To study the aero-optical effect of Laguerre-Gaussian (LG) beams passing through the flow field around a turret, we solve parabolic beam equations of complex amplitude by second-order compact differences and fourth-order Runge-Kutta integration. In the same flow field, light intensity distributions of LG beams with different topological charges, optical path differences (OPD) of the same beam calculated by numerical simulations and integrated along optical path are both compared. Strehl ratio (SR) and imaging displacement are calculated at different Mach numbers, different angles of attack, and different altitudes, and compared among Gaussian beam and LG beams with different topological charges. The simulation results show that in the same flow field, the larger topological charge the LG beam has, the better the shape of amplitude keeps, but the larger the attenuation and imaging displacement are. In the same flow field, the topological charges have nearly no impact on SR of LG beams, and the phase stability of LG beams is always better than Gaussian beam. Changes of altitude and angle of attack have bigger impact on the imaging displacement of LG beams compared with that of Gaussian beams.