Tsallis Entropy Based Velocity Distribution in Open Channel Flows

Abstract

The Tsallis entropy is applied to derive both 1-D and 2-D velocity distributions in an open channel cross section. These distributions contain a parameter m through which the Tsallis entropy becomes a generalization of the Shannon entropy. Different m parameter values are examined to determine the best value for describing the velocity distribution.Two Lagrangian parameters that are involved in the final form of 1-D velocity distribution equation are determined from observations of mean velocity and the maximum velocity at the water surface. For channels which are not wide and where the maximum velocity does not occur at the water surface, a 2-D velocity distribution is more appropriate. The Tsallis entropy is applied to derive 2-D velocity distributions. A new parameter M is introduced which represents the hydraulic characteristics of the channel. The derived velocity distributions are verified using both field data and experimental data. The advantages are found by comparing with Parandtl-von Karman, power law and Chiu’s velocity distributions.