Entropy Theory for Distribution of One-Dimensional Velocity in Open Channels

Abstract

Assuming time-averaged velocity as a random variable, this study develops an entropy theory for deriving the one-dimensional distribution of velocity in open channels. The theory includes five parts: (1) Tsallis entropy; (2) the principle of maximum entropy (POME); (3) the specification of information on velocity for constraints; (4) the maximization of entropy; and (5) the probability distribution of velocity and its entropy. An application of the entropy theory is illustrated by deriving a one-dimensional velocity distribution in open channels in which the dimension is vertical or the flow depth. The derived distribution is tested with field and laboratory observations and is compared to Chiu’s velocity distribution derived from Shannon entropy. The agreement between velocity values are computed with the entropy-based distribution.