A simplified approach has been applied to analyse the mixing and entrainment processes of the engine exhaust through their interaction with the vortex wake of an aircraft. Our investigation is focused on the near field, extending from the exit nozzle until about 30 s after the wake is generated, in the vortex phase. This study was performed by using an integral model and a numerical simulation for two large civil aircraft: a two-engine Airbus 330 and a four-engine Boeing 747. The influence of the wing-tip vortices on the dilution ratio (defined as a tracer concentration) shown. The mixing process is also affected by the buoyancy effect, but only after the jet regime, when the trapping in the vortex core has occurred. In the early wake, the engine jet location (i.e. inboard or outboard engine jet) has an important influence on the mixing rate. The plume streamlines inside the vortices are subject to distortion and stretching, and the role of the descent of the vortices on the maximum tracer concentration is discussed. Qualitative comparison with contrail photograph shows similar features. Finally, tracer concentration of inboard engine centreline of B-747 are compared with other theoretical analyses and measured data.