Wake dynamics in offshore wind farms

Wind turbines within offshore wind farms spend considerable time operating in the wake of neighboring wind turbines. An important contribution to the loads on a wake-affected wind turbine is the slow movement of the wake from the upstream wind turbine across the rotor of the wake-affected wind turbine. A new approach to this so called wake meandering is proposed. Beside the advantage of higher physical realism, the new approach also offers practical advantages compared to the current state-of-the-art method.
An input to the new meandering approach is the time evolution of the so called
spectral velocity tensor. An improved such spectral tensor is therefore developed, which, for neutral atmospheric stratification, predicts spatial correlations comparably to the Mann spectral tensor and temporal coherence significantly better than previously existing models, including the Mann model, which is incapable of predicting any temporal correlations beyond those that follows from the application of Taylor’s frozen turbulence hypothesis. As part of the framework a spectral tensor for Lagrangian correlations in space and time is also developed and validated versus measurements of isotropic turbulence. Combined, the models reproduce the cross-over point between Eulerian and Lagrangian temporal covariances. The applications of the Lagrangian spectral tensor, e.g. in the fields of dispersion and mixing, deserve further investigation.
The values of the input parameters of the spectral tensor are shown to be uniquely determined by the friction velocity, the shear and the dissipation of turbulent kinetic energy, all of them physical properties of the flow. If local equilibrium between the turbulent kinetic energy produced by shear and the turbulent kinetic energy dissipated as heat is assumed, then, for neutral atmospheric stratification, the friction velocity and the mixing length determine the spectral tensor.
The developed spectral tensor also depends on a dimensionless quantity, which
would be beneficial to determine with higher accuracy. An experiment with this
objective, studying the ratio between different components of the cross-spectra at known shear, is proposed. Future work could also include investigating if a Rapid Distortion formulation that also includes a term for buoyancy effects is needed in order to make accurate predictions for non-neutral atmospheric stratification.