We report on the structure of the scalar index-of-refraction field generated by turbulent, gas-phase, incompressible and compressible shear layers and incompressible jets, and on associated beam-propagation aero-optical phenomena. Using simultaneous imaging of the optical-beam distortion and the turbulent-flow index-of-refraction field, wavefront-phase functions were computed for optical beams emerging from the turbulent region in these free-shear flows, in an aero-optical regime producing weak wavefront distortions. Spatial wavefront-phase behaviour is found to be dominated by the large-scale structure of these flows. A simple level-set representation of the index-of-refraction field in high-Reynolds-number, incompressible shear layers is found to provide a good representation of observed wavefront-phase behaviour, indicating that the structure of the unsteady outer boundaries of the turbulent region provides the dominant contributions.