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

Dixit et al. proposed an asymptotic drag scaling for zero-pressure-gradient flat-plate turbulent boundary layers based on the approximation M∼U_τ²δ, where M is the kinematic momentum rate through the boundary layer, U_τ 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∼U_τ²δf(Re_τ), where Re_τ=δU_τ/ν is the friction Reynolds number and f(Re_τ) is given analytically. Application of the correction to the dataset compiled by Dixit et al. shows that the corrected scaling gives an exponent closer to the asymptotic value −1/2 than the uncorrected formulation. The correction should be viewed as a leading-order amendment, since the derivation uses the logarithmic law outside its strict range of validity.