To mitigate global warming, there is a strategic initiative to make wind energy the prominent energy source by 2050. Achieving this ambitious goal entails a fourfold increase in the scale of wind-energy installations within the coming decade. Successfully navigating this endeavor requires an in-depth knowledge and understanding of the complex multi-scale interactions between the atmosphere and wind farms. Computational fluid dynamic simulations, particularly, the Reynolds-averaged Navier-Stokes (RANS) approaches have proven to be invaluable tools for this purpose. However, RANS models that rely on the linear-eddy viscosity hypothesis have been demonstrated to fall short in accurately capturing the physics of flow in the wake of wind turbines. Our study addresses this challenge by augmenting the predictive capabilities of the Reynolds stress tensor (RST) by enhancing our baseline two-equation RANS model. To this end, we initiate our investigation with a thorough examination of a reference wind farm comprising six inline turbines under full-wake conditions, where we compared our results with in-house large-eddy simulation (LES) data. Extending our exploration to a $10 \times 3$ array of wind turbines, we delved deeper into studying the augmented model’s performance, drawing insights from both wind-tunnel experiments and LES results. The comparative analysis across different wind-farm configurations contributes valuable knowledge to the understanding of the intricate interplay between the RST prediction and the fluid mechanics of wind-turbine and wind-farm wakes.