A computational model describing the two-dimensional, turbulent mixing of a single jet of exhaust gas from aircraft engines with the ambient atmosphere is presented. The underlying assumptions and governing equations are examined and supplemented by a discussion of analytical solutions. As an application, the jet dynamics of a B747-400 aircraft engine in cruise and its dependence on key parameters is investigated in detail. The computer code for this dynamical model is computationally fast and can easily be coupled to complex chemical and microphysical models in order to perform comprehensive studies of atmospheric effects from aircraft exhaust emissions in the jet regime.