Modelling the impact of atmospheric turbulence is not often encountered in aircraft noise auralizations despite its relevance to human-ear perception. As sound waves propagating through turbulent media undergo modulations, observable in phase and amplitude fluctuations, the plausibility of aircraft noise auralizations is increased by taking this effect into account. This paper presents an extension of a method first developed by Rietdijk et al., for modelling these fluctuations for spherical sound waves travelling through randomly inhomogeneous media. The extensions of the method presented in this paper are: (1) Height-dependent von Kármán spectra are implemented to model slanted or vertical sound propagation. (2) An overlap-add-method is introduced to model a moving sound source when height-dependent changes of turbulence characteristics are considered. (3) Easier to measure input parameters for the (meteorological) conditions are implemented, like e.g. the day time or relative humidity. The method is integrated into a global framework dedicated to engine noise simulation, propagation and auralization, developed and validated by the German Aerospace Center (DLR). A good match with measured functions of phase and amplitude fluctuations are observed, as well as realistic reproduction of spectrograms, time signals and the psychoacoustic fluctuation strength of the auralizations with respect to real flyovers.