The present document reports on the numerical simulations performed by Cenaero within the European Union funded FAR-Wake project. This project, the acronym of fundamental reseach on aircraft wake phenomena, is mainly devoted to the alleviation of wake turbulence problem behind civil aircraft. In the far-field, the wake of an aircraft is composed of large-scale swirling flow (vortices) that can represent a significant hazard for the following aircraft. This has therefore a major importance in practical applications like safety and capacity of air transport. The first contribution of Cenaero was to investigate the near-field wake generated by the fuselage of an aircraft by means of steady simulations (RANS) as well as unsteady simulations (hybrid RANS-LES), and this, in order to discriminate the influence of each aircraft element to the global wake. The second contribution of Cenaero was dedicated to the study of the unstability mechanisms occuring to longitudinally uniform two-vortex system in ground effect. This has a major importance as it correponds to configurations representative of the take-off and landing phases. Furthermore, the influence of atmospheric conditions was investigated in the form of unsteady turbulent winds (a head-and a cross-wind) advecting the vortices. This far-field study was done using three-dimensional unsteady simulations (LES).