Research Context
The velocity profile across an open channel is hard to estimate, particularly near the bed and at the free surface, where the usual laws break down.
Estimation of two-dimensional velocity distribution profile using general index entropy in open channels
Method
Treating velocity as a random variable, the two-dimensional velocity distribution is derived by maximising the General Index Entropy — a generalisation of Shannon entropy — under the principle of maximum entropy, combined with the cumulative distribution function of Marini et al. (2011).
Key Insights
- The model's parameters are less sensitive to flow conditions than in other entropy-based methods.
- It is simpler to apply, yet more accurate near both the channel boundaries and the free surface.
- Results compare well against several well-known experimental and field datasets.
Abstract
Estimation of velocity distribution profile is a challenging subject of open channel hydraulics. In this study, an entropy-based method is used to derive two-dimensional velocity distribution profile. The General Index Entropy (GIE) can be considered as the generalized form of Shannon entropy which is suitable to combine with the different form of Cumulative Distribution Function (CDF). Using the principle of maximum entropy (POME), the velocity distribution is defined by maximizing the GIE by treating the velocity as a random variable. The combination of GIE and a CDF proposed by Marini et al. (2011) was utilized to introduce an efficient entropy model whose results are comparable with several well-known experimental and field data. Consequently, in spite of less sensitivity of the related parameters of the model to flow conditions and less complexity in application of the model compared with other entropy-based methods, more accuracy is obtained in estimating velocity distribution profile either near the boundaries or the free surface of the flow.