A Correction Term for the Asymptotic Scaling of Drag in Flat-Plate Turbulent Boundary Layers

Dixit et al. proposed an asymptotic drag scaling method for zero-pressure-gradient flat-plate turbulent boundary layers based on the approximation M∼Uτ2δ, where M is the kinematic momentum rate through the boundary layer, Uτ is the friction velocity, and δ is the boundary-layer thickness. In the present paper, an explicit Reynolds-number-dependent correction to this approximation is derived from the logarithmic mean-velocity profile. Integration of the log law across the layer yields M∼Uτ2δf(Reτ), where Reτ=δUτ/ν is the friction Reynolds number and f(Reτ) is given analytically. Application of the correction to the dataset compiled by Dixit et al. shows that the corrected scaling gives an exponent consistent with the asymptotic value −1/2 within bootstrap confidence intervals, whereas the uncorrected formulation does not. The correction should be viewed as a leading-order amendment, since the derivation uses the logarithmic law outside its strict range of validity.