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On the role of Tsallis entropy index for velocity modelling in open channels

Author

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  • Kumbhakar, Manotosh
  • Ray, Rajendra K.
  • Ghoshal, Koeli
  • Singh, Vijay P.

Abstract

Following the work on Shannon entropy together with the principle of maximum entropy, Luo and Singh (2010) and Singh and Luo (2011) explored the concept of non-extensive Tsallis entropy for modelling velocity in open channels. Later, the idea was extended by Cui and Singh (2012, 2013) by hypothesizing an accurate cumulative distribution function (CDF). However, these studies estimated the entropy index through a data-fitting procedure and the values of the index were different for different studies. The present study investigates the role of Tsallis entropy index for modelling velocity in open channels using the method of moments, based on conservation of mass and momentum. It is found that the entropy index depends on the normalized mean velocity and the momentum coefficient. In addition to the physical meaning of the index, it is also found that the modified velocity profile significantly improves for both wide and narrow channels, as shown by small predicted velocity errors. The proposed approach may be further employed for other open channel flow problems, such as sediment concentration, and shear stress distribution.

Suggested Citation

  • Kumbhakar, Manotosh & Ray, Rajendra K. & Ghoshal, Koeli & Singh, Vijay P., 2020. "On the role of Tsallis entropy index for velocity modelling in open channels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    • Handle: RePEc:eee:phsmap:v:557:y:2020:i:c:s0378437120304660
    DOI: 10.1016/j.physa.2020.124901
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    Cited by:

    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).

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