Stochastic generation and organization of uniform momentum zones in rough wall turbulence

Stochastically generated instantaneous velocity profiles are used to reproduce the outer region of rough-wall turbulent boundary layers over a range of Reynolds numbers extending from wind tunnel to field conditions. Each profile consists in a sequence of steps defined by modal velocities reproducing uniform momentum zones (UMZs), separated by velocity jumps reproducing the internal shear layers. Each UMZ is described by a minimal set of attributes: thickness, elevation, streamwise (modal) and vertical velocities. The ensemble of all velocity profiles allows to reproduce rough wall turbulence statistics and attached eddy scaling, consistent with the experimental datasets. These independent profiles are reorganized in the streamwise direction to synthesize a spatially consistent modal velocity field based on their cross correlation with respect to the initial, or prior, velocity profile. This operation, which can be implemented in space or time, allows to stretch or compress the velocity field based on the total number of profiles to reorder. By imposing the velocity auto-correlation to be consistent with experimental results, a physically based resolution Δx (or Δt),), is introduced and the inertial range of the velocity power spectrum is recovered. The findings are validated through comparison with hot-wire and PIV obtained from wind-tunnel experiments, along with sonic anemometry and super-large-scale particle image velocimetry (SLPIV), from the atmospheric surface layer.