Influence of the channel bed slope on Shannon, Tsallis, and Renyi entropy parameters

Abstract

Velocity distribution plays a fundamental role in understanding the hydrodynamics of open-channel flow. Among a multitude of approaches, the entropy-based approach holds great promise in achieving a reasonable characterisation of the velocity distribution. In entropy-based methods, the distribution depends on a key parameter, known as the entropy parameter (a function of the time-averaged mean velocity and maximum velocity), that relates to channel characteristics, such as channel roughness and channel bed slopes. The entropy parameter was regarded as constant for lack of experimental evidence, which would otherwise demonstrate if it had any correlation with channel properties. A series of experiments were conducted to collect velocity data in the laboratory flume for seven different values of the channel bed slope. The experimental data analysis revealed dissimilar fluctuations in entropy parameter values with varying bed slopes, with the lowest coefficient of variation in Renyi's (∼0.5%) and the highest in Shannon's case (∼10%). Performance evaluation of the predicted results substantiated good accuracy for all three entropies with the best results of Renyi entropy and lent strong support for using a constant (overall average) value of the entropy parameter for a specific channel cross-section rather than separate values for each channel bed slope. HIGHLIGHTS Verification of the influence of the channel bed slope on entropy parameters.; Velocity observations for mild, horizontal, and adverse channel bed slopes.; Shannon, Tsallis, and Renyi entropy-based velocity distributions.; Statistical and experimental evidence supporting the constant nature of all the entropy parameters.; Modified equation to estimate mean and maximum velocity ratio in terms of the Renyi entropy parameter.;

Keywords

• bed slope
• channel cross-section
• entropy parameter
• renyi entropy
• shannon entropy
• tsallis entropy