A large eddy simulation (LES) of a cold air outbreak along with organized convection is presented. The computational grid was chosen to be fine enough to explicitly resolve small scale unorganized turbulence, while the size of the model domain was large enough to include the evolution of large scale organized convection. For the first time such an LES was performed with a stationary model domain, being one of the most extensive LES in meteorology so far. During the simulation, convective rolls were formed which showed typical characteristics as observed in nature, such as significantly increasing aspect ratios with increasing distance from the ice edge and orientation of the roll axes in direction of the mean wind shear vector.