Monostatic and bistatic acoustic scattering has been used in studies of the characteristics and motions of the atmosphere. This technique has been successfully implemented in the Monostatic Acoustic Vortex Sensing System (MAVSS) for the measurement of the characteristics of aircraft wake vortices during landing and take-off. In the present study, calculations are performed to simulate the MAVSS. The results of this study are giving information about the acoustic scattering by the vortex, as well as providing a controlled test bed for the instrument's operation. Since the Doppler shifts, characteristic of the vortex velocity, are dependent on the incoherent scattering of the acoustic waves by turbulence advected by the vortex, a statistical model is proposed that describes the turbulence imbedded in the vortex. The simulations are performed using high-order accuracy finite-difference algorithms that have been developed for computational aero-acoustic (CAA) and wave propagation problems.