Asymptotic scaling of drag in flat-plate turbulent boundary layers

Abstract

A new asymptotic -1/2 power-law scaling is derived from the momentum integral equation for the drag in flat-plate turbulent boundary layers. In the limit of infinite Reynolds number, the appropriate velocity scale for drag is found to be M/ν, where M is the boundary layer kinematic momentum rate and ν is the fluid kinematic viscosity. Data covering a wide range of Reynolds numbers remarkably collapse to a universal drag curve in the new variables. Two models, discrete and continuous, are proposed for this universal drag curve, and a robust drag estimation method, based on these models, is also presented.