The velocity profile of an open channel is an important research topic in the context of open channel hydraulics; in particular, the velocity-dip position has drawn the attention of hydraulic scientists. In this study, analytical expressions for the velocity-dip position over the entire cross section and at the centerline of a rectangular open channel are derived by adopting probability methods based on the Tsallis and general index entropy theories. Two kinds of derived entropy-based expressions have the same mathematical form as a function of the lateral distance from the sidewall of the channel or of the aspect ratio of the channel. Furthermore, for the velocity-dip position over the entire cross section of the rectangular open channel, the derived expressions are compared with each other, as well as with two existing deterministic models and the existing Shannon entropy-based expression, using fifteen experimental datasets from the literature. An error analysis shows that the model of Yang et al. and the Tsallis entropy-based expression predict the lateral distribution of the velocity-dip position better than the other proposed models. For the velocity-dip position at the centerline of the rectangular open channel, six existing conventional models, the derived Tsallis and general index entropy-based expressions, and the existing Shannon entropy-based models are tested against twenty-one experimental datasets from the literature. The results show that the model of Kundu and the Shannon entropy-based expression have superior prediction accuracy with respect to experimental data compared with other models. With the exception of these models, the Tsallis entropy-based expression has the highest correlation coefficient value and the lowest root mean square error value for experimental data among the other models. This study indicates that the Tsallis entropy could be a good addition to existing deterministic models for predicting the lateral distribution of the velocity-dip position of rectangular open channel flow. This work also shows the potential of entropy-based expressions, the Shannon entropy and the Tsallis entropy in particular, to predict the velocity-dip position at the centerline of both narrow and wide rectangular open channels.

中文翻译：

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评估确定矩形明渠整个横截面和中心线上速度倾角位置的不同方法


明渠速度剖面是明渠水力学领域的一个重要研究课题；尤其是速倾位置引起了水利科学家的注意。本研究采用基于 Tsallis 和一般指数熵理论的概率方法推导了矩形明渠整个断面和中心线处的速度倾角位置的解析表达式。两种导出的基于熵的表达式具有相同的数学形式，作为距通道侧壁的横向距离或通道的纵横比的函数。此外，对于矩形明渠整个横截面上的速度倾角位置，使用来自文学。误差分析表明，Yang 等人的模型。基于 Tsallis 熵的表达式比其他提出的模型更好地预测了速度倾角位置的横向分布。对于矩形明渠中心线的速度倾角位置，针对文献中的 21 个实验数据集测试了 6 个现有的常规模型、导出的 Tsallis 和一般指数熵表达式以及现有的基于香农熵的模型。结果表明，与其他模型相比，Kundu模型和基于香农熵的表达式对于实验数据具有更高的预测精度。 除这些模型外，其他模型中基于 Tsallis 熵的表达式对于实验数据具有最高的相关系数值和最低的均方根误差值。这项研究表明，Tsallis 熵可以成为现有确定性模型的一个很好的补充，用于预测矩形明渠流的速度倾角位置的横向分布。这项工作还展示了基于熵的表达式（特别是香农熵和 Tsallis 熵）在预测窄和宽矩形明渠中心线的速度倾角位置方面的潜力。