ABSTRACT
U y B w+ += + + ( )1 2κ Π κ
ln η (1)
In equation (1), y+ = y u*/ν and U+ =U/u*, where y is the normal distance from the bed and U is the mean streamwise velocity. Equation (1) includes the universal logarithmic law of the wall and it has been used for description of the mean velocity distributions in pipe and channel flows. In the classical definition of the law of the wall (Eq. 1), the coefficient κ = 0.41 is the well-known von Kármán constant and the constant B is dependent on geometry and bed conditions. In equation (1), w(η) denotes the wake function which accounts for the deviation from the logarithmic law, where η = y/δ and Π is parameter accounting for the strength of the wake. Determination of all parameters included in equation (1) has always been a matter of discussion and different values have been reported in the literature for flows
1 INTRODUCTION
Near-wall turbulence characteristics of open channel flow have been extensively studied because of their importance in providing engineering solutions for river restoration design and bed stability. In the classical turbulent boundary layer theory, the overall description of the flow is dependent on two separate sets of length and velocity scales. Near the bed, the viscous length scale ν/u* and friction velocity u w∗ = ( )τ ρ/ .0 5 are considered to be relevant flow scales. Here, τw is the wall shear stress, ρ is density and ν is kinematic viscosity of the fluid. In the outer region of the turbulent boundary layer, the effect of viscosity is insignificant and the appropriate length and velocity scales are the boundary layer thickness δ and the free stream velocity Ue. The velocity profile in uniform open channel flow can be described by:
in pipes, channels, turbulent boundary layers and open channels. Some of the uncertainties associated with estimation of the friction velocity are due to the experimental difficulties of obtaining accurate velocity measurements near the solid boundaries. As such, determination of the exact vertical location also becomes difficult. Contaminated near-bed velocity measurements could potentially overestimate the turbulence intensities, friction velocity and wall shear stress. The problem becomes more serious as Reynolds number increases and if the wall is rough. Recent studies by George (2007), Nagib & Chauhan (2008) have reported that values of κ and B remain non-universal and vary with Reynolds number. To overcome the experimental difficulties in evaluating the parameters in equation (1), a new diagnostic plot was proposed by Alfredsson et al. (2010). The diagnostic plot has been used to assess the validity of the velocity measurements without having to determine either the position with respect to the wall or the friction velocity. This new tool has been shown by Alfredsson et al. (2012) to work well for velocity distributions in turbulent boundary layer and channel flows. In this paper, we investigate the applicability of the diagnostic plot for the cases of uniform and non-uniform smooth open channel flow.
