  We investigate the interaction of many wind turbines in a wind farm with a
focus on their electrical power production. The operational data of two
offshore wind farms with a ten minute and a ten second time resolution,
respectively, are analyzed. For the correlations of the active power between
turbines over the entire wind farms, we find a dominant collective behavior. We
manage to subtract the collective behavior and find a significant dependence of
the correlation structure on the spatial structure of the wind farms. We
further show a connection between the observed correlation structures and the
prevailing wind direction. We attribute the differences between the two wind
farms to the differences in the turbine spacing within the two wind farms.
