A stochastic modeling framework to generate 2-D rough-wall high-Reynolds-number turbulent boundary layers

Abstract

Atmospheric surface layer flows are computationally challenging, predominantly due to surface roughness and the high Reynolds number, both of which demand exceptionally high spatial resolution in the near-surface region. We have developed a 2-D stochastic-based model for the generation and the streamwise concatenation of instantaneous, step-like velocity profiles featuring key elements of wall turbulent flows, i.e., uniform momentum zones (UMZ) and shear layers (Ehsani et al. 2024a,b), and vortices (Ehsani et al. 2026). The model is extended herein to the top of the logarithmic layer to reproduce the high-Reynolds-number, rough-wall, turbulent boundary layer measured by Saddoughi and Veeravalli(2000), without the support of a UMZ dataset, using only a handful of critical flow parameters: the Taylor microscale λT, the boundary layer height δ, the friction velocity uτ, and the aerodynamic roughness length z0. The primary challenge lies in the integration of the stochastic model with the scaled distributions of the UMZ and vortex characteristics. The resulting statistical moments, energy spectra, and structure functions are compared against the experimental results. The validated code is made available in a GitHub repository.