Derivation of 2D Velocity Distribution in Watercourses Using Entropy

Abstract

Existing entropy-based methodologies for deriving two-dimensional (2D) velocity distributions in open-channel flow are based on the extension of one-dimensional (1D) formulations. Such extensions contain too many parameters and require either experimental calibration or that velocity be known at several points. This information is not always available or does not apply under some particular conditions. Following the approach developed for a rectangular cross section, this paper develops an entropy-based method for deriving a 2D velocity distribution for a generic-shaped cross section. The derived distribution is parsimonious and can be applied to natural watercourses, which usually do not have a regular cross section. The model is consistent with previous results because the velocity distribution for a simple domain can be derived as a particular case of a more complex domain. The method was validated against velocity data collected in almost 200 data series along three rivers. The velocities calculated by the new method were found to be in good agreement with measured data. The results were also compared with two methods available in the literature. One of these methods showed better performance than the proposed model, although it requires much more information.