The wake produced by a model wind turbine is investigated using proper orthogonal decomposition (POD) of numerical data obtained by large eddy simulations at a diameter-based Reynolds number Re = 6:3 × 10 5. The blades are modeled employing the actuator line method and an immersed boundary method is used to simulate tower and nacelle. Two simulations are performed: one accounts only for the blades effect; the other includes also tower and nacelle. The two simulations are analyzed and compared in terms of mean flow fields and POD modes that mainly characterize the wake dynamics. In the rotor-only case, the most energetic modes in the near wake are composed of high-frequency tip and root vortices, whereas in the far wake, low-frequency modes accounting for mutual inductance instability of tip vortices are found. When tower and nacelle are included, low-frequency POD modes are present already in the near wake, linked to the von Karman vortices shed by the tower. These modes interact nonlinearly with the tip vortices in the far wake, generating new low-frequency POD modes, some of them lying in the frequency range of wake meandering. An analysis of the mean kinetic energy (MKE) entrainment of each POD mode shows that tip vortices sustain the wake mean shear, whereas low-frequency modes contribute to wake recovery. This explains why tower and nacelle induce a faster wake recovery.