Synthetic turbulence modelling for offshore wind farm engineering models using coherence aggregation

Turbulent wind fields are known to be a major driver for structural loads on offshore wind turbines, and hence benefit from well-established design standards using wind spectra and  coherence functions calibrated from years of measurements. Multiple 10-minutes wind field realisations obtained by Gaussian process generation are then used in aero-hydro-servo elastic codes to get structural loads. When it comes to large offshore wind farms, however, measurements reveal the importance of large, low-frequency turbulent vortices —previously overlooked in the so-called "spectral gap"— for power fluctuations and hence for wind farm control and grid integration. Also, farm-scale wind fields are needed as input to farm-scale aero-servo-elastic codes for the modelling of wake dynamics. These new concerns motivate an upgrade in the original turbine-scale wind field representation: (1) spectral models need to be based on farm-scale measurements, (2) the frozen-turbulence assumption merging temporal and along-wind coherence must be lifted, (3) simplifications are needed to reduce the number of degrees of freedom as the domain becomes excessively large. This paper suggests models and algorithms for \textit{aggregated} synthetic turbulence generation —lumping the wind field into space-averaged quantities— adapted to the aero-hydro-servo elastic modelling of large wind farms. Starting from the work of Sørensen et al. in the early 2000s for grid integration purposes,  methods for load modelling (through wake meandering and high-resolution wind field reconstruction) are introduced. Implementation and efficiency matters involving mathematical subtelties are then presented. Finally, numerical experiments are carried out to (1) verify the approach and implementation against a state-of-the-art point-based —as opposite to aggregated— synthetic turbulence generation code, and (2) illustrate the benefit of turbulence aggregation for the modelling of large offshore wind farms.