On the Role of Tsallis Entropy Index for Velocity Modelling in Open Channels

TL;DR

This paper explores how the Tsallis entropy index influences velocity modeling in open channels, revealing its dependence on flow parameters and demonstrating improved velocity predictions over traditional methods.

Contribution

It introduces a method to determine the Tsallis entropy index using the method of moments, linking it to physical flow parameters and enhancing velocity profile accuracy.

Findings

Entropy index depends on normalized mean velocity and momentum coefficient.

Modified velocity profiles show significant improvement in accuracy.

The approach can be extended to other open channel flow problems.

Abstract

Following the work on Shannon entropy together with the principle of maximum entropy, Luo & Singh (J. Hydrol. Eng., 2011, 16(4): 303-315) and Singh & Luo (J. Hydrol. Eng., 2011, 16(9): 725-735) explored the concept of non-extensive Tsallis entropy for modelling velocity in open channels. Later, the idea was extended by Cui & Singh (J. Hydrol. Eng., 2013, 18(3): 331-339; 2014, 19(2): 290-298) 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.