Two-dimensional distribution of streamwise velocity in open channel flow using maximum entropy principle: Incorporation of additional constraints based on conservation laws

Abstract

This study derived the vertical and transverse distribution of streamwise velocity in open channels using the information-theoretic concept involving the maximum entropy (MaxEnt) principle, moment constraints expressed by the conservation of mass, momentum, and energy and a hypothesis invoking the connection between probability and space domains through a generalized coordinate system. Explicit analytical solutions were obtained for velocity profiles using a non-perturbation approach along with Padé approximation. The convergence of the series solution was shown both theoretically and numerically. The Lagrange multipliers, arising through the application of MaxEnt principle, were obtained by minimizing a convex potential, and the quasi-Newton method along with BFGS scheme was applied for solving the unconstrained optimization problem. For applying the conservation laws, the momentum and energy coefficients were found to influence the velocity profile in a channel cross-section. With the expressions of these coefficients, the derived velocity equations were validated for a wide range of experimental and field data.