Roozbeh Ehsani | Searcharxiv

arXiv2026

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

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 {\lambda}T, the boundary layer height {\delta}, the friction velocity u{\tau}, 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.

physics.flu-dyn↗

arXiv2024

Stochastic modelling of the instantaneous velocity profile in rough-wall turbulent boundary layers

The statistical properties of Uniform Momentum Zones (UMZs) are extracted from laboratory and field measurements in rough wall turbulent boundary layers to formulate a set of stochastic models for the simulation of instantaneous velocity profiles. A spatio-temporally resolved velocity dataset, covering a field of view of $8 \times 9$ m$^2$, was obtained in the atmospheric surface layer using super-large-scale particle image velocimetry (SLPIV), as part of the Grand-scale Atmospheric Imaging Apparatus (GAIA). Wind tunnel data from a previous study are included for comparison \citep{heisel2020mixing}. The probability density function of UMZ attributes such as their thickness, modal velocity, and averaged vertical velocity are built at varying elevations and modeled using log-normal and Gaussian distributions. Inverse transform sampling of the distributions is used to generate synthetic step-like velocity profiles that are spatially and temporally uncorrelated. Results show that in the wide range of wall-normal distances and $Re_τ$ up to $ \sim O(10^6)$ investigated here, shear velocity scaling is manifested in the velocity jump across shear interfaces between adjacent UMZs, and attached eddy behavior is observed in the linear proportionality between UMZ thickness and their wall normal location. These very same characteristics are recovered in the generated instantaneous profiles, using both a fully stochastic and a data-driven hybrid stochastic models, which address, in different ways, the coupling between modal velocities and UMZ thickness. Our method provides a stochastic approach for generating an ensemble of instantaneous velocity profiles, consistent with the structural organization of UMZs, where the ensemble reproduces the logarithmic mean velocity profile and recovers significant portions of the Reynolds stresses and thus of the streamwise and vertical velocity variability.

physics.flu-dyn↗