Abstract Velocity distributions for open channel flows have been investigated using deterministic and probabilistic approaches. It is well known that the vertical velocity profiles in wide open channels (i.e. aspect ratio width/depth > 5) can be approximated by logarithmic velocity laws and power laws. Recently the entropy concept in the forms of Shannon entropy and Tsallis entropy has been employed to estimate velocity distributions in open channels with different aspect ratios. The accuracy of conventional velocity equations is highly dependent on their parameters that can only be estimated by empirical or semi-empirical analytical relations which requires either a good knowledge of velocity field and/or physical properties of the channel, such as topographic conditions, sedimentation conditions and boundary roughness. In contrast, the entropy based velocity distributions derived based on the least-biased probability density function (PDF) by treating time-averaged velocities as random variables are resilient regardless of the flow and channel conditions. However, a comparison of the velocity profiles computed using deterministic approaches and probabilistic approaches has not been rigorously conducted. Furthermore, the accuracy and reliability of associated velocity distribution equations have not been tested thoroughly using data sets collected using advanced techniques. This paper presents a comprehensive and comparative study to analyze the distinctions and linkages between four commonly used velocity laws and two entropy-based velocity distributions theoretically and quantitatively using selective laboratory and field measurements available in the literature, considering typical sedimentation and channel hydraulic conditions. Amongst all, Tsallis entropy based velocity distribution developed from a generalized form of informational entropy exhibits universal validity to sediment-laden flows in wide alluvial open channels, and is found to be superior to others to predict velocity profiles in large waterways with unmanageable rough beds.

中文翻译：

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基于一维熵的明渠流与常规确定性速度分布方程的比较研究

摘要 已使用确定性和概率方法研究了明渠流的速度分布。众所周知，宽阔通道中的垂直速度剖面（即纵横比宽度/深度> 5）可以通过对数速度定律和幂定律来近似。最近，香农熵和 Tsallis 熵形式的熵概念已被用于估计具有不同纵横比的明渠中的速度分布。传统速度方程的准确性高度依赖于它们的参数，这些参数只能通过经验或半经验分析关系来估计，这需要对速度场和/或通道的物理特性有很好的了解，例如地形条件、沉积条件和边界粗糙度。相比之下，通过将时间平均速度视为随机变量，基于最小偏置概率密度函数 (PDF) 导出的基于熵的速度分布具有弹性，而不管流量和通道条件如何。然而，尚未严格进行使用确定性方法和概率方法计算的速度剖面的比较。此外，相关速度分布方程的准确性和可靠性尚未使用使用先进技术收集的数据集进行彻底测试。本文提出了一项全面的比较研究，使用文献中可用的选择性实验室和现场测量，从理论上和定量地分析四种常用速度定律和两种基于熵的速度分布之间的区别和联系，考虑典型的沉积和河道水力条件。其中，从信息熵的广义形式发展而来的基于 Tsallis 熵的速度分布对宽阔的冲积明渠中的沉积物流动具有普遍的有效性，并且被发现在预测具有无法管理的粗糙床的大型水道中的速度剖面方面优于其他方法。