  The development of advanced simulation tools is essential, both presently and
in the future, for improving wind-energy design strategies, paving the way for
a complete transition to sustainable solutions. The Reynolds-averaged
Navier-Stokes (RANS) models are pivotal in enhancing our comprehension of the
complex flow within and around wind farms and, hence, improving their capacity
to accurately model turbulence within this context is a vital research goal.
The enhancement is essential for a precise prediction of wake recovery and for
capturing intricate flow phenomena such as secondary flows of Prandtl's second
kind behind the turbines. To reach these objectives, here, we propose a
progressive data-augmentation approach. We first incorporate the
turbine-induced forces in the turbulent kinetic energy equation of the widely
used $k-\omega\text{SST}$ model. Afterward, we utilize data from large-eddy
simulations to progressively enhance the Reynolds-stress prediction of this
baseline model, accurately capturing the evolution of eddy viscosity in the
wake, as well as the emergence of secondary flows. We then apply the optimized
model to two unseen cases with distinct layouts and conduct a comparative
analysis focusing on the obtained quantities such as normalized streamwise
velocity deficit, turbulence intensity, and power output. We also examine the
success rate of the augmented model in predicting the secondary flows in the
wake region. Our comparisons and validations demonstrate the superior
performance of the progressive data-augmented model over the standard version
in all cases considered in this study.
