Hemispherical turrets are frequently employed on airborne aircraft for laser communication and targeting. However, the unsteady compressible turbulent flow around such a turret causes aberrations in the optical wavefront which degrades the performance of the system. To overcome this limitation it is necessary to have a deep understanding of the flow and optical environments around the turret, which are very challenging to study both experimentally and numerically. This thesis describes numerical study of this problem using advanced numerical techniques and high performance computers of the present days. Two hemisphere-on-cylinder turrets, with base-height/diameter ratios H/D = 0.375 and 0.3125, respectively, in a Mach 0.4 incoming fow are studied. The simulated flow fields conrm the findings from previous experimental studies, such as the existence of a necklace vortex around the base of the turret and flow separation in the central plane at an angle between 110 degree and 115 degree. Furthermore, it is found that the necklace vortex is well below the optical aperture on the turret and thus has no direct impact on the aero-optical distortions, density fluctuations, which are directly related to optical aberrations, are strongest within the separated shear layer and wake region, and the recirculation bubble behind the turret experiences very little density fluctuations. Optical computations also confirm the experimental results measured using 2-D wavefront sensor. Besides, the effects of elevation angle and azimuthal angle on optical aberrations are studied in a systematic way. It is found that the optical aberration grows almost linearly with elevation angle when the elevation angle is above 110 degree, but it has a more complicated relationship with the azimuthal angle. At small elevation angles it decreases with increasing azimuthal angle and the change is nonlinear; however, when the elevation angle is large, the aberration does not decrease much, and even increases with azimuthal angle at small azimuthal angles but keeps decreasing at large azimuthal angles.