Resolvent analysis for predicting energy-containing structures in the far wake of a wind turbine*

Turbulence generated by turbine wakes can significantly alter the power production and aerodynamic loads of a wind farm. However, the prediction of such turbulence by wake models is often hindered by the complex interplay among wake-induced shear, incoming turbulence and near-wake structures. We demonstrate the use of resolvent analysis to predict energy-containing structures in the far wake of a wind turbine subjected to a turbulent inflow. We assume that the mean flow is axisymmetric and that the effect of small-scale flow structures can be modeled with an eddy viscosity term. We find that resolvent analysis can capture both the dominant and subdominant modes educed from the spectral proper orthogonal decomposition of large-eddy simulation data. We also find that the amplitude gain peaks at a Strouhal number of around 0.2 and at an absolute azimuthal wavenumber of 1, demonstrating that resolvent analysis can capture the role of convective shear instability in generating wake turbulence. Although data driven, the present analysis is linear, making it computationally efficient and thus suitable for adoption in wake models used to design and optimize wind farms.