Probabilistic approach to modeling of velocity distributions in fluid flows

This paper presents a synthesis of a probability-based approach and the underpinning, mathematical and philosophical foundations that have evolved to date, as well as applications in modeling of vertical and two-dimensional velocity distributions that have direct implications to measurements and estimation of transport of mass, momentum and energy in fluid flows. The approach draws inferences from a probability law identified by maximizing the information entropy under the constraints imposed by the available information. It gives predictions considered to be the most probable or objective on the basis of the available information. The probabilistic approach complements the deterministic approach of hydrodynamics. The difference in the point of view between the two approaches creates a different view about the available information. Some information, such as the location and magnitude of maximum velocity, the ratio of mean and maximum velocities, that may not appear to have direct use to the deterministic approach in flow predictions become important and useful to the probabilistic approach.