Stochastic generation of velocity fields to reproduce the energy spectrum in wall turbulence

Leveraging experimental measurements in rough-wall turbulent boundary layers that provided the spatial distribution and statistics of uniform momentum zones (UMZs), we previously introduced a stochastic model to generate two-dimensional modal velocity fields representative of the roughness sublayer and logarithmic region (Ehsani et al. 2024 a J. Fluid Mech. , vol. 979, p. A12; J. Fluid Mech. , 2024 b , vol. 999, p. A56). This synthetic flow comprises a streamwise concatenation of spatially correlated step-like velocity profiles, where each step corresponds to an internal shear layer separating UMZs, and the UMZs follow scaling consistent with wall-attached eddies. Here, we further develop the model to introduce small-scale swirling motions using vortex cores generated stochastically from previously published statistics and placed opportunistically with respect to the internal shear layers. Strategies are discussed to stretch and distribute vortices and extend the spatial resolution of the synthetic field to capture the smallest flow scales. The new synthetic fields for both laboratory and atmospheric settings reproduce with reasonable accuracy the second-order turbulence statistics and the energy spectrum for most of the inertial range, capturing, for the wind tunnel datasets, the transition to exponential decay up to