Drag Determination from Mean Velocity Profiles in Rough-Wall Boundary Layers

A method for determining the friction velocity in wall bounded flows over smooth surfaces has been extended for use with rough-wall boundary layers. The original method, developed and presented by Dixit et al. [Phys. Rev. Lett. 132, 014001 (2024)], requires only the local mean streamwise velocity profile, and is applicable to both zero pressure gradient (ZPG) and non-ZPG boundary layers. No fitting of the data to assumed profile shapes is required, and data from very near the wall is not needed. The present method replaces the kinematic viscosity of the fluid with an effective viscosity that is proportional to the product of the equivalent sandgrain roughness height for the surface and a local characteristic velocity. In all other ways, the present method is the same as the original. The method was tested using data from the literature that included flows in water and air, various roughness geometries, roughness heights ranging from 0.08 to 11.6 mm, and freestream velocities ranging from 0.5 to 24 m/s. The friction velocities determined with the new method were compared to the values determined in the various studies using established methods. For ZPG boundary layers, the match was within 10% in all cases, and within 5% for 87% of the velocity profiles considered. For favorable pressure gradient and moderate adverse pressure gradient cases the match was within 20% in nearly all cases. The new model did not fully capture the effect of strong adverse pressure gradients, but a correction is proposed for use in these cases. The new method is not expected to be as accurate as other methods in all cases. It might still prove useful, however, for providing at least an estimate and check of u_τ when the data and assumptions required for other methods are not available or applicable.