Velocity Distribution in Seepage-Affected Alluvial Channels Using Renyi Entropy

Abstract

Assuming time-averaged normalized velocity as a random variable, the present work developed a Renyi entropy-based model for deriving one-dimensional and two-dimensional velocity distributions in seepage-affected alluvial channels. The model requires the maximization of Renyi entropy using the principle of maximum entropy, subject to specified constraints. The derived velocity distributions can have maximum velocity on or below the free surface. The velocity distributions were evaluated with laboratory observations and were also compared with theoretical velocity distributions reported in the literature. The Renyi entropy-based 2D velocity distributions satisfactorily agreed with experimental data, and compared well with reported distributions. Also, the Renyi entropy provided more accurate 2D velocity distribution in the near-bed flow of seepage experiments than the other technique. The present paper concluded that the Renyi entropy model can be used to predict the velocity distribution in seepage flows.