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

Leveraging on the spatial distribution and statistics of Uniform Momentum Zones (UMZs) attributes in rough wall turbulence, we were able to stochastically generate a 2D modal velocity field of the outer region (Ehsani et al., JFM 2024). The modal field results from the streamwise concatenation of correlated step-like velocity profiles, composed of vertically alternating UMZs separated by internal shear layers. First and second order statistics are used to compare the synthetic velocity field with the corresponding experimental datasets, along with the power spectrum of both streamwise and wall-normal velocity components, across a wide range of Reynolds numbers. One missing feature, which may be responsible for the underestimation of the Reynolds shear stress by our model, is the lack of swirling motions and vorticity outside of the shear layers. To implement this, we will first discuss the scaling and the distributions of both the size and azimuthal velocity of vortex cores extracted from our measurements in the outer region (Heisel et al. JFM 2021). Then, we will stochastically generate prograde and retrograde vortices and explore different strategies to stretch them and distribute them across the 2D generated modal velocity field, with increased spatial resolution. The overall contributions of UMZ and vortex cores to the Reynolds shear stress and turbulent kinetic energy in the logarithmic region of rough wall turbulent layers will be discussed.