Data-driven reduced order model for prediction of wind turbine wake dynamics

Wind turbine wakes are highly turbulent flows for which coherent vorticity structures lead to complex dynamics and instabilities. In this study, high-fidelity large eddy simulations (LES) data of a utility-scale wind turbine is analyzed through proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) in order to detect the main dynamic contributions to the temporal and spatial evolution of a wind turbine wake. Eigenmodes obtained from modal decomposition are clustered as a function of their physical origin, energy, spectral contribution and growth rate. A subset of the eigenmodes is then selected accordingly to a customized objective function in order to represent an optimal blend of the different dynamic contributions. The selected eigenmodes are embedded in a time-marching algorithm enabling the prediction of the wake velocity field and loads on downstream turbines. This reduced order model is characterized by a relatively low rank compared to the dimension of the physical space of the original LES data, thus by a low computational cost. The reduced order model is then embedded within a Kalman filter in order to perform data assimilation of new available observations in order to maximize agreement between the forecast and observations.