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Derivation of vertical concentration profile for nonuniform sediment in suspension using Shannon entropy

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  • Mohan, Shiv
  • Tsai, Christina W.

Abstract

This research paper introduces a novel methodology for quantifying the sediment concentration of nonuniform sediment in suspension within an open channel, employing the concept of Shannon entropy. By treating the normalized sediment concentration as a stochastic variable, a probability distribution function is formulated via the maximum entropy principle. The validity of the proposed cumulative distribution function is established through a comparison with empirical data. Additionally, the newly devised concentration profile for nonuniform suspended sediment is compared with the established deterministic concentration equation and experimental data on grain-size distribution. A relationship between model parameters and Rouse number for nonuniform sediment is also provided. This study’s significance lies in introducing a new way to understand nonuniform sediment transport and its behaviors. The utilization of Shannon entropy not only showcases the versatility of this technique but also underlines its potential for unraveling the complexities inherent in nonuniform sediment dynamics. This study is the first step to introduce the entropy notion in nonuniform sediment and encourages more research to improve it.

Suggested Citation

  • Mohan, Shiv & Tsai, Christina W., 2024. "Derivation of vertical concentration profile for nonuniform sediment in suspension using Shannon entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012158
    DOI: 10.1016/j.chaos.2023.114313
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    References listed on IDEAS

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    1. Kumbhakar, Manotosh & Tsai, Christina W., 2022. "A probabilistic model on streamwise velocity profile in open channels using Tsallis relative entropy theory," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Kumbhakar, Manotosh & Ghoshal, Koeli & Singh, Vijay P., 2017. "Derivation of Rouse equation for sediment concentration using Shannon entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 494-499.
    3. Kumbhakar, Manotosh & Tsai, Christina W., 2023. "Analytical modeling of vertical distribution of streamwise velocity in open channels using fractional entropy," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. D. Pal & K. Ghoshal, 2015. "Grain‐size distribution in open channel flow by mixing length approach," Environmetrics, John Wiley & Sons, Ltd., vol. 26(2), pages 107-119, March.
    5. Shang, Pengjian & Kamae, Santi, 2005. "Fractal nature of time series in the sediment transport phenomenon," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 997-1007.
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