An analytical wind park model
An analytical model based on a momentum balance has been developed at IMK-IFU which computes the reduction of the mean wind speed at hub height in a very large wind park. Additionally the length of the wake of such parks is computed. The model solution depends on surface roughness (this allows for a distinction between onshore and offshore parks), on thermal stability of the atmospheric boundary layer, on the additional turbulence produced by the turbines, and on the spatial density of the turbines in the park.
The basic idea is published in S. Emeis, 2010: A simple analytical wind park model considering atmospheric stability. Wind Energy, 13, 459-469. The illustrations here are taken from that paper.