Robustness of two-dimensional stochastic dynamical wake models for yawed wind turbines

We develop stochastic dynamical reduced-order models of wind farm turbulence that capture the effects of yaw misalignment due to control or atmospheric variability on turbine wakes and their interactions. Our models are based on the stochastically forced linearized Navier-Stokes equations around analytical descriptions of the wake velocity provided by low-fidelity engineering wake models. The power-spectral density of the source of additive stochastic excitation is identified via convex optimization to ensure statistical consistency with high-fidelity models while preserving model parsimony. We demonstrate the utility of our approach in capturing turbulence intensity variations in accordance with large-eddy simulations of the flow over a cascade of wind turbines. While our models are developed to match velocity correlations from sensors that are placed directly behind perfectly aligned wind turbine rotors, their predictions maintain a desirable level of accuracy even when the turbines are yawed.