Stability and optimal forcing analysis of a wind turbine wake: Comparison with POD

Understanding the dynamics and generation of coherent structures in wind-turbine wakes is crucial for efficiency improvement of wind farms, which will most probably represent one of the main renewable power generation sources in 2050. In this paper, we investigate the origin of such coherent structures by performing modal and non-modal stability analysis of the mean flow downstream of a wind-turbine rotor. The database consists of large-eddy-simulation results. Bi-local linear-stability and optimal-forcing analyses are performed at several wake's cross-sections. The most unstable perturbations are compared with the most energetic coherent structures recovered by the proper orthogonal decomposition (POD) analysis, showing a good agreement close to the rotor. Further downstream, these modes are overtaken by others with wavenumbers departing from those of the main POD modes. However, optimal-forcing analysis shows that asymptotically stable modes can be amplified by more than one order of magnitude via quasi-resonance mechanisms, bypassing the growth of the most unstable modes in the far wake. This suggests that the most energetic structures are originated by modal instabilities, which trigger quasi-resonance mechanisms in the far wake, determining the emergence of specific frequencies in the turbulent flow. These findings are crucial for designing efficient control systems to optimize wind farm performance.