Entropy Theory for Two-Dimensional Velocity Distribution

Abstract

Assuming time-averaged velocity as a random variable, this study develops an entropy theory for deriving two-dimensional (2D) distribution of velocity in open channels. The theory comprises five parts: (1) Tsallis entropy; (2) principle of maximum entropy (POME); (3) specification of information on velocity in terms of constraints; (4) maximization of entropy; and (5) derivation of the probability distribution of velocity. The entropy theory is then combined with a hypothesis on the cumulative distribution function of velocity in terms of flow depth to derive a 2D velocity distribution. The derived distribution is tested using field as well as laboratory observations reported in the literature and is compared with known velocity distributions. Agreement between velocity values computed using the entropy-based distribution and observed values is found satisfactory. Also, the derived distribution compares favorably with known distributions.