Reconsideration of the overlap region in smooth shallow open channel flows

Abstract

In this paper, data sets for mean velocity distributions in smooth shallow open channel flow are reconsidered to evaluate the characteristics of the overlap region and estimate the friction velocity (u∗). Both new and existing velocity measurements are used in the analysis. The velocity profiles are obtained using laser Doppler velocimetry and particle image velocimetry at typical Reynolds numbers (20 000–60 000) achieved in laboratory flumes. Validation of the estimated u∗ values using different forms of power law is established by comparing these values with the ones available in literature. Also, the Reynolds shear stress distribution based on two-dimensional measurements validate the estimated u∗. The availability of new data sets allows one to verify the usefulness of the log-law and evaluate the log-law constants. Different fitting methods; least squares, derivative, and scattered methods are used to evaluate the value of von Kármán coefficient. It is found that the value of κ obtained from the least squares method varies between 0.35 and 0.51 and depends on the Reynolds number. This refutes the conventional constant value assumption for the von Kármán coefficient (κ = 0.41). By considering the Prandtl’s mixing-length theory, the present values of the von Kármán coefficient are used to evaluate the mixing length distributions. The mixing length distributions in smooth open channel flow are found to depend on Reθ.