On the scaling and distribution of prograde vortices in wall turbulence

Prograde vortex cores and internal shear layers were identified and analyzed across a set of smooth and rough wall turbulent boundary layer experiments extending up to the atmospheric surface layer. The main focus is on the scaling of  vortex cores and of their azimuthal velocity. Evidence suggests that the diameter of the largest spanwise vortices identified in the velocity field is comparable to the Taylor microscale λ_T, while their azimuthal velocity is governed by the shear velocity u_τ. This emerging scaling is consistent with the average thickness and velocity jump across the internal shear layers, which tend to overlap with organized  prograde vortices. Results highlight the relevance of the large-eddy turnover time and of the interaction between uniform momentum zones, internal shear layers and prograde vortices. A dynamic equilibrium is  inferred to govern the stretching of the vortices at the rate proportional to the attached-eddy time scale associated with the uniform momentum zones confining them. The persistence of u_τ scaling in shear layers and vortex azimuthal velocity, and of the interaction with wall-distance-dependent uniform momentum zone provide phenomenological explanation of why these coherent features are key to the structure of the mean velocity profile.