Data-Driven Modeling of the Wake Behind a Wind Turbine Array

The wake flow in a wind turbine array boundary layer is described using the Koopman operator. Dynamics of the flow are decomposed into the linear and forcing terms, and the low-energy delay coordinates are revealed. The rare events show the non-Gaussian long tails that capture the switching and bursting phenomena. The near-wake region shows the incoherent phase space region, where the dynamics are strongly nonlinear. The far-wake region is marked with the small non-Gaussian forcing term, and the dynamics are largely governed by linear dynamics. The data-driven predictive model is built based on the Hankel-based dynamic mode decomposition and treats the nonlinear state of forcing term as external actuation. The model forecasts the evolution of the flow field for short-term timescales. The mean relative errors between the predictive and test fluctuating velocities are approximately 15%