Comments on "turbulent velocity profile in fully-developed open channel flows"

In a recent paper published in this journal, Bonakdari et al. (Environ Fluid Mech 8:1-17, 2008) presented a new formulation of the vertical velocity profile in the central portion of steady fully developed turbulent open-channel flows which is based on an analysis of the Navier-Stokes equations. The predicted mean streamwise velocity profiles presented by the authors represent dip phenomenon (maximum velocity below the free surface). The discusser would like to point out some contradictions and an error in the main demonstration. This error appears in the right-hand side term of the main Eq. 22 (Environ Fluid Mech 8:1-17, 2008) in the parameter alpha. Our corrected demonstration shows that alpha is equal to ghsin theta/u(*)(2) and not to ghsin theta/u(*)(2) - 1 as obtained by the authors (Environ Fluid Mech 8:1-17, 2008). The values of alpha used by the authors are under-estimated by 1, this difference has a significant effect on velocities and therefore will involve a difference between measured and predicted velocity profiles. Finally, the assumption of partial derivative U/partial derivative z = 0 at the free surface is in contradiction with predicted velocity profiles.