Wall Similarity in Turbulent Open-Channel Flow

Abstract

The present work demonstrates that the assumption of wall similarity in the equilibrium region of open channels leads to the definition of a constant, universal value for the normalized vertical flux of turbulent kinetic energy irrespective of wall roughness. Moreover, by additionally assuming a gradient-flux model for the turbulent kinetic energy, its bed-normal distribution is easily estimated by an expression with parameters that rely on a physical basis. Turbulence measurements performed in smooth-, transitionally rough-, and fully rough-bed (sandgrain) open channels confirm this hypothesis, providing at the same time an alternative way of determining the lower and upper limits of the intermediate region. Finally, based upon wall-similarity assumptions, a new methodology is proposed for estimating mean bed-shear velocities (stresses) in free-surface flows at high local and global Reynolds numbers, irrespective of roughness condition at the bed.