Flow-induced vibrations in wall-bounded flows remain a major challenge in many engineering applications. While fully predictive turbulence-induced vibration simulations generally require scale-resolving approaches, unsteady Reynolds-averaged Navier–Stokes (URANS) methods are employed in practice due to their favorable computational cost. However, their predictive reliability is limited by uncertainty in turbulence-model parameters, structural model–form error, and deficiencies in representing turbulent fluctuations. This work presents a surrogate-based Bayesian calibration framework for the SST – model, incorporating anisotropic pressure-fluctuation reconstruction to quantify and reduce model uncertainty. Global Sobol’ sensitivity analysis, surrogate modeling, and Bayesian inference are combined to identify influential parameters and assimilate high-fidelity reference data. The framework is applied to turbulent channel flow, turbulent annular flow, and a blunt-end cantilevered-rod configuration. Across all cases, the specific dissipation-rate coefficient and the turbulent kinetic-energy dissipation coefficient consistently dominate variability in mean-flow quantities and reconstructed fluctuation statistics. Bayesian calibration constrains these parameters to consistent regions of the admissible space, while less influential coefficients remain weakly informed. Gaussian process regression and polynomial chaos expansion surrogates yield nearly identical posterior and predictive distributions, demonstrating robustness to surrogate choice. Remaining discrepancies with reference data are attributed primarily to structural turbulence model limitations rather than parametric uncertainty.

This study presents a compact data-driven Reynolds-averaged Navier-Stokes (RANS) model for wind turbine wake prediction, built as an enhancement of the standard - formulation. Several candidate models were discovered using the symbolic regression framework Sparse Regression of Turbulent Stress Anisotropy (SpaRTA), trained on a single Large Eddy Simulation (LES) dataset of a standalone wind turbine. The leading model was selected by prioritizing simplicity while maintaining reasonable accuracy, resulting in a novel linear eddy viscosity model. This selected leading model reduces eddy viscosity in high-shear regions—particularly in the wake—to limit turbulence mixing and delay wake recovery. This addresses a common shortcoming of the standard - model, which tends to overpredict mixing, leading to unrealistically fast wake recovery. Moreover, the formulation of the leading model closely resembles that of the established -- model. Consistent with this resemblance, the leading and -- models show nearly identical performance in predicting velocity fields and power output, but they differ in their predictions of turbulent kinetic energy. In addition, the generalization capability of the leading model was assessed using three unseen six-turbine configurations with varying spacing and alignment. Despite being trained solely on a standalone turbine case, the model produced results comparable to LES data. These findings demonstrate that data-driven methods can yield interpretable, physically consistent RANS models that are competitive with traditional modeling approaches while maintaining simplicity and achieving generalizability.

Computational fluid dynamics using the Reynolds-averaged Navier-Stokes (RANS) remains the most cost-effective approach to study wake flows and power losses in wind farms. The underlying assumptions associated with turbulence closures are the biggest sources of errors and uncertainties in the model predictions. This work aims to quantify model-form uncertainties in RANS simulations of wind farms at high Reynolds numbers under neutrally stratified conditions by perturbing the Reynolds stress tensor through a data-driven machine-learning technique. To this end, a two-step feature-selection method is applied to determine key features of the model. Then, the extreme gradient boosting algorithm is validated and employed to predict the perturbation amount and direction of the modeled Reynolds stress toward the limiting states of turbulence on the barycentric map. This procedure leads to a more accurate representation of the Reynolds stress anisotropy. The data-driven model is trained on high-fidelity data obtained from large-eddy simulation of a specific wind farm, and it is tested on two other (unseen) wind farms with distinct layouts to analyze its performance in cases with different turbine spacing and partial wake. The results indicate that, unlike the data-free approach in which a uniform and constant perturbation amount is applied to the entire computational domain, the proposed framework yields an optimal estimation of the uncertainty bounds for the RANS-predicted quantities of interest, including the wake velocity, turbulence intensity, and power losses in wind farms.