Streamwise velocity profile in open-channel flow based on Tsallis relative entropy.

Abstract

The present study derives the two-dimensional distribution of streamwise flow velocity in open channels using the Tsallis relative entropy, where the probability density function (PDF) based on the principle of maximum entropy (POME) is selected as the prior PDF. Here, we incorporate the moment constraints based on the normalization constraint, hydrodynamic transport of mass, and momentum through a cross section of an open channel for the formulation of the velocity profile. The minimization of the Tsallis relative entropy produces a nonlinear differential equation for velocity, which is solved using a non-perturbation approach along with the Padé approximation technique. We define two new parameters in terms of the Lagrange multipliers and the entropy index for assessing the velocity profile, which are calculated by solving a system of nonlinear equations using an optimization method. For different test cases of the flow in open channels, we consider a selected set of laboratory and river data for validating the proposed model. Besides, a comparison is made between the present model and the existing equation based on the Tsallis entropy. The study concludes that the inclusion of the POME-based prior significantly improves the velocity profile. Overall, the proposed work shows the potential of the Tsallis relative entropy in the context of application to open the channel flow velocity.