedimentos em calhas com diversas concentrações e granulometrias. Para isso, foi proposta uma relação entre os parâmetros do princípio da entropia máxima para determinar o índice entrópico e facilitar o cálculo. Os resultados mostraram-se satisfatórios para concentrações acima de 10 g/L com R 2 superiores a 0,88. Os erros quadráticos calculados neste trabalho foram inferiores aos encontrados quando utilizada a teoria da entropia por Tsallis e pela Equação de Rouse, modelos clássicos de estimativa do perfil de concentração de sedimentos. A aplicabilidade do modelo proposto e a facilidade da utilização do método probabilístico, já que reduz a quantidade de dados necessários para realizar a estimativa, torna-o viável em escala global.Palavras-chave: Sedimentologia; Recursos hídricos; Modelagem.RBRH, Porto Alegre, v. 22, e23, 2017Principle of maximum entropy in the estimation of suspended sediment concentration

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“…Alternatively, a two‐dimensional velocity distribution developed by Chiu [] based on the probabilistic principle of maximum entropy is parameterized to fit a variety of flow profile shapes [ Chiu and Chen , ; Chiu and Hsu , ; Chen and Kao , ], including a partially mixed estuary [ Chen and Chiu , ]. The original velocity distribution of Chiu [] was derived with Shannon entropy [ Shannon , ] and recently the Tsallis entropy expression [ Tsallis , ] has been used to formulate a similar two‐dimensional velocity distribution which provides comparable results [ Luo and Singh , ]. Based on the entropy theory, a linear relationship exists between mean channel velocity and the maximum velocity in the channel, allowing discharge to be estimated from a single velocity measurement [ Xia , ; Moramarco et al ., ].…”

Section: Introductionmentioning

confidence: 99%

An entropy‐based surface velocity method for estuarine discharge measurement

Bechle

2014

Water Resources Research

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An entropy-based method is developed to estimate estuarine river discharge from surface velocity measurements. A two-dimensional velocity profile based on the principle of maximum entropy is employed to express the mean velocity as a function of average surface velocity. The entropy-based flow profile is parameterized by the location of maximum velocity in the channel and the shape of the velocity distribution. The entropy parameters are quantified over the tidal cycle to account for the unsteady nature of estuarine flow. The method was tested using experiments conducted at the Danshui River, the largest estuarine system in Taiwan. Surface velocities were measured using an Automated River-Estuary Discharge Imaging System (AREDIS), and full-channel velocity profiles were measured with a moving-boat ADP survey. Entropy parameters were calibrated over the tidal cycle and linearly correlated with the average surface velocity to facilitate estimation from AREDIS measurements. The discharge calculated from average surface velocity and entropy relationships exhibits a 7.7% relative error compared to the ADP velocity profiles. The error nearly doubles when the mean values for entropy parameters are used instead of the variable parameters, indicating the importance of accounting for the unsteady nature of estuarine flows. Furthermore, the effects of measurement coverage area, types of entropy distribution, and wind-induced drift current on the surface velocity-based discharge measurement are evaluated and discussed. Overall, surface velocity measurements in conjunction with the entropy profiles well represent the flow in a complex estuarine environment to provide a reliable estimate of discharge.

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Entropy Theory for Two-Dimensional Velocity Distribution

Cited by 81 publications

References 30 publications

Prediction of Velocity-Dip-Position at the Central Section of Open Channels using Entropy Theory

Prediction of Velocity-Dip-Position at the Central Section of Open Channels using Entropy Theory

Principle of maximum entropy in the estimation of suspended sediment concentration

An entropy‐based surface velocity method for estuarine discharge measurement

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