Estimation of two-dimensional velocity distribution profile using General Index Entropy in open channels

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.