More and larger wind farms are planned offshore. As the most suitable build sites are limited wind farms will be constructed near to each other in so called wind farm clusters. Behind the wind turbines in these farms there is a disrupted flow of air called a wake that is characterized by reduced wind speed and increased turbulence. These individual turbine wakes combine to form a farm wake that can travel a long distance. In wind farm clusters farm to farm interaction will occur, i.e. the long distance wake from one wind farm will impact the wind conditions for other farms in the surrounding area. The thesis contains numerical studies of these long distance wakes. In this study Large Eddy Simulations (LES) using an Actuator Disc method (ACD) are used. A prescribed boundary layer is used where the wind shear is introduced using body forces. The turbulence, based on the Mann model, is introduced as fluctuating body forces upstream of the farm. A neutral atmosphere is assumed. The applied method has earlier been used for studies of wake effects inside farms but not for the longer distances needed for farm to farm interaction. Numerical studies are performed to get better knowledge about the use of this model for long distance wakes. The first study compares the simulation results with measurements behind an existing farm. Three parameter studies are thereafter setup to analyze how to best use the model. The first parameter study examines numerical and physical parameters in the model. The second one looks at the extension of the domain and turbulence as well as the characteristics of the flow far downstream. The third one gathers information on the downstream development of turbulence with different combinations of wind shear and turbulence level. The impact of placing the turbines at different distances from the turbulence plane is also studied. Finally a second study of an existing wind farm is performed and compared with a mesoscale model. The model is shown to be relevant also for studies of long distance wakes. Combining LES with a mesoscale model can be of interest.